Elementary review of dynamic systems. Equations of motion. Numerical solution of ODEs. Linearization. Stability. Laplace transforms and inverse Laplace transforms. Block diagrams. Transfer functions. Feedback loops. Poles and zeros. Transient responses. Stability. The Routh‐Hurwitz criterion. Nonminimum phase systems and their transient responses. Steady state responses. Root locus plots. Nyquist plots. Bode plots. Implications for transient responses. Compensators. Lead and lag compensators. PID controllers. Tuning rules. Stabilization using a stable controller: motivation and sample problems. Discrete time systems; their stability. State space. Standard form for an LTI system.
General solution. Controllability and observability. Pole placement. Connections with classical control. Introduction to optimal control. The linear quadratic regulator. Introduction to time‐delayed control. Simulations of nonlinear systems with linearization based controllers. Case studies from the literature as time permits.

Lecture-wise breakup

I. Elementary review of dynamic systems. Equations of motion. Numerical solution of ODEs. Linearization. Stability. (5 lectures)

II. Laplace transforms and inverse Laplace transforms. Block diagrams. Transfer functions. Feedback loops. Poles and zeros. Transient responses. Stability. The Routh‐Hurwitz criterion. Nonminimum phase systems and their transient responses. Steady state responses. (7 lectures)

III. Root locus plots. Nyquist plots. Bode plots. Implications for transient responses. (5 lectures)

IV. Compensators. Lead and lag compensators. PID controllers. Tuning rules. (4 lectures)

V. Stabilization using a stable controller: motivation and sample problems. (3 lectures)

VI. Discrete time systems. Stability. (2 lectures)

VII. State space. Standard form for an LTI system. General solution. Controllability and observability. Pole placement. Connections with classical control. (8 lectures)

VIII. Introduction to optimal control. The linear quadratic regulator. (2 lectures)

IX. Introduction to time‐delayed control. (2 lectures)

X. Simulations of nonlinear systems with linearization based controllers. Case studies from the literature as time permits. (4 lectures)

References:

1. K. Ogata. Modern Control Engineering (current edition). Prentice-Hall India.
2. G. F. Franklin, J. D. Powell, and A. Emami-Naeini. Feedback Control of Dynamic Systems (current edition). Pearson Education.
3. F. Golnaraghi and B. C. Kuo. Automatic Control Systems. Wiley.