Engrmece3350u Lab Handbook f2014(2) (1)

8/10/2019 Engrmece3350u Lab Handbook f2014(2) (1)

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FACULTY OF ENGINEERING AND APPLIED SCIENCE

ENGR/MECE 3350U

Control Systems Laboratory Manual

Fall 2014

Supported by

Revised by Cliff Chan


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Lab 1: Motor Static Relationship

and

Motor Parameter Estimation


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An overview of the system can be obtained by the pictures, schematic diagrams, and the

block diagrams. This gives the representations of a system, which emphasizes the aspects

of the system that are relevant for the control and suppresses many details. The work is

guided by focusing on the variables that are of primary interest for control.

The block diagram presents a natural partition of the system. The mathematical

descriptions of the behavior of the subsystems representing each block are necessary to

have a complete model. In control it is often sufficient to work with the linearized models,

where the dynamics are represented by the transfer functions. These transfer functions can

be obtained from the first principles by applying the basic physical laws that describe the

subsystems or by experiments on a real system. First principle modeling always requires a

good knowledge of the physical phenomena involved and a good sense for reasonable

approximations.

Experiments on the actual physical system are good complements to the first principles of

system modeling. This can also be used when the knowledge required for first principles

modeling is not available.

It is a good practice to start the experiments by first determining the static input-output

characteristics of the actual system. For the systems with several inputs (Multi-Inputs as

for the case of the motor in the DCMCT) one can often obtain an additional insight to the

dynamics of the system by exploiting all the input signals.

4. Nomenclature

The following list of nomenclature, as described in Table 1.1, is used for the modeling of

an open-loop control system.


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Table 1.1: Open-Loop System Nomenclatures

Symbol Description Unit

m Motor speed which can be computed from the motor angle rad/s

Vm Voltage from the amplifier which drives the motor V

Td Disturbance torque externally applied to the inertial load N.m

Tm Torque generated by the motor N.m

Im Motor Armature Current A

km Motor Torque Constant N.m/A

Rm Motor Armature Resistance

Lm Motor Armature Inductance mH

Jm Moment Of Inertia Of Motor Rotor kg.m2

J1 Moment Of Inertia Of Inertial Load kg.m2

Jeq Total Moment Of Inertia Of Motor Rotor And The Load kg.m2

K Open-Loop Steady-State Gain rad/(V.s)

Open-Loop Time Constant s

M1 Inertial Load Disc Mass kg

r1 Inertial Load Disc Radius mH

h Sampling Interval s

s laplace Operator rad/s

t Continuous Time s

5. Laboratory Session

5.1. QICii Modeling Module

The main tool for this laboratory experiment is the front panel of the module entitledModeling in the QICii software, which should be similar to the one shown in Figure 1.1.

As a quick module description, Table 1.2 lists and also describes the main elements

composing the QICii Modeling module user interface. Every element is uniquely

identified through an ID number and located in Figure 1.1.


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Figure 1.1: Modeling Module of the QICii Software

Table 1.2: QICii Modeling Module Nomenclatures

ID# Label Parameter Description Unit

1 Speed m Motor Output Speed Numeric Display Rad/s

2 Current Im Motor Armature Current Numeric Display A

3 Voltage Vm Motor Input Voltage Numeric Display V

4Signal

GeneratorType of Generator For The Input Voltage Signal

5 Amplitude Generated Signal Amplitude Input Box V

6 Frequency Generated Signal Frequency Input Box Hz

7 Offset Generated Signal Offset Input Box V

8 Speed mScope With Actual (in red) and Simulated (in

blue) Motor Speedsrad/s

9 Voltage Vm Scope With Applied Motor Voltage(red) V

10 K K Motor Model Steady-State Gain Input Box rad/(V.s)

11 Motor Model Time Constant Input Box s

12 Tf Tf Time Constant of Filter for Measured Signal s


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The Modeling Module program runs the process in the open-loop condition by utilizing

the motor voltage given by the signal generator. There are two windows that show the

time histories of the motor speed and the motor voltage, respectively.

A simulation study of the system runs in parallel with the hardware. The output of the

simulation study can be used for the model fitting and the parameter validation. The inputfor the simulation study is equal to the motor voltage while the output of the simulation is

displayed (blue trace) in the same window as the actual motor speed (red trace).

The parameters K and tof the simulation model could be adjusted from the front panel.

The simulated motor speed, s is obtained from the simulated transfer function and the

actual motor voltage as illustrated in the following

1

)(

)( s

sKV

sm

s

The implemented digital controller in the QIC runs at 100Hz. Thus the sampling interval

is therefore being equal to h= 0.01 [s]

The actual speed is obtained by filtering the position signal using the following filter:

1

sT

s

f

mm

where m is the position of the motor shaft measured by the encoder.

5.2. Module Startup Procedure

Power up the DCMCT: To start and use the Modelling module, first launch the QICii

software and then selectModelling in the drop-down menu.

To download the controller code, follow the steps described below:

1.

Press theDownload programbutton on top of the QICii window.

2.

Click on the Write (F4)button of thePIC downloaderpopup window.

3.

Push theResetbutton on the QICii to actually start the download. The two LED's

stop flashing.

4. Once the download is complete, press down the Reset button on the QICii one

more time. The two LED's should now start flashing again.

5.

Close thePIC downloaderwindow.


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Once it is loaded, the controller code stays on the QICii (even when the power to the

DCMCT is off).

To start the controller, press down the DCMCT User Switch (i.e., the pushbutton next to

the two flashing LED's). The two LED's stop flashing The controller starts running.

