Modern Control Systems (MCS). Lecture-1 Introduction to the Subject & Review of classical control theory. Dr. Imtiaz Hussain Assistant Professor email: firstname.lastname@example.org URL : http://imtiazhussainkalwar.weebly.com/. Lecture Outline. Introduction to the subject
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Modern Control Systems (MCS) Lecture-1 Introduction to the Subject & Review of classical control theory Dr. Imtiaz Hussain Assistant Professor email: email@example.com URL :http://imtiazhussainkalwar.weebly.com/
Lecture Outline • Introduction to the subject • Review of Classical Control Theory • Transfer Function • Poles & Zeros • Stability • S-plane • Introduction to Root Locus
Transfer Function • The transfer function G(S) of the plant is ratio of Laplace transform of output to the Laplace transform of input considering initial conditions to zero. G(S) Y(S) U(S)
Transfer Function • Transfer function helps us to check • The stability of the system • Time domain and frequency domain characteristics of the system • Response of the system for any given input
Stability of Control System • Roots of denominator polynomial of a transfer function are called ‘poles’. • And the roots of numerator polynomial of a transfer function are called ‘zeros’.
Stability of Control Systems • The poles and zeros of the system are plotted in s-plane to check the stability of the system. LHP RHP s-plane
Stability of Control Systems • If all the poles of the system lie in left half plane the system is said to be Stable. • If any of the poles lie in right half plane the system is said to be unstable. • If pole(s) lie on imaginary axis the system is said to be marginally stable. LHP RHP • Absolute stability does not depend on location of zeros of the transfer function s-plane
What is Root Locus? • The root locus is the path of the roots of the characteristic equation traced out in the s-plane as a system parameter varies from zero to infinity. • Why we need to trace the root locus?
Introduction • Consider a unity feedback control system shown below. • The open loop transfer function G(s) of the system is • And the closed transfer function is
Introduction • The open loop stability does not depend upon gain K. • Whereas, the location of closed loop poles vary with the variation in gain.
Introduction • Location of closed loop Pole for different values of K (remember K>0).
How to Sketch root locus? • One way is to compute the roots of the characteristic equation for all possible values of K.
How to Sketch root locus? • Computing the roots for all values of K might be tedious for higher order systems. • Therefore we need a proper way to trace the root locus.
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