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# Modern Automatic Control

The first order of business in the analysis of a real world system is the construction of a mathematical model of that system. In this course, we discuss mathematical modeling of systems from mechanical and electrical engineering, as well as from physics and biology. Nonlinear systems are emphasized to acknowledge the critical role that nonlinear phenomena are playing in science and technology. The models presented are the ones that will be used to design controllers. These models are constructed from the control engineering point of view. Two main types of dynamical systems are common in applications: those for which the time variable is discrete and those for which the time variable is continuous. When the time variable is discrete, the dynamics of such systems are usually modeled using difference equations. In the case when the time is continuous, ordinary differential equations are frequently chosen for modeling purposes. Both types of models are considered in the course.

## ECE68000

3

### Learning Objective:

To familiarize students with current trends in dynamical system control while at the same time equipping them with the tools necessary for advanced feedback design. The emphasis will be on design in order to show how control theory fits into practical applications. In particular, models of a robotic manipulator, turbine engine, the hypothalamic-pituitary-thyroid (HPT) axis, and hypothalamic-pituitary-adrenal (HPA) axis will be used as testbeds for the controllers' designs. Another course objective is to show the interdisciplinary character of automatic control. Deeper understanding of the area of automatic control will be promoted to enable the student to read papers from the area technical publications such as the IEEE Control Systems Magazine, IEEE Transactions on Control Systems Technology, and the IEEE Transactions on Automatic Control.

### Description:

The first order of business in the analysis of a real world system is the construction of a mathematical model of that system. In this course, we discuss mathematical modeling of systems from mechanical and electrical engineering, as well as from physics and biology. Nonlinear systems are emphasized to acknowledge the critical role that nonlinear phenomena are playing in science and technology. The models presented are the ones that will be used to design controllers. These models are constructed from the control engineering point of view. Two main types of dynamical systems are common in applications: those for which the time variable is discrete and those for which the time variable is continuous. When the time variable is discrete, the dynamics of such systems are usually modeled using difference equations. In the case when the time is continuous, ordinary differential equations are frequently chosen for modeling purposes. Both types of models are considered in the course.
Course Syllabus

### Topics Covered:

Lyapunov's stability theory and its extensions are used in the analysis of dynamical system models. The objective of the stability analysis is to determine the system behavior without solving the differential, or difference, equations modeling the system. The Lyapunov theory is used in the controller construction for different types of dynamical systems considered in this course. Dynamical system concept; Formulation of the control problem; Modeling---design and simulation models; Analysis of modeling equations. Review of controllability and observability of linear systems. Stability; Lyapunov's first and second methods and their applications in the controller design. Optimal control methods;, linear quadratic regulator, dynamic programming, Pontryagin's minimum principle. Robust feedback control of dynamical systems; controller design using linear matrix inequalities (LMIs). Adaptive control. Model-based predictive control (MPC) design. Model-free controller design. State observers; Combined controller-observer compensators; Fault detection and isolation (FDI) using observers.

### Prerequisites:

• ECE 60200, Lumped System Theory
• Linear algebra, ordinary differential equations, and calculus of several variables. In particular: matrix manipulation, linear spaces, quadratic forms, differentiation of real-valued functions of n variables, gradients, and the chain rule.

### Applied / Theory:

30 / 70

https://engineering.purdue.edu/~zak/ECE680/index.htm

### Web Content:

In addition to the course website, course information and grades will be available via Blackboard. Other information such as lecture notes, homework assignments, solutions, chat room, and message board.

### Homework:

Assignments will be submitted through Blackboard.

None.

### Exams:

There will be two one-hour exams, each weighted 100 points. The final exam will be worth 200 points.

### Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Required--Stanislaw H. Zak, "Systems and Control," Oxford University Press, New York, 2003, ISBN 9780195150117

### Computer Requirements:

ProEd Minimum Requirements. MATLAB, Version 7 or higher.

None.

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