Control Theory


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





Responsible teacher

Rui Alexandre Nunes Neves da Silva


Weekly - 4

Total - 77

Teaching language



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.


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 approval in the Control Theory UC presents the previous requirement to obtain frequency in the practical component. Obtaining the frequency is conditioned to an average of 9.5 values (in 20) in the evaluation of 3 laboratory works.

The evaluation of the theoretical component is obtained through:

1. The average of the results of two tests performed during the semester; OR

2. The result of an exam in an appeal period (or special period).

For 1. and 2. there is a minimum score of 9.5 values in 20.

The final result of the evaluation will be calculated by the formula:

FR = 25% (Practical Comp) + 75% (Theoretical Comp)

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.