Select the Connect to data sourcebutton on top of the QICii window in order to be ableto receive / send data from / to the controller. LED2 should now turn on.

Table 1.3: Default Module Parameters

Signal

Type

Amplitude

[V]

Frequency

[HZ]

Offset

[V]

K

[Rad/V.S]

[S] Tf [s]Square

Wave 2.0 0.4 0.0 10.0 0.2 0.0

5.3. Static Relationship

Experimental Procedure

A procedure of this type is very useful in order to make sure that a system will function

properly.

Please follow the steps exactly as described below:

1.

Run the system as an open-loop one by changing the voltage to the motor. The

motor voltage is set by the signal generator. With zero signal amplitude, change

the signal offsetto generate a constant DC voltage. Sweep the voltage gently over

the full signal (voltage) range and observe the steady-state speed, current, and the

motor input voltage. What are the minimum and maximum voltages you can input

to the system? What exactly happens to the variables as you change the offset (i.e.

change the offset from -3V to +3V)? Can you determine the following

relationships: i) input voltage vs motor speed; and ii) current vs motor speed?

2.

Start with a zero value of voltage on the motor and increase the voltage gradually

until the motor starts to move. Determine the value of the voltage (start-up

voltage) when this occurs. Repeat the test with negative values of voltages. What

forces are restricting the motor from spinning?


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3. Determine the actual maximum value of the motor velocity and compare it with

the calculate one. To determine the calculated value, you have to record the motor

velocity values subjected to the change of the input voltage from -3V to 3V with

an increment of 1V. Then, draw a best-fit-line through these data points. Next,

extrapolate the motor velocity values to determine the calculated maximum valueof the motor velocity. Do you see the difference between the actual and the

calculated values? (Hint:You may or may not see the difference. In either case,

explain your observation.)

5.4. Estimate The Motor Resistance

Some of the parameters of the mathematical model of the system can be determined by

measuring how the steady-state velocity and the current would change with the appliedvoltage.

To estimate the motor resistance experimentally, follow the steps described below:

1. Set the generated signal amplitude to zero. If the signal offset is different from

zero then the motor will spin in one direction, since a constant voltage is applied.

You can change the applied voltage by entering the desired value in the Offset

numeric control of the Signal Properties box. You can also read off the actual

value of the current of the motor from the digital display. The value is in Amperes.

Fill up the following table (i.e., Table 1.4). For each measurement hold the

motor shaft stationary by grasping the inertial load to stall the motor.Note that for zero Volts you will measure a current,Ibiasthat is possibly a non-zero

value. This is an offset in the measurement, which you will need to subtract from

the subsequent measurements in order to obtain the exact value of the current

(Im(i) = Imeas(i)-Ibias). Note also that the current value shown in the digital display

is filtered and you must wait for the value to settle down (steady state is reached)

before writing it down.


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Table 1.4: Motor Resistance (Experimental results)

SAMPLE

i

Vm (i)

[V]

Offset in Measured

Current: I bias[A]

0 0

SAMPLE

i

Voltage

Offset [V]

Vm (i)

[V]Measured Current: I

meas[A]

Corrected for

Bias: Im (i) [A]

Resistant:

Rm(i) []

1 -5

2 -4

3 -3

4 -2

5 -1

6 1

7 2

8 3

9 4

10 5

Average Resistant: Ravg []

From the values noted in Table 1.4, calculate the values of the motor resistance Rm(i)for

every iteration and obtain an average value for it, Ravg. Explain the procedure that you

have used to estimate the resistanceRm.

2.

From the system parameters, which are given in Appendix A, the value of the

resistance is 10.6 10%. Compare the estimated value forRm(i.e.,Ravg) with the

specified value and discuss your results in detail.


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5.5. Estimate The Motor Torque Constant

To estimate the value of the motor back-EMF constant experimentally, follow the steps

described below:

1. With the motor free to spin, apply the same procedure as given above and fill the

given table (i.e., Table 1.5). You can read off a value for the motor angular speedfrom the digital display. Wait a few seconds after you entered a new voltage value

as the displayed speed values are low-pass filtered. The values of the angular

speed are in radians per seconds. The current measurement may have an offset,

which you should need to account for. The speed measurement will have a very

small offset, which also need to be compensated for. Calculate the motor back-

EMF constant for each measurement iteration and then calculate an average value

for the 10 measurements. You should use the value ofRmthat you have estimated

in the previous section.

Note that kmcan be calculated using

m

mmm

m

IRVk

2.

From the system parameters that are given in Appendix A,km = 0.0502Vs/rad.

Compare the estimated value for km(i.e., km_avg) with the specified value, and then

discuss your results in detail.

5.6. Obtain the Transfer Function of the Motor

The open-loop transfer function of the system can be described as

1)(,

s

KsG V

wheremk

K1

system constant; and2

m

meq

k

RJ system time constant

From the above estimates, determine a numerical expression for the open-loop transfer

function G,V of the motor (Jeq = 0.0000221 kg.m2, 130.0 s). What are the estimated

open-loop steady-state gain value and the time constant?


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Table 1.5: Back-EMF Constant Experimental Results

SAMPLE

i

Vm (i)

[V]

Offset in Measured

Current: I bias[A]

Raver

[]

0 0

SAMPLE

i

Offset

Voltage [V]

Vm (i)

[V]

Measured Speed:

m (i) [Rad/S]

Imeas (i)

[A]

Im (i)

[A]

Km (i)

[V.s/Rad]

1 -5

2 -4

3 -3

4 -2

5 -1

6 1

7 2

8 3

9 4

10 5

Average Back EMF--Constant: Km(i) [V.s/Rad]

5.7. Estimate The Measurement Noise

The measurement noise could be determined experimentally. Please follow the steps

described below:

1.

