Control System Engineering

PE-3032Prof. CHARLTON S. INAODefence Engineering College, Debre Zeit , Ethiopia

Week 10 Data Presentation System

Electromechanical SystemTransfer Functions

• Systems that are hybrids of electrical and mechanical variables is the electromechanical systems.

• Other applications for systems with electromechanical components are robot controls, sun and star trackers, and computer tape and disk-drive position controls.

• An example of a control system that uses electromechanical components is shown in Figure 1

NASA flight simulator robot arm with electromechanical control system components.

Potentiometer

Input: Rotation Output :

Voltage

Eq. 1

Motors

Motor onstruction

DC Motor Modeling

Eq. 2

Eq. 3

Eq. 4

Eq. 5

Eq. 6

Eq. 7

Eq. 8

Modeling of Thermal Systems

Mode of Heat Transfer

• Conduction

• Convection

• Radiation

ConductionConduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. Conduction can take place in solids, liquids, or gases.

In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons.

A cold canned drink in a warm room, for example, eventually warms up to the room temperature as a result of heat transfer from the room to the drink through the aluminum can by conduction.

Thermal Conductivities

CONVECTIONConvection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer.

RADIATIONRadiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules. Unlike conduction and convection, the transfer of energy by radiation does not require the presence of an intervening medium. In fact, energy transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth.

1 Thermal resistanceThe thermal resistance R is the resistance

offered to the rate of flow of heat q (Figure a) and is defined by:

where T1- T2 is the temperature difference through which the heat flows.

R=L/kA, oC/W

Application Example of Thermal Resistance

Sample No.1

Application Example Thermal Resistance

Sample No.2

2 Thermal capacitance

The thermal capacitance (Figure b) is a measure of the store of internal energy in a system. If the rate of flow of heat into a system is q1 and the rate of flow out q2 then the rate of change of internal energy of the system is q1 - q2. An increase in internal energy can result in a change in temperature:

change in internal energy = mc x change in temperature

where m is the mass and c the specific heat capacity. Thus the rate of change of internal energy is equal to mc times the rate of change of temperature. Hence:

This equation can be written as:

where the capacitance C = mc.

Example

Develop a model for the simple thermal system of a thermometer at temperature T being used to measure the temperature of a liquid when it suddenly changes to the higher temperature of TL(Figure ).

Example• Determine a model for

the temperature of a room (Figure) containing a heater which supplies heat at the rate q1 and the room loses heat at the rate q2.