PendCon

Educational Topics

The main educational topics of the individual experiments are:

Rate Control for a DC Motor and Position Control for a DC Motor: These experiments are mainly designed to teach the most basic principles of control engineering such as: Dynamics of very simple plants of type 0 or type 1, the idea of feedback, tracking and disturbance rejection, P, PD and PI control.

Position Control for a Pendulum: This experiment is ideally suited to understan stability, nonlinearity, equilibrium points and linearization. Since the (linearized) hanging pendulum is a weakly damped second order system, frequency response and resonance can nicely be demonstrated. For the unstable inverted pendulum is, it will be shown that feedback can be used to stabilize an unstable system

Altitude Control for a Helicopter: This is an example for a cascaded closed-loop system. The task of the inner loop is to control the angular velocity of the rotor whereas the controller of the outer loop has to track an altitude command.

Position Control for Two Masse Coupled by a Spring: This experiment can be used to get a deeper understanding of poles and zeros and of frequency response for a plant of higher order which has oscillatory behavior. Using a frequency generator, the role of a complex conjugate pair of zeros can impressively be shown. Controller design becomes much harder for this plant and satisfactory results can only be achieved if the controller concept will be extended.

Level Control for a Three-Tank-System: If the three-tank-system is operated with only one or two tanks, it is a process control equivalent to the dc motor experiment and also very well suited to teach the fundamentals of control engineering. Another important topic of this experiment is linearization and the subsequent analysis of the linearized plant. Depending on the selected configuration, the plant can be of type 0 or 1. If all three tanks are active, the plant is a nice example where controller design can successfully be done by applying methods based on the Nyquist stability criterion.

Temperature Control for a Thin Rod: The temperature in the rod is governed by the heat equation and consequently, this is an example where the transfer function is non-rational. It will be shown that a suitable finite element approximation leads to a series combination of a few PT1 systems and controller design can be carried out by using methods which are based on the Nyquist stability criterion.

Rotary Pendulum Basic: In this experiment, a thin rod has to be balanced on the tip of a rotating horizontal bar. This task cannot be solved adequately by applying PID control and motivates to introduce state space methods. The simplest one is to design a controller by pole placement and to obtain the rates by the application of differentiators. In a somewhat more sophisticated approach, an observer such as the Luenberger observer is used to get the unmeasured states.