Determine the measurement noise for the speed control by running the motor with

a constant positive as well as a constant negative voltage and observe the

fluctuations in the velocity, if any.

2.

Does the noise level depend on the velocity and /or the direction of rotation? Do

you also observe any repeatable fluctuations in the velocity signal? Can you find

their causes?

Hint: Can the fluctuations in the velocity signal be related to the motor position?


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Lab 2: Dynamics Modeling

Experimental Determination of System Dynamics


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Assuming that the input changes with u and that the corresponding change in the

steady-state output is y, an estimate of the steady-state gain is then given by:

[2.2]

The quantity (time constant) is approximately given by the time the output has reached

63% of its total change at steady state.

4.1.2 Experiment Process

Please read Appendix B which describes how to use the QICii plots to take measurements

of the acquired data, to start and stop the plots, and to measure point coordinates on the

plots. Please follow the steps below:

1. Apply a series of step inputs to the open-loop system by setting the QICii module

parameters as described in Table 2.1.

Signal

Type

Amplitude

[V]

Frequency

[Hz]

Offset

[V]

K

[rad/(V.s)] [s]

SquareWave

2 0.4 3 0 0.0

Table 2.1: Module Parameters for the Bump-test experiment

2. The open-loop controller now applies a constant-amplitude voltage square wave

to the motor. Step voltages are applied to the motor from the signal generator with

a period that is so long that the system well reaches steady-state at each step. Themotor should run at the corresponding constant speeds. Determine the transfer

function from the voltage Vm to angular velocity m using the obtained bump

tests.

K y

u


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3. Determine the parameters Kand of the model defined in [2.1].

4. Repeat the procedure for a few different signal amplitudes, as well as for the

rising and falling steps. Average your estimated parameters.

4.2 Model Validation

4.2.1 Preamble

A simple form of the model validation can be done because the software Modelling

contains a first-order simulation, whose model expressed by Equation [2.1] is driven by

the actual open-loop motor voltage. This model is running in parallel with the motor,

which can be used for model fitting. The simulation parameters Kand can be adjusted

from the front panel. The output of the model is displayed together with the actual motor

speed.

To measure how closely a model fits the actual system, we can calculate the root mean

squared (RMS) error measured within the validation period as given below:

[2.3]

where is the output of the actual system, is the output of the simulation model,

iis the index of the data point, and nis the index of the last (at the end of the validation

period) data point.


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Alternatively, Eq. [2.3] can be expressed in terms of its relative percentage error, given

by:

[2.4]

4.2.2 Experiment Process

Follow the procedures described below:

1. Activate the model by changing the simulation parameters Kand .

2. Set Kand to the values which you have previously estimated from the bump

test. Do you obtain a good fit between the estimated and the actual responses?

3. Try to minimize the error between the simulated response and the actual response

by adjusting the simulation parameters Kand on-the-fly until you obtain a good

fit. This procedure is called model fitting.

4. Change the signal amplitude to see if you have to change the values of the

simulation parameters in order to get a better fit.

5. Is your model valid? Apply Eq. [2.4] to determine if your model is valid and

summarize your observation.


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Lab 3: Qualitative Properties of PI Control


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1. Laboratory Objective

The objective of this laboratory is to develop an understanding of the PI (Proportional +

Integral) control (applied to speed control), how does it work, and how it can be tuned to

meet the required specifications.

In particular, in this experiment you will explore:

Pure proportional control action.

Pure integral control action

Proportional and integral control action

2. Preparation and Pre-Requisites

A pre-requisite to this laboratory is to have successfully completed the modelling andmodel validation laboratory in Lab 1 and Lab 2.

Before the lab, you should also review the Proportional + Integral (PI) control from your

textbook.

The system can be represented by the block diagram as shown in Figure 3.1. This block

diagram illustrates the parts of the system that are relevant for the speed control.

Figure 3.1 DCMCT Block Diagram for the Speed Control

The process is represented by a block which has the motor voltage Vmand the torque Tdas the inputs and the motor speed mas the output. The torque is typically a disturbance

torque that you can apply manually to the inertial load.


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The referencer(t) is also called the set-point or the command. The linear behaviour of thecontroller is governed by three parameters:

kp: proportional gain ki: integral gain

bsp: set-point weight

Further in this experiment, we introduce a fourth parameter, aw, which governs thenonlinear properties of the controller.

Sometimes the filtered measurementyf(t)is also used in the control loop. It is computed

from Tf, the time constant of filter for measured signal. The filter time constant Tf istypically set to a constant value and it is often combined with the sensor. The filter

provides the roll-off at high frequencies.

It is important to reduce the effects of the sensor noise, which it improves robustness. Inthis particular case, the filtering is incorporated in the calculation of the velocity from the

encoder signal.

3.2 The magic of Integral Action

A nice property of a controller with the integral action is that it always gives the correct

steady-state value provided that there is equilibrium. This can be seen simply byassuming that there is a steady-state value with constant u(t)= uss, r(t)= rss, andy(t)=yss.

Equation [3.1] can then be written as:

Since the left-hand-side is a constant, the right-hand-side must also be a constant. This

requires thatyss= rss. Notice that the only assumption, which has been made about theprocess is that there exists an asymptotic steady-state value.

4. Laboratory Session

4.1QICii Modeling Module

The main tool for this experiment is the front panel of the module entitled Speed Control

in the QICii software, which should be similar to the one shown in Figure 3.2.


