PendCon

Educational Topics

In a second course on control systems design, more sophisticated controllers than the PID con-troller are introduced. These are normally needed if the plant has more then one pole with a nonnegative real part. Typical examples for such plants are the rotary pendulum or the double pendulum. Both are ideally suited to teach advanced methods.

Accuracy of the simulation model. If a controller has to be designed, normally a model of the plant is built and one starts with a relativel simple synthesis method. For example, the rotary pendulum can be successfully stabilized by pole placement controller in combination with two differentiators. It will be observed that real system has a limit cycle. If asked, the students often have no idea where this oscillation comes. Switching on and off the Coulomb friction in the mathematical model shows that this kind of friction is the reason and the students learn that a carefully made simulation model is really a powerful tool for design and analysis of the closed-loop system.

In some situations, the simulation model is stable whereas the real hardware is not. In such a situation, the motor switches with a high frequency between its minimum and maximum torque and this sounds rather dramatically. There is no obvious explanation for this effect and it turns out that high-frequency resonance in the palnt is the reason. If the plant is suitably accom-plished, everything can be explained.

Iterative design method. Normally, controller design is an iterative procedure which is done in several steps. If the relatively simple controller of step one does not give satisfactory results, a redesign is necessary. In some situations, it is sufficient to adapt some parameters by trial and error and in other cases, a redesign using a more sophisticated method is required. These methods oftten require the definition of weights or even of a weighting scheme. They offer a lot of freedom in the specification of controller, but for the students it is difficult to use this freedom successfuly. In the documentation of the experiements, the students are guided very carefully through this design process.

Adding dynamics to the plant. For the rotary pendulum and the double pendulum, stabiliza-tion of the pendulum in the inverted position is possible by pole placement in combination with two differentiators as observer. More advenced methods are only needed when additional per-formance requirements are posed. This changes if the plant is changed by additional mechani-cal or electrical devices. Then, even the pure stabilization problem can require advanced meth-ods and this shows the students very convincingly that such methods are actually necesary.