Introduction to Control Systems

Unit - 1

Unit - 1 Introduction to control system

Topics to be covered….

IntroductionOpen-loop control Systems (OL)Closed-loop Control Systems (CL)Difference between OL and CL systemsLaplace TransformTransfer Function

Unit - 1 Introduction to control system

Unit - 1 Introduction to control system

Control System?Control System?

A control system Mechanism that alters the future of a system

consists of subsystems and processes assembled for the purpose of obtaining a desired output, e.g. a radio controlled car is an example of a basic control system. Other examples include…

Traffic Lights

Lifts

Microwave

Air Conditioning Systems

Theme Park Rides

Automatic Doors

Burglar Alarm

Train Networks Robots

What is a Control System?What is a Control System?

Security Lights

A control theory is a strategy to select appropriate inputs

Simplified description of a control system

Unit - 1 Introduction to control system

Important Terminologies

Plant : physical object to be controlledSystem: It is a combination of components that act together and perform a certain objectiveInput: objective, stimulus, independent variable, desired response

Output: result, response, dependent variable, actual response

Introduction to control systemUnit - 1

Open loop Systems

- the output has no effect on the control action

- the output is not measured - the output is not compared back with the

reference input - It can not compensate for the effect of the

disturbance

Introduction to control systemUnit - 1

Bread Toaster

Unit - 1 Introduction to control system

Closed loop Systems

- Also referred to as feedback control system

- Measures the output and compares the results from the reference or input. The difference between the two, is called error causes the actuating signal to drives the controller and correct correct the difference

- Compensates the effect of disturbances

Introduction to control systemUnit - 1

Open and Closed Loop System

Unit - 1

Closed-loop control system

Unit - 1 Introduction to control system

Introduction to control systemUnit - 1

Comparison of Systems

System Type Advantages Disadvantages

Open-loop control systems

1. Simple to construct and ease of maintenance

2. Less expensive than a closed-loop system

3. There is no stability problem

4. Convenient when output is hard to measure or measuring the output precisely is economically not feasible

1. The system response is very sensitive to external disturbance and internal variations in system parameters.

2. Recalibration is necessary from time to time in order to maintain the required quality of the output

Comparison of Systems

Unit - 1 Introduction to control system

System Type Advantages Disadvantages

Closed-loop control systems

1. Makes the system response relatively insensitive to external disturbances and internal variations in the systems parameters

2. Possible to use relatively inexpensive components.

3. Better control of the transient and steady-state response.

4. Increase accuracy5. Increased ability to

reproduce output with varied inputs

1. Risk of instability

2. Complex analysis.

3. Expensive implementation

Laplace Transform Table for Derivatives

Laplace Transform Table

Unit - 1 Introduction to control system

Example of Laplace Transform

1. Given the differential equation, using Laplace, solve for y(t) if all initial conditions are zero (relaxed system). u(t) is a unity step function

𝒅𝟐𝒚 (𝒕)𝒅𝒕𝟐

+𝟏𝟐𝒅𝒚 (𝒕)𝒅𝒕

+𝟑𝟐𝒚=𝟑𝟐𝒖(𝒕)

Transfer Function

The transfer function is the ratio of the output Laplace Transform to the input Laplace Transform assuming zero initial conditions.

Example of Transfer Function

𝒅𝒄 (𝒕)𝒅𝒕

+𝟐𝒄(𝒕)=𝒓 (𝒕 )

1. Find the transfer function C(s)/R(s) represented by the equation below.

2. Also find the response c(t) to an input r(t)=u(t)