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4Signal





8 Speed m,rScope With Actual (in red) and Reference (in

blue) Motor Speeds rad/s


10 Kp Kp Controller Proportional Gain Input Box V.S/rad

11 Ki Ki Controller Intergral Gain Input Box V/rad

12 bsp bsp Controller Set-point Weight Input Box

13 aw awController Windup protection Parameter Input

Box


Table 3.1 QICii Modeling Module Nomenclatures

4.2Module Startup

Power up the DCMCT: To start and use the Speed Controlmodule, launch the QICiisoftware and select the Speed Control in the drop-down menu.


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1. Press theDownload programbutton on top of the QICii window.2. Click on the Write (F4) button of thePIC downloaderpopup window.

3. Push theResetbutton on the QICii to actually start the download. The two LED's

stop flashing.4. Once the download is completed, press the Resetbutton on the QICii one moretime. The two LED's should start flashing again.

5. Close thePIC downloaderwindow.

Once loaded, the controller code stays on the QICii (even when the power to the DCMCTis off).

To start the controller, press the DCMCT User Switch (i.e. pushbutton next to the two

flashing LED's). The two LED's now stop flashing. The controller starts running. Select

the Connect to data sourcebutton on top of the QICii window to be able to receive/send

data from/to the controller. LED2 should turn on.

Table 3.2: Default Parameters for the Speed Control Module

Signal

Type

Ampl itud

e [Rad/s]

Frequency

[HZ]

Offset

[V]

Kp

[V.S/Rad]

Ki

[V/rad]b sp a w T f [s]

Square

Wave

50.0 0.4 100.0 0.0 1.0 0.0 0.0 0.01

4.3Qualitative Properties of the Proportional and Integral Control

The goal of the following procedures is to develop an intuitive feel for the properties ofthe proportional and integral control.

1. Pure Proportional Control

Start by exploring the properties of the pure proportional control. Please follow the stepsbelow:


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Step 1:

Set the reference signal to a square wave. Reasonable amplitude is 50 rad/s. When you

change the reference signal level ensure that the control signal does not reach saturation.It may be useful to adjust the Offsetof the signal generator so that the sign of the velocity

does not change. In this way you will avoid the effects of the Coulomb friction.

What is saturation?

Saturationis a nonlinear response and it also determines the physical control limit of

a system (e.g. how high the voltage you can supply to the motor until it stopsincreasing the speed, as depicted in Fig. 4.1 below). When you sweep the control

signal from low to high level, the motor speed may behave nonlinearly when it

approaches its physical limits (upper and lower bounds). Saturation can limit the

controllable range of a system. Hence, it is important to know the saturationcharacteristic of a system before a controller can be constructed. The effect of

saturation can be seen on a time-domain plot where a portion of the plot is choppedoff horizontally when the system is reaching its upper or lower limit. If such scenariohappens, you should lower the value of the control signal so to eliminate the effect of

saturation.

Fig. 4.1 Effect of saturation (circled in blue)


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2. Pure Integral Control

In this procedure we will explore the pure integral control. Please follow the steps below:

Step 1:

Set the proportional gain to zero. Set the integral gain to 0.02 V/rad to start with.Ensure that the parameters of the QICii module window, as listed in Table 3.4, are set

properly.

Signal

Type

Amplitude

[rad/s]

Frequency

[Hz]

Offset

[rad/s]

kp

[V.s/rad]

ki

[V/rad]

aw

Square

Wave50 0.4 100 0 0.02 0

Table 3.4: Module Parameters for Pure Integral Control

Step 2:

Change the integral gain by incremental steps of 0.5 V/rad to investigate the closed-

loop system for the integral controllers (kp= 0) with different gains.

What are your observations?

Step 3:

Determine the critical gain, kicwhere the system becomes critically stable and astable oscillation is sustained.

Also determine the critical period Ticof the corresponding oscillations.

Step 4:

Determine a value of the integral gain, which gives a set-point response without the

overshoot. Determine the settling time for the closed loop system.

Step 5:

Repeat the previous observations. Change theAmplitudeof the reference signal and

observe under what conditions the control signal saturates?


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Step 6:

Summarize your observations in your report. Select some representative results,

screen captures, and plots.

3. Proportional and Integral Control

The combination of the proportional and integral control action will now be explored.

Please follow the steps below.

Step 1:

Set the parameters of the QICii module window as listed in Table 3.5.

SignalType

Amplitude[rad/s]

Frequency[Hz]

Offset[rad/s]

bsp aw

SquareWave

50 0.4 100 1 0

Table 3.5 Module Parameters for Proportional and Integral Control

Step 2:

Set the proportional gain to a constant value, like kp= 0.1 V.s/rad, and change theintegral gain. Observe the tracking error and the control signal.

Step 3:

Set the integral gain to a constant value, like ki= 0.5 V.s/rad, and change theproportional gain. Observe the tracking error and the control signal.

Step 4:

Summarize your observations in your report. Select some representative results,

screen captures, and plots.


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Lab 4: Speed Control


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1. Laboratory Objective:

The objective of this laboratory experiment is:

to develop an understanding of the Proportional plus Integral (PI) control (appliedto speed control),

as how the system works, and

as how it can be tuned in order to meet the required specifications.

In particular you will explore in this experiment the followings:

Ziegler-Nichols method

Set-point Weighting

Response to load disturbance

2. Preparation and Pre-Requisites:

A pre-requisite to this laboratory is to have successfully completed the modelling and the

PI control in the previous Lab 3.

Before you start the experiment, you should also review the Proportional-plus-Integral

(PI) controller action from your lecture notes and textbook.

