Lecture 1: (1/12) Introduction. What is control? control definitions, applications, Laplace Transform and inverse Laplace Transform.
Lecture 2: (1/14) Laplace Transform examples, properties, rational transfer functions, stricly proper transfer functions.
Lecture 3: (1/16) Inverting Laplace Transform, Partial Fraction Expansion, simple poles, complex poles, repeated poles, examples, Final value theorem, DC gain.
Holiday (1/19)
Lecture 4: (1/21) Initial Value Theoerm, solving differential equations using Laplace Transform, Circuit review (KVL,KCL, op amps, and use of Laplace Transform).
Lecture 5: (1/23) Interconnection of systems (isolate input from output), response versus poles and zeros, step response (rise time, overshoot, and settling time), matlab implementation of transfer functions.
Lecture 6: (1/26) State space description, RLC-circuit example, Linear Algebra background. PS 1 due.
Lecture 7: (1/28) Linear Algebra background, characteristic polynomial, eigenvalues and eigenvectors.
Lecture 8: (1/30) RLC-circuit example (state space representation, physical states; current through inductor and voltage across capacitor), state space to transfer function.
Lecture 9: (2/2) transfer function to state space, control canonical form, nonuniqueness of state space realizations, similarity transformations.
Lecture 10: (2/4) similarity transformations, example, (SISO) output feedback control, open loop versus closed loop, gain, motor control example.
Lecture 11: (2/6) sensitivity, stabilizing unstable plants, proportional feeback control, motor control example (2 state system), gain versus dynamic response and pole locations. proportional control. PS 2 due.
Lecture 12: (2/9) stability, characteristic polynomial roots, Routh's test, integral control, proportional integral (PI) control.
Lecture 13: (2/11) proportional integral (PI) control, proportional derivative (PD) control, proportional integral derivative (PID) control, motor control example, unstable plant example.
Lecture 14: (2/13) unstable plant example (P,PD,PI,PID) control, steady state error, system type, general inputs and disturbances.
Lecture 15: (2/18) examples, general inputs and disturbances, pole placement for unity feedback systems.
Lecture 16: (2/20) root locus, simple examples, problem, rules, PS 3 due.
Lecture 17: (2/23) root locus continued, rules and derivations.
Lecture 18: (2/25) root locus summary of rules, examples.
Lecture 19: (2/27) root locus summary, examples, generalization, finding gain, dynamic compensation.
Lecture 20: (3/2) lead and lag compensation, lead compensation motivation and example, circuit implementation.
Lecture 21: (3/4) summary lead compensation, lag compensation motivation, example, and circuit implementation, autopilot design example. PS 4 due.
Lecture 22: (3/6) frequency response, sinusoid response to stable causal linear time invariant systems, first order system frequency response, second order system frequency response, introduction to Bode plots.
Lecture 23: (3/9) review session.
Lecture 24: (3/11) Exam 1.
Lecture 25: (3/13) Review Exam, Bode plots for first and second order systems, Bode plots for general systems.
Lecture 26: (3/16) Review Bode plots, minimum phase condition, determining steady state error and stability from Bode plots, Nyquist stability criterion introduction.
Lecture 27: (3/18) Nyquist criterion, conformal maps and encirclement of origin, open loop transfer function, encirclement of -1, rules for determining stability of closed loop transfer function, N=Z+P.
Lecture 28: (3/20) Nyquist stability criterion review, obtaining Nyquist plot from Bode plot, range of K where closed loop system is stable, examples. PS 5 due.
Lecture 29: (3/30) Nyquist stability criterion review, examples, poles on the imaginary axis, unstable systems.
Lecture 30: (4/1) Nyquist plot examples, unstable systems, gain and phase margins, relationship between phase margin and transient response, determining gain and phase margins from Nyquist and Bode plots.
Lecture 31: (4/3) Relationship between phase margin and transient response, gain and phase margins for more complex systems and for systems with RHP poles. control system design for open loop minimum phase systems. PS 6 due.
Lecture 32: (4/6) Bandwidth, compensators (frequency system design), PD compensators, example, Lead compensation, design (gain, pole and zero location).
Lecture 33: (4/8) Lead compensation example, design parameters (crossover frequency, PM, and low frequency gain), procedure, examples.
Lecture 34: (4/13) Lead compensation review and example, PI compensator, lag compensator.
Lecture 35: (4/15) Lag compensation procedure, example, PID compensator. PS 7 due.
Lecture 36: (4/17) Review compensation design procedures, sensitivity, sensitivity functions, stability robustness.
Lecture 37: (4/20) Sensitivity functions, bounding PM and gain margins, robust models of plant, introduction to state space control system design.
Lecture 38: (4/22) Exam 2.
Lecture 39: (4/24) State space review, control canonical form, state space dynamic response, example, similarity transformation review.
Lecture 40: (4/27) state feedback for control canonical form, controllable systems, controllability matrix, transformation to control canonical form.
Lecture 41: (4/29) controllability matrix, transformation to control canonical form, state feedback for controllable systems, example, estimator design, observer canonical form.
Lecture 42: (5/1) closed loop estimator design, example, observability, estimator design for observer canonical form, transformation to observer canonical form, state feedback for observable systems. PS 8 due.
Lecture 43: (5/4) combined control and estimation, compensator design, separation principle, example, physical meaning of controllable and observable, reference inputs.