Automatic Control
- Introduction: Why feedback, conceptual components of feedback systems, physical components of feedback systems, the magic of feedback, the characteristics of feedback systems, stability, tracking, disturbance attenuation, noise rejection, and insensitivity to model uncertainty.
- System Representation: Laplace transform, modeling of the systems with transfer functions, block diagrams, simplifications rules, signal flow graph, Mason rule, permanent magnet DC motor model, state-space representation.
- Linear system time response: impulse and step response, first and second-order time response characteristics, rise time, settling time, steady-state error, overshoot, decay ratio, time, and frequency domain relation.
- Stability analysis: BIBO stability definition, characteristic polynomials, poles, stability condition, Routh - Horwitz stability criteria.
- Root Locus: Closed-loop pole relation to the loop gain, Root locus graphical method of pole representation, magnitude, and angle laws.
- Root Locus: Rules of root locus representation, gain selection, static feedback design, desired characteristics, time, and frequency domain relation.
- Root Locus: The effect of adding poles and zeros, Controller design with RL, P, PD, Lead and Lag Controller design with the use of RL.
- Midterm Exam
- Frequency Analysis: Bode response, Bode theorem, the relation between magnitude and phase, cross over frequency, quick bode diagram plot, first and second-order systems, unstable and non-minimum phase systems, higher-order systems.
- Frequency Analysis: Nyquist diagram, Nyquist plot from bode diagram, conformal map, Cauchy argument principle, Nyquist contour, encirclements, and the number of closed-loop poles, Nyquist stability criteria.
- Frequency Analysis: Ultimate point, stability characteristics, poles and zeros on the imaginary axis, the relation between Bode and Nyquist plot, encirclements, and the number of closed-loop poles, Nyquist plot for simple to challenging examples.
- Frequency Analysis: Motivation, peak resonance, resonant frequency, bandwidth, gain and phase cross-over frequencies, roll-off rate, the frequency response of second-order systems.
- Dynamic feedback design: Basic definitions, stability margins, gain, and phase margin, stability margins from bode diagram, Nichols chart, M circles, sensitivity, and complementary sensitivity transfer functions, loop gain, and feedback characteristics in Nichols chart.
- Dynamic compensator design: P controller design based on stability margin, Lead and PD controller design based for bandwidth compensation, Lag and PI controller design for steady-state compensation on disturbance inputs. Lead-Lag and PID controller design, simulation, and tuning techniques, comprehensive example.
- Sensitivity-based feedback controller design: Motivation, sensitivity function and its complement, desired complementary sensitivity functions, design of casual controllers, stability concern and interpolation condition theorem, controller design for unstable, non-minimum phase systems, design examples.