The system can be represented by the block diagram shown in Figure 4.1. This block

diagram illustrates the parts of the system that are relevant for speed control.

Figure 4.1: DCMCT Block Diagram for the Speed Control

The process is represented by a block which has the motor voltage Vmand the torque Tdas the inputs and the motor speed mas the output. The torque is typically a disturbance

torque that you will apply manually to the inertial load.


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The velocity is actually computed in the PIC by filtered the differences of the motor

angle musing the following relationship:

where Tfis the filters time constant ands is the Laplace transform operator.

The controller block represents the control algorithm in the computer and the poweramplifier. Vsdis a simulated external disturbance voltage.

Make sure that you understand this fully.

The linear behaviour of the system is described by the transfer functions given in the

block diagram. The major nonlinearities are the saturation of the motor amplifier at 15 V,the Coulomb friction corresponding to 0.5 V, and the quantization of the encoder.

The major un-modeled dynamics is due to the effects of the sampling and filtering. The

former can be approximated by a time delay of one sampling period.

3. Introduction

3.1 The Ziegler-Nichols Method

A good way to find the ball park values of the controller parameters is to look at pureproportional and integral controllers and to determine the gains where the system become

critically stable (a.k.a., a stable). The Ziegler-Nichols frequency response method is a

classical tuning rule based on this idea. A proportional controller is adjusted so that thesystem reaches the stability limit. The critical gain kpc where this occurs is observed

together with the period of oscillation Tpc.

In the early 1940s J.G. Ziegler and N.B. Nichols experimentally developed the PIDtuning methods based on the closed-loop tests. However the Ziegler-Nichols method

suffers from one major drawback.

That is the physical system has to tolerate to be brought into a critically stable state

without catastrophic consequences. For example, the sustained oscillation is generally outof the question for most industrial processes.

The Ziegler-Nichols closed-loop method recommends the following PI controller gain

tuning:


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Figure 4.3: Speed Control Module of the QICii Software

As a quick module description, Table 4.1 lists and describes the main elementscomposing the QICii Speed Control module user interface. Every element is uniquelyidentified through an ID number and located in Figure 4.3.

The Speed Controlmodule program runs the process in the closed-loop using the motorreference speed given by the signal generator. There are two windows that show the time

histories of motor speed (control output) and the motor voltage (control input).

The implemented digital controller in the QIC runs at 100Hz. Thus the sampling intervalis:

h = 0.01 [s]

The actual speed is obtained by filtering the position signal using the following filter:

1

sT

s

f

mm

where mis the position of the motor shaft, measured by the encoder.


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Table 4.1 QICii Modeling Module Nomenclatures





4Signal





8 Speed m,rScope With Actual (in red) and Reference (in

blue) Motor Speeds rad/s


10 Kp Kp Controller Proportional Gain Input Box V.S/rad

11 Ki Ki Controller Intergral Gain Input Box V/rad

12 bsp bsp Controller Set-point Weight Input Box

13 aw awController Windup protection Parameter Input

Box


4.2Module Startup

Power up the DCMCT: To start and use the Speed Controlmodule, launch the QICii

software and select Speed Control in the drop-down menu.


1. Press theDownload programbutton on top of the QICii window.

2. Click on the Write (F4)button of thePIC downloaderpopup window.3. Push theResetbutton on the QICii to actually start the download. The two LED's

stop flashing.


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4. Once the download is complete, press the Reset button on the QICii one more

time. The two LED's should start flashing again.5. Close thePIC downloaderwindow.

Once loaded, the controller code stays on the QICii (even when the power to the DCMCT

is off).

To start the controller, press the DCMCT User Switch(i.e. the pushbutton next to the two

flashing LED's). The two LED's will stop flashing. The controller starts running. Selectthe Connect to data sourcebutton on top of the QICii window to be able to receive/send

data from/to the controller. The LED2 should turn on.

Table 4.2: Default Parameters for the Speed Control Module

Signal

Type

Amplitud

e [Rad/s]

Frequency

[HZ]

Offset

[V]

Kp

[V.S/Rad]

Ki

[V/rad]b sp a w

T f

[s]

Square

Wave50.0 0.4 100.0 0.0 1.0 0.0 0.0 0.01

4.3Manual Tuning: Ziegler-Nichols

In Lab 3, we have obtained a good feel for the properties of the Proportional and theIntegral control. This knowledge will now be used to develop manual tuning procedures.

Manual tuning procedures are generally used when no mathematical model of the systemis available to perform control system design. Typically in the manual control, we first set

the integral gain to zero and increase the proportional gain until the system reaches the

stability boundary. At this point a critically stable condition (i.e. a stable output

oscillation) is achieved and the critical gain kpc, where this occurs and the frequency ofthe oscillation Tpcare determined. Similarly, applying the same technique to pure integral

control gives kic and Tic. The values of kpc and kicgive the ranges for the proportional

gain and integral gain respectively. Suitable values can then be determined empirically orby the traditional tuning rules.

Please carry on with the following process:

Step 1:Set the parameters of the QICii module window as following table.

Signal

Type

Amplitude

[rad/s]

Frequency

[Hz]

Offset

[rad/s]

bsp aw

Square

Wave50 0.4 100 1 0


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Set both the proportional and the integral gains to the recommended values by the

Ziegler-Nichols method as

Kp = 0.4 Kpc and Ti = 0.8 Tpc then

Ki = Kp/ Ti or Ki = 0.5Kpc/ Tpc

1. What is the resulting 2 % settling time?

2. What are your observations?

Step 2:Adjust the proportional and the integral gains manually to give a very slightly

under-damped set-point response with no saturation.

