1 Teaching Innovation - Entrepreneurial - Global The Centre for Technology enabled Teaching & Learning, M G I, India DTEL DTEL (Department for Technology Enhanced Learning)

DEPARTMENT OF MECHANICAL ENGINEERING VI-SEMESTER AUTOMATIC CONTROL 2 CHAPTER NO.3 Time domain Response

CHAPTER 3:- SYLLABUSDTEL. Time domain response analysis 1 Steady state error analysis and error constant 2 PID controller and application 3 3

CHAPTER-3 SPECIFIC OBJECTIVE / COURSE OUTCOMEDTEL Understand the Time domain response analysis. 1 Understand PID controller and application 2 4 The student will be able to:

DTEL 5 LECTURE:- 1 The time response of a control system consists of two parts 1.Transient response - from initial state to the final state – purpose of control systems is to provide a desired response. 2. Steady-state response - the manner in which the system output behaves as t approaches infinity – the error after the transient response has decayed, leaving only the continuous response. Introduction

DTEL 6 LECTURE:- 1 Transient response specification for second order system with step input 1)Delay time: It is time required for the output response to reach fifty percent of final value in the first attempt 2) Rise time: For the under-damped system, it is time required for the output response to rise 0 to 100% in the first attempt 3)Peak time= It is the time required for the output response to reach its peak value 4)Setting time: it is the time required for the final output to settled within the specified tolerance band 5)Peak overshoot: It is the maximum overshoot above 100% output lines Introduction

DTEL 7 Performances of Control Systems Specifications (time domain) Max OS, settling time, rise time, peak time Standard input signals used in design actual signals unknown standard test signals step, ramp, parabola, impulse, etc. sinusoid (study freq. response later) Transient response Steady-state response Relate to locations of poles and zeros LECTURE 1 Control Systems

DTEL 8 First Order System r(s) c(s) e(s) Fig 3.1Test signal is Step function, R(s)=1/s LECTURE :-2 Step Function

DTEL 9. First order system Taking inverse Laplace transform, we have the step response Time Constant : It is referred to as the time constant of the response. In other words, the time constant is the time it takes for the step response to rise to 63% of its final value. Because of this, the time constant is used to measure how fast a system can respond. The time constant has a unit of seconds.. LECTURE :-2 Step Function

DTEL 10.. Second – Order System Second-order systems exhibit a wide range of responses which must be analyzed and described. Whereas for a first- order system, varying a single parameter changes the speed of response, changes in the parameters of a second order system can change the form of the response. For example: a second-order system can display characteristics much like a first- order system or, depending on component values, display damped or pure oscillations for its transient response. T.G.P.C.E.T. LECTURE :-3 Second – Order System

DTEL 11.. (A) For transient response, we have 3 specifications: (a) T r – rise time = (b) T p – peak time = (c) %MP – percentage maximum overshoot = (B) Steady State Response (a) Steady State error LECTURE :-3 Specification

DTEL 12.. Transient Response Analysis 1) Rise time, Tr. Time the response takes to rise from 0 to 100 % LECTURE :-3 Transient Response Analysis

DTEL ) Peak time, Tp - The peak time is the time required for the response to reach the first peak, which is given by ; LECTURE :-3

DTEL ) Percent overshoot, %Mp - The percent overshoot is defined as the amount that the waveform at the peak time overshoots the steady-state value, which is expressed as a percentage of the steady-state value. LECTURE :-3

DTEL 15. 4) Setting time, Ts - The settling time is the time required for the amplitude of the sinusoid to decay to 2% of the steady-state value. To find T s, we must find the time for which c(t) reaches & stays within +2% of the steady state value, c final. The settling time is the time it takes for the amplitude of the decaying sinusoid in c(t) to reach 0.02, or LECTURE :-3

DTEL 16. LECTURE :-4 Problem on unit step response Fig 3.2 Problem on unit step response

DTEL 17. LECTURE :-4 Problem on unit step response Fig 3.3 Problem on unit step response

DTEL 18 LECTURE :-5 18 Simple, easy to use Wide Application: Petrochemical, Pharmaceuticals, Food, Chemical, Aerospace and Semiconductor, etc. Robust: Insensitive to changes to plant parameter and disturbance. Why PID Control Over 90% control loops are PID with two exceptions: 1.On/off control for those with low control requirement loops 2.Advanced control for those difficult systems and with high control quality. PID Control

DTEL 19 Proportional Function The controller output u is proportional to error signal e : is proportional bandwhere P control has steady state error. LECTURE :-5 Proportional Function

DTEL 20 Integral Function Controller output is proportional to error e. Output of I control is constant only e=0, no steady state error. Reduce system stability. I control is always slower than that of P control, Open loop gain is proportional to S 0, increase S 0 reduce system stability. LECTURE :-5 Function

DTEL 21 General rules of Design PID Controller Use D function, if system has large time constant and time delay. Using PD if the system allows steady state error, otherwise, using PID Use PI, if system has small time constant, small disturbance and requires no steady state error. Use P, if system has small time constant, small disturbance and allow steady state error. Use more advanced control scheme, if system has large time constant, large time delay and disturbance. LECTURE :-5 Design PID Controller

DTEL 22 LECTURE :-6 A typical hydraulic system Hydraulic System Fig 3.5 A typical hydraulic system 1 – pump 2 – oil tank 3 – flow control valve 4 – pressure relief valve 5 – hydraulic cylinder 6 – directional control valve 7 – throttle valve

DTEL 23 LECTURE :-6 Hydraulic fluids - tasks They have the following primary tasks: oPower transmission (pressure and motion transmission) oSignal transmission for control Secondary tasks: oLubrication of rotating and translating components to avoid friction and wear oHeat transport, away from the location of heat generation, usually into the reservoir oTransport of particles to the filter oProtection of surfaces from chemical attack, especially corrosion Hydraulic Fluid S

DTEL 24 LECTURE : /2006 I. Hydraulic fluids - requirements Functional oGood lubrication characteristics oViscosity should not depend strongly on temperature and pressure oGood heat conductivity oLow heat expansion coefficient oLarge elasticity modulus Economic oLow price oSlow aging and thermal and chemical stability  long life cycle

DTEL 25 THANK YOU

DTEL References Books: 1.Automatic control system by Farid Golnaraghi. 2.Modern control System Engineering by Katsuhiko Ogata 3.Feedback Control System by R. A. Barapate 4.Automatic control system by Benjamin 26