BIRLA VISHWAKARMA MAHAVIDHYALAYA ELECTRONICS & TELECOMUNICATION DEPARTMENT o – ANKUR BUSA o – KHUSHBOO DESAI UNDER THE GUIDENCE OF PROF. AMIT CHOKSHI Proportional Integral Derivative control CONTROL SYSTEM ENGINEERING

Contents Introduction Characteristics of PID controller Tips for designing PID controller Example Limitations Applications Summary

Introduction PID control is the most common form of feedback control. In process control today, more than 95% of the control loops are of PID type, most loops are actually PI control. PD controllers can these days be found in all areas where control is used.

A PID controller has proportional, integral and derivative terms that can be represented in transfer function form as : where Kp represents the proportional gain, Ki represents the integral gain, and Kd represents the derivative gain, respectively. By tuning these PID controller gains, the controller can provide control action designed for specific process requirements.

 The proportional term drives a change to the output that is proportional to the current error. This proportional term is concerned with the current state of the process variable.  The integral term is proportional to both the magnitude of the error and the duration of the error. It (when added to the proportional term) accelerates the movement of the process 8 towards the set point and often eliminates the residual steady-state error that may occur with a proportional only controller.  The rate of change of the process error is calculated by determining the differential slope of the error over time (i.e., its first derivative with respect to time). This rate of change in the error is multiplied by the derivative gain

The Characteristics of P, I, and D controllers A proportional controller (Kp) will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error. An integral control (Ki) will have the effect of eliminating the steady-state error, but it may make the transient response worse. A derivative control (Kd) will have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response.

CL RESPONSERISE TIMEOVERSHOOTSETTLING TIMES-S ERROR KpDecreaseIncreaseSmall ChangeDecrease KiDecreaseIncrease Eliminate KdSmall ChangeDecrease Small Change

General tips for designing a PID controller When you are designing a PID controller for a given system, follow the steps shown below to obtain a desired response : 1. Obtain an open-loop response and determine what needs to be improved 2. Add a proportional control to improve the rise time 3. Add a derivative control to improve the overshoot 4. Add an integral control to eliminate the steady-state error 5. Adjust each of Kp, Ki, and Kd until you obtain a desired overall response.

Example let's take a look at a PID controller. The closed-loop transfer function of the given system with a PID controller is : After several trial and error runs, the gains Kp=350, Ki=300, and Kd=50 provided the desired response. To confirm, enter the following commands to an m-file and run it in the command window.

You should get the following step response. we have obtained the system with no overshoot, fast rise time, and no steady-state error.

Limitation of PID Control PID controllers are applicable to many control problems, and often perform satisfactorily without any improvements or only coarse tuning, they can perform poorly in some applications, and do not in general provide optimal control. The fundamental difficulty with PID control is that it is a feedback system, with constant parameters, and no direct knowledge of the process, and thus overall performance is reactive and a compromise. While PID control is the best controller in an observer without a model of the process, better performance can be obtained by overly modelling the actor of the process without resorting to an observer. PID controllers, when used alone, can give poor performance when the PID loop gains must be reduced so that the control system does not overshoot, oscillate or hunt about the control set point value. They also have difficulties in the presence of non-linearities, may trade-off regulation versus response time, do not react to changing process behaviour.

Application of PID Controller PID controllers is a control loop feedback mechanism widely used in industrial control systems. PID controllers are used in temperature control. It can be also used in motor drive system. It is used in brushless DC motors.

Summary Thus as PID controller is combination of P + PI + PD controllers and can eliminate many limitations of those controllers. Hence having less limitations compared to other controllers it is widely used.

Thank you.