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Modern Control Systems (MCS)

Modern Control Systems (MCS). Lecture-1 Introduction to the Subject & Review of classical control theory. Dr. Imtiaz Hussain Assistant Professor email: imtiaz.hussain@faculty.muet.edu.pk URL : http://imtiazhussainkalwar.weebly.com/. Lecture Outline. Introduction to the subject

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Modern Control Systems (MCS)

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  1. Modern Control Systems (MCS) Lecture-1 Introduction to the Subject & Review of classical control theory Dr. Imtiaz Hussain Assistant Professor email: imtiaz.hussain@faculty.muet.edu.pk URL :http://imtiazhussainkalwar.weebly.com/

  2. Lecture Outline • Introduction to the subject • Review of Classical Control Theory • Transfer Function • Poles & Zeros • Stability • S-plane • Introduction to Root Locus

  3. Course Outline (MCS)

  4. Course Outline (MCS)

  5. Review of Classical Control Theory

  6. 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)

  7. 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

  8. 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’.

  9. 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

  10. 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

  11. Root Locus

  12. 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?

  13. 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

  14. Introduction • The open loop stability does not depend upon gain K. • Whereas, the location of closed loop poles vary with the variation in gain.

  15. Introduction • Location of closed loop Pole for different values of K (remember K>0).

  16. How to Sketch root locus? • One way is to compute the roots of the characteristic equation for all possible values of K.

  17. 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.

  18. To download this lecture visit http://imtiazhussainkalwar.weebly.com/ End of Lectures-1

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