Discrete Control - 05

Question 1

What are the basic stages in control design?

Answer 1

1. Modelling of the plant (optional)
2. Design and modelling of the controller
3. Verification of the controller: Are the specifications met? This can be investigated for the closed-loop system or
   the controller only.
4. System is not verified: Back to step 2. Otherwise: Implementation the control, e.g., on a programmable logic controller
   (PLC).
5. Validation of the controller: Are the requirements met for the real plant?

Question 2

What is the difference between heuristic and systematic control design?

Answer 2

Heuristic Control Design: Heuristic refers to the art of achieving good solutions with limited knowledge and time based on experience.
* All discrete controllers in the lecture and the exercises have been designed heuristically so far.
* Heuristic control design requires engineering ingenuity.
* Heuristic controllers are not designed systematically → their verification is important before deployment.
Systematic Control Design: The controller is automatically obtained in a systematic control design when the model
of the plant is known, and the intended behavior is specified. Both aspects are often not provided!

Advantages over heuristic: Guaranteed to find a controller that meet the specification if such a controller exists,, can be found automatically if one has a model of the plant, the control laws are typically simples compared to heuristic controllers. Disadvantages: For large plants modeling is too hard, requires state knowledge.

Question 3

What are the advantages of Petri nets compared to non-deterministic automata for control design?

Answer 3

• More compact models of the plant, especially in the presence of concurrent processes.
• More compact specification
  – Forbidden transitions in Petri nets often result in the cancelling of many more transitions in reachability
  graphs.
  – The specification of forbidden markings can be simplified by the don’t care symbol.
• The more compact modelling of Petri nets results in a reduced modelling the effort, such that a systematic control
  design is more often useful compared to non-deterministic automata.

Question 4

If the state is unknown what is a possible solution?

Answer 4

Design a state observer and combine it with the static controller, resulting in a dynamic one.