Automatic Regulation

Degree
B.Eng. in Electronics Engineering
Cod.TypeCourseSem.Theory cr.Prac. cr.Acad. course
13085Obligatory51st sem.3 1.5 2010-2011
Coordinator
José Miguel Espí Huerta

Goals

To introduce the student into the modern control theory based on the matrix description of multivariable systems.


Theory program
Theme 1: Classic Analysis and Design of Control Systems
1.1 Continuous and discrete LTI SISO systems
1.2 Continuous-discrete hybrid control systems. Equivalent discrete system
1.3 Static analysis of feedback systems
1.4 Dynamic analysis of continuous and discrete feedback systems. Absolute and relative stability criterions.
1.5 Classic design of analog and digital compensators
1.5.1 Design based on the frequency response
1.5.2 Digital design based on the frequency response
1.5.3 Analog and digital designs based on the root locus

Theme 2: LTI Systems Description Using State-Equations
2.1 State-equation definition
2.2 Obtaining state-equations of systems. Controllable and observable canonical forms. Simulation diagrams
2.3 Solution to the continuous state-equation. Continuous transition matrix
2.4 Transfer matrices in S
2.5 Solution to the discrete state-equation. Discrete transition matrix
2.6 Transfer matrices in Z
2.7 Calculation of the continuous transition matrix. The Cayley-Hamilton theorem
2.8 Discrete state models of continuous systems

Theme 3: Controllability and Observability
3.1 Definition of controllability
3.2 Modal interpretation
3.3 General criterion of controllability
3.4 Definition of observability
3.5 Modal interpretation
3.6 General criterion of observability
3.7 Controllability, observability and zero-pole cancellation

Theme 4: State-Space Methods for Controllers Design
4.1 State feedback
4.2 Pole-assignment in state feedback
4.2.1 Coefficients identification
4.2.2 Pole assignment general method
4.3 Design of controllers
4.3.1 Case 1: Proportional control
4.3.2 Case 2: Integral control

Theme 5: Observers Design
5.1 Introduction
5.2 Continuous-time full state observers
5.3 Discrete-time full state observers
5.4 Continuous-time reduced state observers
5.5 Discrete-time reduced state observers
5.6 The separation principle

Theme 6: Design of Optimal Control Systems (LQR)
6.1 Introduction. Cost function
6.2 Continuous LQR control
6.2.1 The Hamilton-Jacobi-Bellman condition
6.2.2 Optimal control law
6.2.3 Equations for the LQR design
6.2.4 Performance of the LQR control
6.3 Discrete LQR control
6.3.1 The minimum condition of H-J-B
6.3.2 Optimal control law
6.3.3 Design equations. Discrete Riccati equation
6.3.4 Equivalent discrete cost matrices
6.4 The LQG problem
6.4.1 Design of the optimal Kalman observer
6.4.2 The loop transfer recovery (LTR) method

Practical program
1 Classic methods for designing compensators
2 Systems representation using state-equations and transfer matrices
3 Design of homogeneous control systems
4 Controllers design
5 Observers design
6 Digital control of an inverted pendulum

Bibliography
-Modern Control Theory, W. L. Brogan, Third Edition, Prentice Hall. ISBN 0-13-589763-7.
-Sistemas de Control en Tiempo Discreto, Katsuhiko Ogata. Prentice Hall Hispanoamericana, México 1996. ISBN/ISSN: 968-880-539-4.
-Control System Design Using Matlab, Baram Sanian, Michael Hassul. ISBN 0-13-014557-2.

Evaluation

Both the theory and the laboratory sub-matters will be grade. The final mark will result as a weighted mean of both the theory and the laboratory marks, accordingly to the number of credits of each.
The theory and laboratory marks come from the qualification of their respective exams. The laboratory mark can be maintained until the end of the next course.


Web

http://www.uv.es/~jespi/RA/RA.html