Didactic Unit 0: (0.5h, session 1) Systems science and feedback control in scientific
and engineering applications:
- Examples: energy network control, biotechnology, biomedicine, biology,
automobiles, robotics, process industry, chemistry, civil engineering,...
- Systems Science and feedback control. ¿What for?
- Course scheduling. ¿What do we expect you to learn?
Didactic Unit 1: (4.5h theory) First principles-based modelling of continuous systems.
State space representation.
- Concept of system. Concept of signal.
- What it is a model? Types of models: pilot plant, qualitative, quantitative. Examples.
- Signals in a system. Types. Variables and parameters (invariant vs. time-varying
systems) . Inputs (manipulable and perturbations), outputs, internal.
- What is having dynamical behaviour? Static and dynamic systems. Examples.
- Classes of dynamical systems: linear vs. nonlinear, continuos vs. discrete,
deterministic vs. stochastic, lumped vs. distributed parameters, hybrid continuousdiscrete-event systems.
- Representation of continuous dynamical systems by means of differential equations.
- Elementary models of simple physical de systems using balance equations.
- Concept of state. State space representation.
Didactic Unit 2: (5.5h theory + 2.15h lab) Getting the temporal response of a
continuous system. Simulation. Linearisation.
- What is simulating?
- Basic notions of numerical integration. Approximation using Taylor series. Implicit
and explicit Euler’s method.
- Simulation with MATLAB. Application on a nonlinear state space model.
- Essential characteristics observed in the temporal response of a dynamical system:
Forced/free response
transient/steady state
Stability
- Linear systems and the superposition principle. Observed response.
- Getting approximate linear models by means of linearisation around an equilibrium
point.
- Comparison of response between the linearised model and the original nonlinear
one at different equilibrium points, and for different input signal amplitude.
Didactic Unit 3: (1.5h theory, session 6 + 2.15h lab) Application of simulation to
experimental parameters identification of continuous models:
- What is system identification? How do you formulate the problem?
- Process identification steps.
- parameters identification as an optimisation problem: algorithms based on the
evaluation of a prediction error cost function. Need of model simulation to predict.
- Lab session: Application using MATLAB.
Didactic Unit 4: (6.0h theory) Getting the temporal response of a linear continuous
system. I/O representation. Laplace transform.
- Solution of differential equations by means of Laplace transform. first and second order
basic cases. Basic properties of Laplace transform.
- Input/Output representation. Transfer functions. Firs and second order cases.
- Higher order cases:
Going from state space to I/O representation.
Block diagrams and simplification. Basic cases: series, parallel, feedback loops.
- Getting the temporal response using MATLAB.
Didactic Unit 5: (9.0h theory + 2.15h lab) Analysis of dynamical systems.
- Poles and zeroes.
- Poles and stability of continuous systems.
- Characterisation of the time response and its relationship with the system poles and
zeroes. First and second order systems.
- Effect of zeroes.
- Higher order systems
- Reduced models for higher order systems. Dominant poles.
- Experimental identification by means of the temporal response.
- Lab session: Identification of a d.c. motor.
Didactic Unit 6: (9.0h theory + 2.15h lab) Feedback and feedback control.
- Feedback loops. Positive and negative feedback. Effects on the dynamic behaviour.
- Basic scheme of a feedback control loop. Components. Essential transfer functions:
setpoint, control input, and perturbations to output.
- Effects of feedback control. Analysis using transfer functions:
modification of temporal response
robustness to external perturbations
robustness to variations in loop components
- Control specifications and their mathematical representation.
- Basic control strategies
- On/off control. Example: temperature control using a thermostat.
- Basic control actions. proportional, derivative, integral.
- Experimental tuning of PID controllers.
- Model based tuning of PID controllers for low order processes.
- Lab session: velocity and position control of a d.c.