Matlab Apps

We offer 4 Matlab Apps on the topics of the Nyquist Criterion, Robustness and Stability, Loopshaping, and Controllability and Observability. The relevant skills are taught in the lecture "Einführung in die Regelungstechnik".

The IST Matlab Apps were delevoped at the Institute for Systems Theory and Automatic Control of the University of Stuttgart and accompany the lecture "Einführung in die Regelungstechnik". The students may use them to apply the material from the lecture on randomly generated exercises in order to practice newly learnt concepts and deepen their understanding. There is an English and a German version of all Matlab apps. For more information on the Matlab apps and their underlying concepts, we refer the reader to a paper with the title "Facilitating learning progress in a first control course via Matlab Apps" that we submitted to IFAC World Congress 2020.

In the app on the Nyquist Criterion, the stability of the closed loop is analyzed using the Nyquist stability criterion. A Nyquist plot of the open loop is given and the encirclements of the critical point (-1,0) and finally, the stability of the closed loop are to be determined.

In the app on Robustness and Stability, robustness margins are to be determined from the open loop ("Easy"). Furthermore, at higher difficulty levels "Medium" and "Advanced" the stabilization of the closed loop can be tested with a P-controller via the locus of the open loop or the Bode diagram of the open loop.

The Loopshaping App is organized as a tutorial where a P-, PI-, P-controller with a lead-element, and a PI-controller with a lead-element are to be designed one after another. Afterwards, the students can design a controller for a CD player. All controllers for which the closed-loop has no steady-state error to a unit-step and a crossover frequency of at least 5000rad/s can be entered in the highscore list where the evaluation criterion is a large robustness, i.e. a large phase and gain margin. The Loopshaping App also generates random tasks or even allows the students to enter their own control systems and control them using loopshaping.

In the app on Controllabilty and Observability, the controllabilty or observability matrix is to be calculated in order to determine whether a  given system is controllable or observable ("Easy"). Besides, the poles of the closed loop system or the error dynamics of the observer are to be calculated ("Medium"). Finally, a system and desired poles are given. The task, here, is to design a suitable controller or observer ("Difficult").

Creative Commons License The IST Nyquist Matlab App, the IST Robustness Matlab App, the IST Loopshaping Matlab App as well as the Controllability and Observability Matlab App by the Institute for Systems Theory and Control is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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