Step 3:Summarize your observations and your calculations in your report. Select some

representative results, screen captures, and plots.

4.4Set-Point Weighting

We have only investigated the effects of the proportional gain kpand the integral gain ki.The PI controller does however, have more parameters to examine. In this Section we

will explore the effects of the set-point weight for the proportional gain b sp. Thisparameter, which ranges from 0 to 1, was set to bsp = 1 in the earlier experimental

procedures.

You will observe that the set-point weight has a significant effect on the response to

command signals. However as expressed by Equation [3.1] in Lab 3, it only affects thereference signal input but does not influence the response to load disturbances.

where u(t) is the control signal and r(t) is the reference or set-point (defined by theamplitude, offset and frequency settings).

Experimental Process:

Step 1

Set the values of kp= 0.23 V.s/rad and ki= 2.3 V/rad. Choose a Square Wave signal fromthe QICii signal generator.

Investigate the effects of the set-point weight on the step response and the control signalby initially setting the value of bsp to 0 then gradually increase the value with an


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increment of 0.20 until the value reaches unity. Capture the graph each time when you

increase the value.

Step 2

Make some analysis that explains your observations based on the equation [3.1].

Step 3

In your report document your results and your analysis and illustrate with typical

responses.

4.5Response to the Load Disturbance

In this session the students will carry out an experimental investigation into the systemresponse to the applied load disturbances.

4.5.1 Manual Load Disturbance

A load disturbance can be introduced by manually applying a torque to the inertial load.

Please follow the steps below:

Step 1

The regulation problem, at r= 100 rad/s, is investigated. Set the QICii module parameters

as given in the following table.

Amplitude [rad/s] Offset [rad/s] aw

0 100 0

Step 2

Choose a pure proportional controller (i.e., ki= 0) with the given value of the gain beingkp= 0.10 V.s/rad, and bsp= 1.0.


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Step 3

Apply a torque manually by gently touching the inertial load with your finger. Observeclosely as what happens when you change the proportional gain of the controller (e.g.

gradually increase the value of kpwith an increment of 0.10 Vs/rad until kpcis reached).

Step 4

Investigate a controller with the pure integral action. To do so, set the proportional gain

to zero (kp= 0) and the initial value of the integral gain to unity (ki= 1.0 V/rad). Nowapply a disturbance torque manually and observe what happens when you increase the

integral gain of the controller gradually with an increment of 0.50 V/rad until kicis

reached.

4.5.2 Simulated Load Disturbances: Disturbance Response With PI Control

A disturbance torque can be simulated by applying an additional voltage, V sd, to themotor input (i.e. control signal disturbance).

Experimental Process

Step 1

The regulation problem at zero velocity (i.e., r = 0 rad/s) should be investigated.

Set the QICii module parameters as given in the following table.

Amplitude [rad/s] Offset [rad/s] aw

0 0 0

Step 2

Emulate a load disturbance torque by pressing down and holding or releasing the User

Switch.


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Step 3

Investigate the behaviour of the closed-loop system for the pure proportional controllers(i.e., ki= 0 and bsp= 1) with different values of the gain. You can start off with kp= 0.10

Vs/rad and step up the value with an increment of 0.10 Vs/rad until kpcis reached.

1.

Summarize your observations in your report.2. Determine the steady-state error ss_P.

3. Select some representative results, screen captures, and plots.

Step 4

Investigate the behaviour of the closed-loop system for the pure integrating controllers(i.e., kp= 0 and aw= 0) with different values of the gain. You can start off with ki= 1.0

V/rad and step up the value with an increment of 0.50 V/rad until kic is reached.

Summarize your observations in your report. Select some representative results, screen

captures, and plots.

Step 5

Can you estimate from your experiment as how much voltage disturbance, Vsd, is applied

when you press the DCMCT User Switch?Please explain in detail as how you havearrived at this.


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University of Ontario Institute of Technology

Lab 5: Position Control

PD, PI and PID Controllers


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1. Laboratory Objectives:

The objective of this laboratory experiment is to develop an understanding of PID control of

motor rotational angle, how it works, and how it can be tuned to meet the required

specifications.

In particular you will explore the followings:

Qualitative properties of the proportional, derivative, and the integral actions

Comparisons with the PI control of motor speed

2. Preparation and the Pre-requisite:

A pre-requisite to this laboratory is to have successfully completed the modelling experiment

and the model validation experiment described in Laboratories 1 and 2, respectively. Before

the start of this lab experiment, you should also review the topic of the Proportional-plus-

Integral (PI) control of motor speed, as you have performed in Laboratories 3 and 4.

For the purpose of the position control, the system can be represented by the block diagram as

shown in Figure 5.1. This block diagram illustrates the parts of the system that are relevant for

the position control.

Figure 5.1 DCMCT Block Diagram for the Position Control

The process is represented by a block, which has the motor voltage Vmand the torque Tdas

the load disturbance and the motor rotational angle mas the output. The torque disturbance Td

is typically a torque that you could apply manually to the inertial load (e.g. using your finger

to apply a retarding force to the flywheel momentarily, as seen in Lab 4). The PID controller

block represents the control algorithm in the computer and the power amplifier unit. The

control signal disturbance Vsdis a simulated external disturbance voltage.


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The linear behaviour of the system is described by the transfer functions given in the block

diagram. The major sources of nonlinearities are the saturation of the motor amplifier at 15 V,

the Coulomb friction corresponding to 0.4 V (i.e., the minimum voltage required to start-up

the motor from stationary), and the quantization of the encoder which, causes a time delay of

1 sampling period (i.e., due to a combination of the encoder resolution of 4096 counts per

revolution and the sampling rate of the encoder being set at h= 100 Hz).

