#### Course Details

Subject {L-T-P / C} : EE3302 : Advanced Control Systems {3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Susovon Samanta

#### Syllabus

State Space Analysis: State space modeling of different dynamical systems, Conversion of transfer functions to various canonical representation, Linearization of non-linear system, Solving the state space equations, Eigenvalues and Eigenvectors, Different methods of calculations the state transition matrix, Controllability and Observability, state feedback control, pole placement through state feedback, State feedback with integral control, Observer design Digital Control: Introduction to discrete time systems, Sample and Hold, Z-transform, State variable analysis of digital control systems Optimal Control: Principal of optimality, Continuous time LQ control, Infinite-Horizon Control, Linear Quadratic Regulator Lyapunov stability analysis: Basic concepts, stability theorems, Lyapunov functions for LTI systems Nonlinear Control System Characteristics of nonlinear systems, common nonlinearities, phase plane, describing function

#### Course Objectives

1. The objectives of this subject are to
1. Consolidate fundamental knowledge of state space and state feedback
2. How to get the transient response of a system represented in state space form
3. How to design using pole placement technique, state observers
4. Study the stability of Non Linear and Linear systems
5. Equip the students with the basic knowledge of discretization, canonical forms for digital control systems, design the controller and observer for digital control systems
6. Make students understand the optimal control problems and their types, liner regulator and tracking systems

#### Course Outcomes

At the end of the course, students will be able to
1. Construct the state space model for the given linear and nonlinear dynamical systems and apply linearization techniques when appropriate
2. Solve the state space dynamical systems to get the transient response with different inputs.
3. Define and explain the basic properties of linear systems such as controllability, observability.
4. Design pole placement controller and/or observer for the given system to achieve desired specifications, design the full order and reduced order observer
5. Check the stability of the dynamical systems using Lyapunov method
6. Understand mathematical models of linear discrete-time control systems using transfer functions and state-space models
7. Design controllers and observers for linear discrete-time control systems so that their performance meet specified design criteria
8. Identify various optimal control problems with performance measure with minimum time, minimum fuel, minimum energy, terminal cost and general problems.
9. Derive linear quadratic optimal controllers for scalar systems, and evaluate how design parameters influence the closed-loop system properties
10. Study the nonlinear system behaviour by phase plane and describing function methods