# ME 3501 Dynamical Systems and Control Theory

**Course Description**

This course is an introduction to a unified approach to lumped-element modeling and analysis of mechanical, electrical, hydraulic, and multi-energy domain systems. Topics include: graphical and computer modeling; formulation of state-space equations; analysis of linear systems; determination of time and frequency domain response of such systems to transient and periodic inputs; block diagram representation of dynamic systems using Laplace Transform. Feedback control systems, including PID control, root locus, stability analysis, and computer modeling.

**Learning Outcomes**

Upon the completion of this course, you should be able to:

1. Create mathematical models of simple electrical, mechanical, and hydraulic systems.

2. Use the state-space equations representation of the system and solve for one physical variable (e.g., torque for a gear) as a function of time.

3. Use the block diagram method for dynamic systems and controls analysis.

4. Describe the basic theory behind a linear, feedback control system (e.g., PID).

5. Use Laplace Transforms to solve for the time response of a linear engineering system due to a general input function.

Suggested Textbook

1. Control Systems and Engineering, 7th Edition, Norman S. Nise, Wiley, 2015

2. Modern Control Engineering – OGATA – Prentice Hall (optional)

**Course Content**

1. Introduction to Control Systems (Chapter 1)

System concepts, examples on system modeling

Mathematical models, classification

2. Laplace Transformation (Chapter 2)

Properties of Laplace transformation

Inverse Laplace transformation using partial fraction expansion

Final value theorem

Solution of ODE’s via Laplace transformation

3. Transfer Functions and Block Diagrams (Chapter 2)

4. Modeling of Physical Systems (Chapter 2)

Electrical, mechanical, thermal, & fluid flow problems

Examples on how to interconnect different physical systems

5. Linearization of Nonlinear Systems (Chapter 3)

Concept of equilibrium and operating point,

Taylor series expansion

State space formulation of ODE

6. Response of Linear Models (Chapter 4)

7. Stability of Linear Time Invariant Systems (Chapter 6)

Characteristic equation

s-plane stability regions

Routh’s test

8. Time Domain Analysis of Control Systems (Chapter 4)

Performance specifications in time domain

9. Introduction to Automatic Control System Design in Time Domain

P, PD, PID control system, design according to the performance specifications

10. Frequency response of Linear Time Invariant Systems

Asymptotic Bode Plot

Mathematical models from frequency response data