3. Introduction : PID controller

The PID controller is a classical control algorithm. It is used for a variety of purposes and it

often works very well. For systems with simple dynamics it can give close to optimal

performance and for processes with complicated dynamics, it can often give good

performance provided that specifications are not too demanding. Better performance can,however, be obtained by using more complicated controllers.

3.1 The PID Control Law

The linear behaviour of a PID controller can be described by the following equation:

where, u(t) is the control signal, r(t) being the reference signal and y(t) is the measured

process output. The reference signal r(t) is also called the set-point or the command signal.

The linear behavior of the PID controller is governed by the following parameters:

kp : proportional gain

ki : integral gain

kd : derivative gain

bsp : proportional set-point weight

bsd: derivative set-point weight

Tf : time constant of the filter for the measured signal


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Sometimes the filtered measurementyf(t)is also used in the control loop. It is computed from

Tf, the time constant of the filter for the measured signal. The filter time constant Tf is

typically set to a constant value and it is often combined with the sensor. The filter provides

the roll-off at high frequencies. It is important to reduce the effects of the sensor noise as it

improves the system robustness.

The PID controller is similar to the PI controller and the additional derivative term provides

added flexibility. In particular, it improves the possibilities of introducing the damping effect

because it is an approximate prediction of future measurements.

3.2 The Magic of Integral Action

An interesting property of a controller with an integral action is that it always gives the

correct steady-state value provided that there is equilibrium. This can be seen simply by

assuming that there is a steady-state value with the constant values of u(t) = uss, r(t) = rss, and

also y(t) =yss.

Equation [5.1] can now be written as:

Since the left-hand-side is a constant, then the right-hand-side must also be a constant. This

requires thatyss= rss. Notice that the only assumption that has been made about the process

is that there should be an asymptotic steady-state condition.

The load disturbance response of a PID controller has an interesting property, which can be

seen as follows:

where, eis the control error, as defined:


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)(y)(r)(e ttt

One can assume that the PID controller is connected to a process and also the closedloop

system remains stable. Apply a load disturbance in the form of a step function to the system.

There will be a transient response and the error will then approaches to zero because the

system is stable. The above equation implies that:

The value of u() is the steady-state control signal required to eliminate the load disturbance.

We can conclude from Equation [5.2] that the integral of the error signal due to a load

disturbance is inversely proportional to the integral gain of the controller.

3.3 Controls with TwoDegreeofFreedom

A PID controller with the set-point weights bsp= 1 and bsd= 1 is a controller with the error

feedback because the control actions are based on the error e= ry. A controller where, one

of the setpoint weights is different from one is said to have twodegreesoffreedom

because the signal transmission from the reference rto the control uis different than from thesignal transmission from the measurementyto the control u.

A controller with twodegreesoffreedom has two inputs and one output, as shown in the

block diagram of Figure 5.1.

The set-point weights have no effect on the load disturbance response or on the system

dynamics but they can influence the response to command signals significantly. Both the set-

point weights range from 0 to 1.

4. Laboratory Content

4.1 The QICii Position Control Module

4.1.1 Module Description


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The main tool for this laboratory experiment is the front panel of the module entitled Position

Controlin the QICii software, which should be similar to the one shown in Figure 5.2.

Figure 5.2: The Position Control Module of the QICii Software

As a quick module description, Table 5.1 lists and describes the main elements composing the

QICii Position Control module user interface.

Every element is uniquely identified through an ID number and located in Figure 5.2.

The Position Control module program runs the process in the closedloop with the motorreference position angle given by the signal generator. There are two windows that show the

time histories of the motor position (i.e., the control output) and the motor voltage (i.e., the

control input).


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The motor position is measured by an encoder generating 4096 counts per revolution. Theposition time derivative (speed) is obtained by filtering the position signal using the following

filter:

where, m is the position of the motor shaft measured by the encoder.

4.1.2 Module Startup

First, power up the DCMCT unit and in order to start the experiment use the Position Control

module, launch the QICii software and then select Position Control in the dropdown menu.


1. Press theDownload programbutton on the top of the QICii window.

2. Click on the Write (F4) button of thePIC downloaderpopup window.3. Push theResetbutton on the QIC to actually start the download.

The two LED's will stop flashing.4. Once the download is completed, press the Resetbutton on the QIC one more time.

The two LED's should now start flashing again.

5. Close thePIC downloaderwindow.

Once it is loaded, the controller code stays on the QIC (even when the power to the DCMCTis off).

To start the controller, press the DCMCT User Switch (i.e. the pushbutton next to the twoflashing LED's). The two LED's will stop flashing. The controller now starts running. Select

the Connect to data source button on the top of the QICii window in order to be able toreceive/send data from/to the controller. LED 2 should turn on.

The default module parameters, loaded after the download, are given in Table 5.2.


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Table 5.2: Default Parameters for thePosition ControlModule

Signal Type Amplitude

[rad]

Frequency

[Hz]

Offset

[rad]

kp

[V/rad]

kd

[V.s/rad]

ki

[V/(rad.s)]

Square Wave 1.0 0.4 0.0 3.0 0.05 0.0

bsp bsd Tf[s]

1.0 0.0 0.006

4.2 Qualitative Properties of the Proportional and Derivative Control

The goal of the following experiments is to develop an intuitive feel for the properties of the

proportional and the derivative control actions.

