# Control Theory

## Objectives

The student attending these classes with success should understand the following concepts:
- What is a system, how is characterized and what mathematical representations admits;
- Functional scheme of a system;
- Stability and performance;
- Time and complex frequency domain;
- Frequency response; minimum and non-minimum phase.
- Feedback and closed loop stability;
- What is control and their application limits;
additionnaly, the student should know:
- Model a physical process using diffrential equations and convert them to transfer functions; Compute the free and forced response;
- Identify the poles and zeros of the transfer function and estimate the performance/stability from its pole-zero diagram;
- Plot the closed-loop root-locus diagram;
- Plot the Bode and Nyquist diagrams;
- Conclude about the stability of a closed loop system from its open loop Bode and Nyquist diagrams (including gain and phase margins);
- Design a PID controller using the Ziegler-Nichols rules;
- Compute the descritive function of a static non-linearity;
additionally, the student acquires the following non-technical competences:
- Make a report on experimental work; manage time and meet deadlines;
- Collaborative team work; Abstract and formal reasoning;
- Abstract modelling of problems; sub-optimal solutions;

## General characterization

3752

6.0

##### Responsible teacher

Rui Alexandre Nunes Neves da Silva

Weekly - 4

Total - 77

Inglês

### Prerequisites

Although not mandatory, because of the chaining subjects, it is convenient to have successfully performed the previous course on Signal Theory in the previous semester or equivalent in other school.

### Bibliography

B. J. Kuo, Automatic Control Systems, Prentice-Hall

Katsyhiko Ogata, System Dynamics, Prentice-Hall.

#### Other books:

Katsyhiko Ogata, Modern Control Engineering, Prentice-Hall.

Franklin; Powell; Emami-Naeini, Feedback Control of Dynamic Systems, Addison-Wesley

M. J. Roberts, Signals and Systems, McGraw-Hill.

D. K. Lindner, Signals and Systems, McGraw-Hill.

### Teaching method

-Theorectical-practical classes and individual study for knowledge acquisition.

-Practical and laboratory group sessions to test acquired knowledge.

### Evaluation method

The success in the course of Control Theory can be achieved through one of two alternative ways:

1. An average above 9.5 points in 2 tests (~90 min) during the semester (with equal weights) and 3 labworks (also with equal weights) . The lab part contributes with 15% (3 in 20) of the final grade in the continuous evaluation process.

2. A mark above 9.5 points in the final exam. The final grade will be the grade of the exam.

## Subject matter

-Sytems and type of systems. Functional diagram.
-Systems characteristics: initial conditions, linearity, causality.
-Modelling physical systems. Differential equations.

-Time response. Natural and forced response.
-Complex frequency domain. Transfer function.

-Pole-zeros diagram and stability.
-Feedback and root-locus plot.
-Complex domain for sinusoidal signals. Frequency response. Amplitude and phase shift.
-Nyquist plot. Nyquist stability critirium. Gain and phase margins.
-Bode plot. Gain and phase margins on the Bode plot.
-Lead and lag compensators.
-PID controllers. Ziegler-Nichols tuning method.

## Programs

Programs where the course is taught: