Automatic Control
- Introduction: basic concepts of control systems, feedback, components of control systems, characteristics of control systems, stability, tracking, disturbances in systems, noise, insensitivity to model components.
- System display: Laplace transform, modeling systems with transfer functions, block diagrams, simplification rules, Masons law, DC motor model, state space display.
- Time response of linear system: impulse and step response, characteristics of first and second order time response, rise time, settling time, steady state error, overshoot, etc., relationship between time and frequency domain
- Stability analysis: definition of BIBO stability, characteristic polynomials, poles, stability conditions, Routh-Horwitz stability criteria.
- Root Locus: closed loop pole relationship with loop gain, Root Locus graphical method for displaying pole, amplitude and angle rules.
- Root Locus: Root Locus display rules, gain selection, static feedback design, desirable features, relationship between time and frequency domains.
- Root Locus: The effect of adding poles and zeros, controller design with RL, P, PD, Lead and Lag controller design using RL.
- Frequency analysis: Bode response, Bode theorem, relationship between amplitude and phase, cross over frequency, Bode diagram drawing, first and second order systems, unstable systems, higher order systems.
- Frequency analysis: Nyquist diagram, Nyquist drawing using Bode diagram, Cauchy theorem, number of closed loop poles, Nyquist stability criteria.
- Frequency analysis: end point, stability characteristics, poles and zeros on imaginary axis, relationship between Bode and Nyquist diagram, number of closed loop poles, Nyquist diagram for simple to challenging examples.
- Frequency analysis: resonance peak, resonance frequency, bandwidth, phase and gain crossover frequencies, roll-off rate, frequency response of second order systems.
- Dynamic feedback design: basic definitions, stability margin, gain and phase margin, stability margin from Bode diagram, Nichols diagram, M circles, sensitivity and its transfer functions, loop gain and feedback characteristics in Nichols diagram.
- Dynamic compensator design: P controller design based on stability margin, Lead and PD controller design for bandwidth compensation, Lag and PI controller design for steady state compensation in disturbance inputs. Lead-Lag and PID controller design, simulation and tuning techniques,
- Design of feedback controller based on sensitivity: sensitivity function and its complement, optimal complementary sensitivity functions, design of normal controllers, stability issue and interpolation conditions, controller design for unstable systems, design example.