Feedback Control System

UNIT 1: INTRODUCTION TO CONTROL SYSTEMS

Control system are important and are present almost everywhere in our daily lives. Control system provides an output or response for a given input or stimulus. Examples of control system are:

a) Man made     : CD player, radio antenna, rocket/missile,  robots, oven, room 

                          air condition

b) Our bodies    : Pancreas – regulate our blood sugar, Eyes – follow the

                          moving  object to keep it in view.

c) Non physical :  Automatic control of a student performance – input (study 

                          time), output (grade)

Control system can be classify into signal, mathematical model and group. The signals divided into two types are continuous and discrete control system. The mathematical model also divided into two types are linear and non linear control system. The groups are divided into two type which are kinetic and process control system. 

There are four advantages of a control system. 

Power Amplification

For example, a radar antenna, positioned by the low-power rotation of a knob at the input, requires a large amount of power for its output rotation. A control system can produce the needed power amplification or power gain. 

Remote control                                                                                 

Robots designed by control system principles can compensate for human disabilities. Control systems are also useful in remote or dangerous locations. For example, a remote-controlled robot arm can be used to pick up material in a radioactive environment. 

Convenience of input form                                                               

Control systems can also be used to provide convenience by changing the form of the input. For example, in a temperature control system, the input is a position on a thermostat. The output is heat. Thus, a convenient position input yields a desired thermal output. 

Compensation for disturbances                                                      

For example, consider an antenna system that point in a commanded direction. If wind forces the antenna from its commanded position, or if noise enters internally, the system must be able to detect the disturbance and correct the antenna’s position. 

There are three objective in designing control system:

a) Transient response : The plant is changing from one steady state to another between specification are required.
b) Stability : A system produce a consistence/ steady state output is a stable system.
c) Steady state response : Exist for a stable system. Important characteristics for design is the steady state error should be minimize as small as possible. Steady state error different between input and output values. 

Step in designing a control system

Open Loop Control System (OLCS)

a) With disturbance/noise, the desired response cannot be achieved, actual unequal desired response.

b)  Example : toaster, washing machine, traffic light.

c)  System that work base on time are open OLCS.

d) The reference input corresponds to a fixed operating condition. The result may not be accurate.

Closed Loop Control System (CLCS)

a)  The output signal of a CLCS is feedback to influence the control action and improve overall system performance.

b)  The difference (actual and desired response) will be used to determine the control action.

Differences between  (OLCS) and (CLCS)

Modelling

Modelling is a process to obtain mathematical equation that represents the dynamic behavior of a system.Mathematical model of a physical system is required to understand, analyse and control the system.Mathematical model for dynamic systems are derived from the conservation and fundamentals laws of physics and the engineering properties of the system.Example of fundamental physical laws of science and engineering :

a)  Electrical system    : Ohms, kirchoff's and Lenz laws

b)  Mechanical system : Thermodynamic and newton law

The mathematical model can be described in three forms:

a)  The classical representation of a single nth - order differential equation

b)  The transfer function format, which give the output in terms of the input.

c)  The state space format of n simultaneously first-order differential equations

UNIT 2: MATHEMATICAL MODEL OF SYSTEMS 

Introduction

As a mention in a sub topics Modelling, mathematical model can be describe in three forms; differential equation, transfer function and state space equation. For this course we are focusing on differential equation and transfer function.

Differential equation

Example 2.1 : Find the transfer function for the differential equation below. Assuming initial condition is zero.