Control Engineering

Chapter 1: Introduction

Prof. Dr.-Ing. Pu Li

Lab of Process Optimization

2

Spacecraft systems Controlled variables:• Position• Speed• Acceleration• Mass

3

Chemical processes Controlled variables:• Temperature• Pressure• Concentration• Flow

4

Industrial robots Controlled variables:

• Position

• Speed

• Force

5Local control systems

6Central control systems

7Example: Temperature control at home

1) You are watching TV in bed (temperature is at the desired value). 2) It snows heavily outsides (a disturbance comes). 3) You feel cold (your body notices a lower temperature).4) You tune the heater (an action against the disturbance).5) The room temperature will increase (effect of the action).6) You are happy now (back to the desired state).

This leads to a closed loop control!

8Example: Temperature control at home

This leads to a closed loop control!

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Controlled variable : room temperature, Disturbance : outside temperature, Manipulated variable : heating flow,

Setpoint of controlled variable : desired room temperature, e.g. 22°CMeasured value of controlled variable : actual room temperature, e.g. 20°CError of the controller : Setpoint minus measured value

θ

Aθ

Sθ

u

θθθ −S

Variables in the control loop (mathematical description):

These variables are time-dependent, i.e. dynamic!

Example: Temperature control at home

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When the room temperature (actual value) is lower than the desierd value (setpoint), you will increase the opening of the valve of the heating flow.

)()( ttu S θθ −∝

The controller (you):

When the room temperature (actual value) is higher than the desired value (setpoint), you will decrease the opening of the heating flow valve.

This means the heating flow (manipulated variable) should be proportional to the error of the controller:

Controller:

Example: Temperature control at home

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How will the room temperature (controlled variable) increase, when you increase the opening of the heating flow (manipulated variable)?

[ ])()( 2 tft Aθθ =

The Process to be controlled (the room):

How will the room temperature (controlled variable) decrease, when the outside temperature (disturbance) decreases?

[ ])()( 1 tuft =θ ⇒

⇒

Example: Temperature control at home

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The control loop (the whole system):

Example: Temperature control at home

13Feedback: the heating will be tuned based on the controller error.

Feed forward: the heating will be tuned based on the forecast of the outside temperature to compensate its effect on the room temperature.

14Example: Temperature control in a greenhouse

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The implementation of the control loop (the whole system):

sensorcontroller

control valve

heater

Example: Temperature control in a greenhouse

16The control loop (the whole system):

General description:

17Air pressure control in a wind canal

control piston

oiljet tube

turning plate

membrane

nozzle

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Aims of a control loop:

• follow the changes of the setpoint.

• Keep the setpoint in spite of the disturbance.

• Which characteristics has the process?

• Which algorithm should be used for the controller?

• How will be the control loop implemented?

General description:

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What are required for a control system design?

Process technology• Analysis of the process• Modeling• Simulation and experimental validation

Control engineering• Mathematical solution methods• Design of control loops• Feasibility/stability

Computer engineering• Hardware and software development• Programming for the numerical computing• Realization using process control system

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Chapter 3: Laplace transformation• Laplace transformation typical functions• Properties of Laplace transformation• Transfer function

Chapter 2: Modeling of linear processes • Modeling with differential equations• Linearization of nonlinear systems• State space model

Content of this lecture:

Chapter 4: Analysis of control systems in time domain• Dynamics of different plants• Reply of typical input signals• Functions of typical controller

Chapter 5: Design of control systems in frequency domain• Influences of the operating frequency• Nyquist diagram and Bode diagram• Stability analysis and controller design