4.2.1 Pure Proportional (P) Control

Start by exploring the properties of the pure proportional control. Please follow the steps

indicated below:

1. Set the reference signal to a square wave. Reasonable amplitude is 3 rad. When you

changed the reference signal level ensure that the control signal does not saturate.

Set both the integral and the derivative gains to zero (ki= kd= 0).

To start with the proportional gain is set to 0.1 V/rad, ensure that the followingparameters of thePosition Controlwindow, as displayed in Table 5.3, are set properly.

Table 5.3: Module Parameters for the Pure Proportional Control Test

Signal Type Amplitud

e[rad]

Frequency

[Hz]

Offset

[rad]

kp

[V/rad]

bsp

Square Wave 3 0.4 0 0.1 1

2. To investigate the closedloop system for the proportional controllers, with different

gains, change the proportional gain to the following values: kp= 1, 2, and 4 V/rad.What are your observations? Explain in detail.

3. Describe the steadystate error in response to a step function input for the above kpvalues.


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4. In Step 2, under what conditions the control signal will saturate (e.g., at what voltage

limit)? What should you do to keep the control signal away from saturation?

5. Set the Amplitudeto 0 rad and Offsetto 0 rad too; apply a torque (load disturbance)

on the inertial load by gently touching and rotating the flywheel with your finger.

Observe the effect on the position. What do you feel when you turn the flywheel and

then what does the motor do after you let go of the flywheel?

6. Now simulate a control signal disturbance Vsdby pressing the User Switchof the

module. You should press the switch down and hold it until steady state is reached,then release the switch. Observe the effect on the position.

7. Summarize your detailed observations in your Lab report. Select some representativeresults, screen captures, and plots and include them in your report.

4.2.2 Proportional and Derivative (PD) Control Actions

The combination of the proportional and derivative control actions will now be explored.

Please follow the steps given below:

1. Set the proportional gain to 2.0 V/rad and fix the derivative gain to 0.0 V.s/rad to start

the test. Set the parameters of the QICii module window as listed in Table 5.4.

Set the integral controller action gain to zero (i.e., ki= 0).

Table 5.4: Module Parameters for the ProportionalplusDerivative Control Test

Signal Type Amplitude

[rad]

Frequency

[Hz]

Offset

[rad]

kp

[V/rad]

kd

[V.s/rad]

bsp bsd

Square Wave 2 0.4 0 2.0 0 1 1

Change the derivative gain with the following values to investigate the closedloopsystem for the PD controllers with different derivative gains:

2. Try again but with the values of gains: kd = 0, 0.05, 0.1, 0.15 and 0.2 V.s/rad.

What are your observations? Explain in detail.


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3. Determine a value of the derivative gain, which gives a setpoint response without any

overshoot. Determine the settling time and the steady-state error for the closedloop

system.

4.

Now set the Amplitudeto 0 rad, Offsetto 2 rad, and change the derivative gain withthe following values: kd = 0, 0.05, 0.1, 0.15 and 0.2 V.s/rad. Then, apply a torque on

the inertial load by gently touching and rotating the flywheel with your finger.Observe the effect on the position. What do you feel when you turn the flywheel and

then what does the motor do after you let go of the flywheel?

5. Simulate a control signal disturbance Vsdby pressing the User Switchof the module.

You should press the switch down and hold it until steady state is reached, then releasethe switch. Observe the effect on the position. Compare the system response of this

PD control with that of the pure proportional (P) control in the previous section?

6. Summarize your overall observations in your Lab report. Select some representative

results, screen captures, and plots and include them in your report.

4.2.3 Proportional and Integral (PI) Control Actions

1. Repeat Section 4.2.2 with module parameters being configured to the values depicted

in Table 5.4. Change the integral gain with the following values: ki = 0, 1, 2, 5 and

10 V/rad.s. Observe the system response as you change the integral gain.

2. Now set the Amplitudeto 0 rad, Offsetto 2 rad and then change the integral gain

value in according to the values in Step 1. Then, apply a torque on the inertial load bygently touching and rotating the flywheel with your finger. Observe the effect on the

position. What do you feel when you turn the flywheel and then what does the motor

do after you let go of the flywheel? How does this PI control differ from the PD

control in the previous section?

3. Simulate a control signal disturbance Vsdby pressing the User Switchof the module.

You should press the switch down and hold it until steady state is reached, then releasethe switch. Observe the effect on the position. How does this PI control differ from the

PD control in the previous section?

4. Look up your Lab Report from the PI control of the motor speed described in Lab

experiments 3 and 4, and compare the process outputs and the control signals for the

speed and position controls in response to a reference input.


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4.2.4 Proportional, Integral and Derivative (PID) Control Actions

The combination of the proportional, integral and derivative control actions will now be

explored.

Please follow the steps given below:

1.

Set the proportional gain to 2.0 V/rad and the derivative gain to the value you havedetermined in Step 3 of Section 4.2.2 (zero overshoot scenario) to start the test. Set theparameters of the QICii module window as listed in Table 5.4.

2. Manually tune the integral gain kisuch that the steady-state error reaches zero. Whatare the parameter values of your PID controller?

3. Now vary the Amplitudeof the set point with the following values: 0.5, 1.0, 2.0, 4.0,and 5.0 rad. Observe what happen to the system response such as steady-state error,

overshoot, settling timeetc. as you change the amplitude of the set point. Do you see

any changes in the system response? At what set point amplitude the control signal

starts to saturate (i.e. this will determine the controllability of the motor systemsubjected to your PID parameter values)?

4. What conclusion can do draw from this experiment? In your own words, describe the

roles and significances of kp, ki, and kdin both speed and position controls.

Engrmece3350u Lab Handbook f2014(2) (1)

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