# Virtual Control Lab

Supporting the lectures, this section will be extended step-by-step. The virtual experiments are provided in order to render topics of automatic control more tangible to students.

## General Remarks for Operation

The following experiments are Java applets. They can be run on any computer that has the Java runtime environment, version 6, update 32 and higher, installed.

Feel free to download the individual modules as .jar file and run them. Remember that the Java Runtime needs to be installed. All modules were developed based on Easy Java Simulation. Students are also invited to have a look at the source code and the underlying algorithm of the experiments.

A) Damped Single-Mass Oscillator

This model uses a damped single-mass oscillator to visualize a number of important control engineering terms. Amongst others, parameter changes have a direct effect on the system properties that can be observed. The goal is to make the relationships between the functional diagram, impulse and step response as well as the pole-/zero plot more tangible.

B) Frequency Response of the Damped Single-Mass Oscillator

This experiment is designed to demonstrate the meaning of the frequency response. For this, plots of the Bode diagram, the Nyquist plot, as well as the pole-/zero diagram of a damped single-mass oscillator are available. When adjusting the parameters, amplitude and phase response change, as does the Nyquist plot. Thereby, the effects of the single parameters on the system become clear. In addition, the result of a harmonic input signal with the excitation frequency “omega” on the system output – the deflection of the mass – is shown in a time response plot.

C) Damped Single-Mass Oscillator with Linear Actuator for Position Control

A single-mass oscillator with a linear actuator for position control is shown. For control, P-, I-, and D- parameters can be enabled and adjusted. Finally, the system behavior can be examined in the presence of disturbances. In the case without controller, the actor force can be set manually.

D) Controller Setting using the Bode Diagram

In this experiment, the stability criteria based on the simplified Nyquist criterion can be understood with the help of a Bode diagram. As plant model, a first-order lag element with delay, called PT1Tt , is used. The controller is of PI-type. Both the plant and controller parameters can be varied within certain limits. The effects of the parameter changes on the amplitude and phase responses are immediately shown. For controller setting and stability test, the frequency ωπ needs to be determined manually. The main intention of this experiment is to help understanding the procedures performed when setting a controller based on the Bode diagram.

E) Inverse Pendulum

This applet visualizes an inverted pendulum, which is also one of the exhibits physically existing in the IRT laboratory. The system consists of a DC servo motor that drives a linear guide on which the pendulum, mass m = 1.5 kilogram, length L = 1 meter is mounted. The bearing used to mount the pendulum has a friction constant of B = 0.005 Nm*sec/rad. The full traveling distance is limited to 2.7 meters by means of two end switches. The goal of the control task is to keep the pendulum upright using two PD controllers.

F) Bode Diagram versus Nyquist Plot

In this experiment, the Bode diagram and the Nyquist plot are compared face-to-face. This is with the help of the frequency responses of a controller GR, a plant GS and their series connection GR* GS.

G) Convolution Integral

The experiment involving the convolution integral points out the use of a calculation rule that enables to determine the output signal y(t) that results from an arbitrary input signal u(t). The calculation can be performed when the unit impulse response g(t) is known. The basic idea is to approximate the input signal using a series of impulses. The output signal then results as the sum of the system’s responses to these impulses.