TECHNICAL PROJECT ON“CONTROLLER DESIGN FOR DESIRE

TERMINAL PERFORMANCE SPECIFICATION FOR

HIGHER ORDER SYSTEM”

SUBMITTED TO:- SUBMITTED BY:-

ROHIT GUPTA VIKAS GUPTA

ABSTRACT Proportional-integral-derivative controllers are widely

used in industrial control systems.

The design of PID controllers for plants with under damped step response and provides the means for a systematic adjustment of the controller gain in order to meet transient performance specification.

Since, all the the development of the methodology relies solely on concepts introduced in a frequency-domain based control course.

INTRODUCTION They are used in industrial control system. They provide control signals that are proportional

1. To the error between the reference signal and theactual output (proportional action).

2. To the integral of the error (integral action).3. To the derivative of the error (derivative action)

u(t)= P e(t) + Iʃ e(t) + D de(t)/dt

A transient response or natural response is the response of the system to a change from equilibrium.

The response can be classified into 3 types are:

An underdamped response is one that oscillates within a decaying envelope. The damping ratio is always <1 .

A critically damped response is the response that reaches the steady state value the fastest without being underdamped. The damping ratio =1.

An overdamped response is the response that does not oscillate about the steady state value. The damping ratio is >1.

Transient Response Specifications of a Second Order System

Fig: overdamped response

Fig: critically response

Rise time

Rise time refers to the time required for a signal to change from a specified low value to a specified high value.

Overshoot

Overshoot is when a signal or function exceeds its target. It is often associated with ringing.

Settling time

Settling time is the time elapsed from the application of an ideal instantaneous step input to the time at which the output has entered and remained within a specified error band.

Delay-time

The delay time is the time required for the response to reach half the final value the very first time.

Peak time

The peak time is the time required for the response to reach the first peak of the overshoot

Transient‐Response Specifications

PID CONTROL STRUCTURE The controller is used in a closed loop unity feedback

system according to Fig. 1.

Figure 1: Block scheme of closed loop control system.

The combination of proportional and integral terms is important to increase the speed of the response and also to eliminate the steady state error.

TIME RESPONSE OF THE VARIABLE UNDER PID CONTROLLER

Time responses of the output variable under PID controller 2

Naslin

1.8 Opt. Magnitude

G-Lath.

1.6 Butterw.

Z.-Nichols1

Z.-Nichols2

1.4 C.-Coon

Dir. Synthesis

1.2

Y

1

0.8

0.6

0.4

0.2

0

0 5 10 15 20 25 time

Figure 4: Step responses of closed loop systems variable (y) under PID controller

ZIEGLER-NICHOLS FOR TUNING PID CONTROLLER

MOR is a technique for reducing the computations complexity

of mathematical model in numerical simulation .

The technique is essentially a match of time-moments of the full model's impulse response to those of the reduced model.

Consider an nth order transfer function of the large scale system

G(s) = ( a21 + a22s + …… + a2;m+1sm/ 1 + a12s + a13s2 + …. + a1;n+1sn ;m<n)

MODEL ORDER REDUCTION

BASIC MODEL OF PID CONTROLLER TUNING

Output of the PID CONTROLLER TUNING

No peak overshoot at all.

It is suitable for systems with monotonic step response as well as with under damped step response.

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.

APPLICATIONS It is widely used in industrial control system

to eliminate steady-state error of the response.

It is used in manufacture of plastic gloves, as no peak overshoot at all.

It is used where more no. of parameters are involved.

CONCLUSIONPI and PID controller have been proposed

on the basis of plant step response(monotonic step response).

PID controllers can be designed for plants with under damped step response.

They provide systematic means to adjust the proportional gain in order to have no overshoot on the closed-loop step response.