Hong Chen - AMSStcct.amss.ac.cn/newsletter/2016/201608/images/hong.pdf · Hong Chen State Key...

2016 Chinese Control Conference, Chengdu

Triple-step Nonlinear Control Design: Methodology and Automotive Applications

Hong Chen State Key Laboratory of Automotive Simulation and Control

Jilin University, China

❈ Motivation

❈ Triple-Step Design Technique

❈ Automotive Applications: Case Study

❈ Conclusions

Outline 2

Case 1: Vehicle stability control

Control Requirements

Make the vehicle response according to the action of the driver

Guarantee the vehicle dynamics stability

Motivation 3

Make sideslip angle and yaw rate track the desired references

Control Problem Description

Case 1: Vehicle stability control

Motivation 4

Make sideslip angle and yaw rate track the desired values

Control Output

Modeling

Control-oriented model

Motivation 5

Newton’s second law

The principle of moments

Tire dynamics: magic formula, UniTire model, lookup tables

Modeling

Motivation 6

Control outputs：

Control inputs：

Time varying parameters：

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

α f (rad)

Fyf

(N)

Lateral Force of Tyre - Fyf (αf,µ)

µ = 0.1µ = 0.3µ = 0.5µ = 0.7µ = 0.9

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-5000

0

5000

α r (rad)

Fyr

(N

)

Lateral Force of Tyre - Fyr(αr,µ)

µ = 0.1µ = 0.3µ = 0.5µ = 0.7µ = 0.9

With time varying parameters Lookup tables in the right side Non-affine in control input

How to design the controller

Balance


Motivation ASME JDSMC (2011) VSD (2011) Mechatronics (2011)

Improve smoothness of shift process

7

Case 2：Shift control of automated transmissions



Improve smoothness of shift process

Make the speed difference of clutch track a reference trajectory

Speed difference of clutch

does not exceed the required shift time

the change rate at is zero the change rate at should be small

Control Output

8

Case 2：Shift control of automated transmissions


Inertia Phase

Valve pressure dynamics The principle of moments

9

Case2：Shift control of transmissions

Modeling

is nonlinear and in the form of DE contains lookup tables with time varying parameters may be non-affine as in the case of vehicle stability control

Model Concept

Control input :

Time varying parameter :

Control output :

Model Features Data-physics-mixed model

Motivation

How to design the controller

DCT/AT Engine Torque Map Torque Converter Engine Friction Properties Map

10

Triple Step Design Technique

Take 2nd order systems as example

First Step: Steady State Control

， Plant

Steady State Control

Let and

with

for affine systems 11

Introduce reference variation in feed-forward Improve the transient of tracking

， Plant

Steady State Control Feed-forward

Let and

Gains depend on the system states and varying parameters

Triple Step Design Technique for affine systems

Second Step: Reference Variation Based Feed-forward Control

12

， Plant


2. Step: Reference Variation Based Feed-forward Control

1. Step: Steady State Control

Triple Step Design Technique for affine systems 13

Third Step: Error Feedback Control

Error dynamics


Define Lyapunov function


Gain-scheduling PID

LaSalle's invariance principle


Closed-loop error dynamics

Final Control Law (Second order)


If

If

If

If





If

If

Let Analytical solution can be obtained Solved numerically and presented in look-up tables

First Step: Steady State Control

Take SISO as example

Triple Step Design Technique for non-affine systems

， Plant


20

Second Step: Reference Variation Based Feed-forward Control

Let

with

Triple Step Design Technique for non-affine systems

， Plant


Let

21


Let

，

Feed-forward

Plant


Gain-scheduling PI Reference

Triple Step Design Technique for non-affine systems 22

ISS

Design

Closed-loop error dynamics

Define

Final Control Law

Triple Step Design Technique for non-affine systems 23

affine in ue

Engineering-oriented model-based controller design

All the procedure is algebraic operation

3 parts: steady state part, reference variation feedforward, error feedback

The gains of all parts depend on system states and varying parameters

Introduce the reference variation in the feed-forward

Merits

Triple Step Design Technique 24

variations Nonlinear systems with

❈ look-up tables

❈ time-varying parameters

❈ non-affine

Merits

Triple Step Design Technique 25

variations Nonlinear systems with

❈ look-up tables

❈ time-varying parameters

❈ non-affine

❈ Closed loop stability in sense of ISS

• Tracking error is asymptotically stable if no disturbances

• Bounded tracking error for bounded disturbance/uncertainty

Case study I : Vehicle Dynamics Control in EV J FRANKLIN I (2014)

2-Input-2-Output, 2nd Order, Non-affine

Stability Control of In-wheel Motor Electric Vehicles

First step: steady state control

• Implemented by look-up tables

26

Case study I : Vehicle Dynamics Control in EV

Second Step: reference variaiton feedforward

Third Step: tracking error feedback

Reference：

( Define: )

27

Case study I : Vehicle Dynamics Control in EV 28

Coupled Non-affine System: De-coupled Closed-loop Error Dynamics

Decoupling

Cornering maneuver :（Initial velocity 60km/h）

Double lane change:

Case study I : Vehicle Dynamics Control in EV 29

2 Input 2 Output, 4th Order, Non-affine

IEEE CST (2016)

Steady State Control Reference variation based FF Gain-scheduling PID

Vehicle Control After a Tire Blowout:

