Control Engineering

At the end of this course, the students should be able to: 1. develop the mathematical model of the physical systems; 2. analyse the response of the closed and open loop systems; 3. analyse the stability of the closed and open loop systems; 4. design the various kinds of compensator; 5. explain alternate representations of dynamic systems (time domain, frequency domain, state space); 6. define and explain feedback and feed-forward control architecture and discuss the importance of performance, robustness and stability in control design; 7. interpret and apply block diagram representations of control systems and design PID controllers based on empirical tuning rules; 8. compute stability of linear systems using the Routh array test and use this to generate control design constraints; 9. employ Evans root locus techniques in control design for real world systems; 10. compute gain and phase margins from Bode diagrams and Nyquist plots and understand their implications in terms of robust stability; 11. design Lead-Lag compensators based on frequency data for an open-loop linear system; 12. analyse the stability of systems by root locus and frequency response methods; 13. draw Bode diagrams, root locus graphs and Nyquist plots for the analysis of control systems solve numerical problems on control systems; and 14. utilise MATLAB/Simulink to analyse open and closed loop performance and design linear feedback controllers.

Introduction to control system: Concept of feedback and Automatic control, Effects of feedback, Objectives of control system, Definition of linear and nonlinear systems, Elementary concepts of sensitivity and robustness. Types of control systems, Servomechanisms and regulators, examples of feedback control systems. Transfer function concept. Pole and Zeroes of a transfer function. Properties of Transfer function. Mathematical modelling of dynamic systems: Translational systems, Rotational systems, Mechanical coupling, Liquid level systems, Electrical analogy of Spring– MassDashpot system. Block diagram representation of control systems. Block diagram algebra. Signal flow graph. Mason’s gain formula. Control system components: Potentiometer, Synchros, Resolvers, Position encoders. DC and AC tachogenerators. Actuators. Block diagram level description of feedback control systems for position control, speed control of DC motors, temperature control, liquid level control, voltage control of an Alternator. Time domain analysis: Time domain analysis of a standard second order closed loop system. Concept of undamped natural frequency, damping, overshoot, rise time and settling time. Dependence of time domain performance parameters on natural frequency and damping ratio. Step and Impulse response of first and second order systems. Effects of Pole and Zeros on transient response. Stability by pole location. Routh Hurwitz criteria and applications. Error Analysis: Steady state errors in control systems due to step, ramp and parabolic inputs. Concepts of system types and error constants. Stability Analysis: Root locus techniques, construction of Root Loci for simple systems. Effects of gain on the movement of Pole and Zeros. Frequency domain analysis of linear system: Bode plots, Polar plots, Nichol’s chart, Concept of resonance frequency of peak magnification. Nyquist criteria, measure of relative stability, phase and gain margin. Determination of margins in Bode plot. Nichol’s chart. circle and Contours in Nichols chart. Control System performance measures: Improvement of system performance through compensation. Lead, Lag and Lea lag compensation, PI, PD and PID control.