Introduction to control system 2

Introduction to control system 2

1. Introduction to Control System Definition and Representation Controllers and algorithms Transfer function and gain of a system Introduction to Digital Computer Control

2. Controllers : Definition and Types Definition A controller is a mechanism which seeks to minimize the difference between actual value of a system (process variable) and desired value of the system (set point). A controller is a comparative device . It : Receives an input signal from a measured process variable Compares this value with that of a predetermined control point value (set point) Determines the appropriate amount of output signal required by the final control element to provide corrective action within a control loop. Electronic controller uses electrical signals and digital algorithms to perform its receptive, comparative and corrective functions.

3. Controllers : Definition and Types Working Principles An electronic sensor (thermocouple, RTD or transmitter) installed at the measurement location continuously sends an input signal to the controller. At set intervals the controller compares this signal to a predefined set point. If the input signal deviates from the set point, the controller sends a corrective output signal to the control element. Features of a Controller An electronic controller is best suited for applications where large load changes are encountered and/or fast response change s are required. Electronic Controllers have full auto tuning and PID capabilities, offer available options, including user selectable inputs and ranges , outputs, setback functions, and alarms. E conomical “on/off ” style is also available for simple control applications.

4. Controllers : Definition and Types Uses of Controllers The important uses of the controllers are as follows: Controllers improve the steady state accuracy by decreasing the steady state error. As the steady state accuracy improves, the stability also improves . Controllers also help in reducing the unwanted offsets produced by the system. Controllers can control the maximum overshoot of the system. Controllers can help in reducing the noise signals produced by the system. Controllers can help to speed up the slow response of an over damped system.

5. Controllers : Definition and Types Types of Controllers There are two main types of controllers: Continuous Controllers. b. Discontinuous Controllers. In discontinuous controllers, the manipulated variable changes between discrete values . Depending on how many different states the manipulated variable can assume, a distinction is made between two-position, three position and multi position controllers. Compared to continuous controllers, discontinuous controllers operate on very simple, switching final controlling elements. In continuous controllers is the controlled variable (aka. manipulated variable) can have any value within controller’s output range. In the continuous controller theory, there are three basic modes.

6. Controllers : Definition and Types Types of Controllers Proportional Controller The output (also called the actuating signal) is directly proportional to the error signal . To use a proportional controller in a system, there are two conditions : The deviation should not be large (There should be not be a large deviation between the input and output). The deviation should not be sudden . Mathematical Represenstation Output is directly proportional to error signal → A(t) ∝ e(t) or, A(t)= K p *e(t ) where K p is proportional constant/controller gain.

7. Controllers : Definition and Types Types of Controllers (proportional c ontroller contd.) Advantages Proportional controller helps in reducing the steady state error , thus makes the system more stable. Slow response of the over damped system can be made faster with the help of these controllers . Disadvantages Due to presence of these controllers we get some offsets in the system. Proportional controllers also increases the maximum overshoot of the system.

8. Controllers : Definition and Types Types of Controllers b. Integral Controller T he output (also called the actuating signal) is proportional to the integral of the error signal. Mathematical Representation Output is proportional to the integration of error signal → A(t) ∝ or, A(t)=K i * where K i is integral constant/controller gain.  

9. Controllers : Definition and Types Types of Controllers ( i ntegral c ontroller contd.) Advantages Due to their unique ability they can return the controlled variable back to the exact set point following a disturbance that’s why these are known as reset controllers . Disadvantages It tends to make the system unstable because it responds slowly towards the produced error.

10. Controllers : Definition and Types Types of Controllers c. Derivative Controller T he output (also called the actuating signal) is proportional to the derivation of the error signal . Mathematical Representation Output is proportional to the integration of error signal → A(t) ∝ or, A(t)= K d * where K i is derivational constant/controller gain.  

11. Controllers : Definition and Types Types of Controllers (derivative c ontroller contd.) Advantages The major advantage of derivative controller is that it improves the transient response of the system . Disadvantages It never improves the steady state error . It produces saturation effects and also amplifies the noise signals produced in the system.

12. Controllers : Definition and Types Types of Controllers Combinational Controllers The combination of these modes are used to control particular system such that the process variable is equal to the set point (or as close as can be got it). These three types of controllers can be combined into new controllers: i . Proportional and integral controllers (PI Controller) A(t)=K i * + K p *e(t) ii. Proportional and derivative controllers (PD Controller) A(t)=K d * +K p *e(t) Proportional integral derivative control (PID Controller ) A(t)=K i * + K d * + K p *e(t)  

13. Algorithms used in Controllers PID Controller Tuning The process of setting the optimal gains for P, I and D to get an ideal response from a control system is called tuning. Closed Loop System Ziegler-Nichols method Modified Ziegler-Nichols method Tyreus-Luyben method Damped oscillation method Open Loop System Open loop Ziegler-Nichols method C-H-R method Cohen and Coon method Fertik method Ciancone -Marline method IMC method Min. error criteria (IAE, ISE, ITAE) method

14. Transfer Function and gain of a system Transfer Function A transfer function represents the relationship between the output signal of a control system and the input signal, for all possible input values. If the input is represented by R(s) and the output is represented by C(s), then the transfer function will be : The transfer function of a control system is defined as the ratio of the Laplace transform of the output variable to Laplace transform of the input variable assuming all initial conditions to be zero .

15. Transfer Function and gain of a system (transfer function contd.)

16. Transfer Function and gain of a system (transfer function contd.)

17. Transfer Function and gain of a system Advantages The output can be easily determined for any given input. Complex differential and integral equations are transformed into simple and easy algebraic equations . Disadvantages The key disadvantage of this analysis is that transfer functions can be applied only on linear time invariant systems.

18. Transfer Function and gain of a system Gain In a control loop, the controller gain is the strength of action a controller will take at a particular point below or above the set point. Process Gain Model Parameter. D escribes important aspects of a given process’ dynamic behavior . C an be determined using step test data . Controller Gain T uning parameter. Contributes to the PID controller’s responsiveness to disturbances. Assigning a value requires both specific knowledge of the PID controller and the unique objective for the control loop.