The main objective of this course is that the students learn the basics concepts to perform computer control of discrete-time systems by two different methods: classic control, and state space. To achieve these objectives, the student must acquire a range of skills and abilities.
At the end of the course, the student will be able to:
1. Obtain the z transform for a given discrete-time sequence and the time sequence corresponding to a function in the z domain. Solve the difference equation of an invariant linear system, obtaining its transfer function in z and the time response.
2. 2. Choose a suitable sampling period. Obtain the transfer function of a continuous system with a zero-order hold and a sampler. Obtain the transfer function of a closed loop digital control system. Determining the output error for different inputs.
3. Determine the stability of an open loop discrete-time system with unitary feedback. Get the location of the roots of a discrete system, and study the system response by the analysis of the root locus.
4. Discretize a continuous controller. Design an adequate controller (P, PD,PI, PID) using the root locus method. Design a discrete regulator by direct synthesis.
5. Get the state space model for a system defined by differential equations. Obtain the transfer function of a discrete-time system from the state space representation. Get a linearized model of a nonlinear system.
6. Get the solution of the state equation for a continuous linear model. Get the discrete-time model from the model solution of the continuous-time representation (transition matrix). Get the solution of the state equation for a discrete-time system. Obtain different representations of a system in the state space using transformation matrices.
7. Determine the controllability (state and output) and the observability of a system.
8. Design control systems in the state space using the pole positioning method (state feedback matrix).
9. Design a full-order observer for a state space system and study its effects. Study the dynamics of the combined system with a full-order observer and a state feedback matrix. Design a minimum-order observer.
In terms of general skills, we will work in different aspects:
a. General overview of the control problem for lineal systems.
b. Ability to design controllers for linear dynamic systems, as well as to analyse the results. In particular, the lab sessions and the seminars will be helpful in this aspect.
c. Ability to work cooperatively in teams, being critical and respectful with the other members of the group.
d. Recognition of the need for continuous learning. Ability to obtain and apply the information required by accessing to the related technical literature of the area in both Spanish and English.
e. Ability to communicate effectively both orally, written, or graphic in both Spanish and English (exercises, debates, labs, etc.).