Case study II: Vehicle Control After a Tire Blowout

Without control：go to the side of the failed tire

Ensure driving safety： Maintain vehicle directional stability Follow the center line of the road

yaw angle lateral displacement

30

Simulation Results Test 1: Left front bursts: straight road


Improve Directional

Stability

Path Following

Performance

31


Simulation Results Test 2: Left front bursts: curved road

Improve Directional

Stability

Path Following

Performance Lateral Displacement Deviation

32

Description: Rail pressure stable and track a given reference

Detailed control specifications

Objective: Inject precise and desired quantity of fuel into cylinder

Settling time: within 100ms

Steady state error: <1 bar

Maximum fluctuation: <5 bar

System description

Control output: Rail Pressure Control input: Inlet flow of the high

pressure pump

ry p=

uu q=

IET CTA (2014) ACC (2014)

Rail Pressure System

Case Study III : Rail Pressure Control in GDI Engines

GDI

33

0

input

Control Valve

High Pressure Pump

Check Valve

Plunger

Pressure Dynamics in HPP:

Motion Dynamics of Plunger:

Outflow:

0

input

output

Common Rail Common Rail Pressure:

Outflow:

Case Study III : Rail Pressure Control in GDI Engines 34

Needle valve Input Output

Neglecting the transient dynamics： Fast subsystem Reduced order system

Injecting Pressure Injector


Control Input： Control Output：

Time-varying Parameter:

35

0 1

* * * *2

1

1 221

0 221

( ) ( )( , ) ( ) ( 1) ,

( )( , , , ) 2 ( ( ) ),

( )( , ) 2 (1 ),

( )( , ) 2 ,

( )( , ) 2

r r

p p ps p rpm ri p

r r

p r ff p ri

f r

p rP p

f

p rI p

f

pD p r

dh V Vu y p A q y q p y

d V VV V K

u y p y y p y p q y pK V

V Vf y p p y k k

KV V

f y p p y k kKV V

f x p p p

θ θω η

θθη

θη

θη

θ

= + − − + −

= − − +

= − − +

= − −

= − −

1 221

( ( )),r fri r

f r

Kk k q p

K Vη+ −

Control law for rail pressure control:


Implement according to ECU computational resource

neglect less-dominant terms e.g. 2. order derivative of reference

implement with lookup tables

36

GDI HiL Platform

Engine speed：1000,2000,3000,4000, 5000 , 6000rpm；Load：20-75 (%)，

Engine speed：1000-3500 rpm Load：15-75 (%)

GDI Testbench


Tracking error

Rail pressure

operating conditions

Tracking error

Rail pressure

operating conditions

37

Extended Applications : Transmission Actuator Control and SCR Control

IEEE TIE (2014)

Transmission Actuator Control urea-SCR Control

3rd Order System

Steady State Control Reference variation based FF Gain-scheduling PIDD

Gain Scheduling

• Improve the performance of the position tracking control for a novel electric clutch actuator

• For simultaneously achieving high NOx conversion efficiency and low ammonia slip

PWM duty rate Displacement of Screw nut

Ammonia coverage ratio Mass flow of Ammonia

38

Nonlinear systems

Conclusions 39

with lookup tables with time-varying parameters may be non-affine Triple step design technique

Engineering-oriented model-based controller design

3 parts: steady state, reference variation feedforward, error feedback

The gains of all parts depend on system states and varying parameters

Introduce the reference variation in the feed-forward

Tracking error stability in the sense of ISS

Case study rail pressure control, shift control (2nd order, affine) vehicle stability control (MIMO, non-affine) actuator control and SCR control (3rd order, affine)

1. H. Chen, X. Gong, Q. Liu and Y. Hu. Triple-step method to design non-linear controller for rail pressure of gasoline direct injection engines. IET CTA, 8(11): 948-959, 2014

2. B. Gao, H. Chen, Q. Liu and H. Chu. Position control of electric clutch actuator using a triple-step nonlinear method. IEEE T Industrial Electronics , 61(12):6995-7003, 2014

3. Q. Liu, H. Chen, B. Gao, Y. Gao. Shift control of Dual Clutch Transmission using Triple-Step nonlinear method. IFAC World Congress, 47(3): 5884-5889, 2014.

4. Y. Hu, D, Hu, Y, Fan, et al. Electronic throttle controller design using a triple-step nonlinear method[C]. Proc. 11th WCICA, 2014: 816-821.

5. H. Zhao, B. Gao, B. Ren and H. Chen. Integrated control of in-wheel motor electric vehicles using a triple-step nonlinear method. J. Franklin Institute, 352(2):519-540, 2015

6. Q. Liu, X. Gong, H. Chen, B. Xin and P. Sun. Nonlinear GDI rail pressure control: Design, analysis and experimental implementation. Proc. 34th CCC, 8132-8139, 2015

7. F. Wang, H. Chen, D. Cao. Nonlinear Coordinated Motion Control of Road Vehicles After a Tire Blowout. IEEE T Control System Technology, 24(3): 956 - 970, 2016

8. H. Chu, B. Gao, W. Gu and H. Chen. Low Speed Control for Permanent Magnet DC Torque Motor Using Observer-based Nonlinear Triple-Step Controller. IEEE T Industrial Electronics (online).

9. H. Zhao, Y. Hu, X. Gong, H. Chen. Modelling and control of urea-SCR systems through the triple-step non-linear method in consideration of time-varying parameters and reference dynamics. Transactions of the Institute of Measurement and Control (accept).

10. …

References 40

Acknowledgement

Bingzhao Gao Fei Wang Qifang Liu Haiyan Zhao Yunfeng Hu Hongqing Chu Xun Gong

41

Pengyuan Sun, FAW Baiyu Xin, FAW

Thank you！

2016 Chinese Control Conference, Chengdu

Hong Chen - AMSStcct.amss.ac.cn/newsletter/2016/201608/images/hong.pdf · Hong Chen State Key...

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