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Sysquake Pro – Table of Contents

Sysquake – Table of Contents

Sysquake for LaTeX – Table of Contents

relay.sq

Relay controller

A relay with hysteresis is used as a controller. The hysteresis prevents the system to oscillate at high frequency.

First contact

A second-order system is controlled by relay with hysteresis. A null set-point is assumed. The left figure shows the time response (starting with null initial conditions and the relay in the high level); the right figure shows the phase plane. In both figures, green lines represent the value of the relay hysteresis, which you can increase or decrease interactively. Increase the hysteresis and observe how the oscillation frequency grows, until the system output is not large enough to reach the hysteresis value; then the relay is not triggered and the system does not oscillate.

Figures

Output

The system output is displayed in black, and the hysteresis level of the relay as green horizontal lines. The hysteresis level can be manipulated.

Input

The system input (output of the relay with the opposite sign) is displayed in black.

Phase Plane

The system output is displayed in black in the phase plane; the horizontal axis is the output, and the vertical axis its derivative. The hysteresis level is displayed as green lines and can be manipulated.

Nyquist

The Nyquist diagram of the system is displayed in black, and -1/N(a) in red, where N(a) is the descriptive function as a function of the amplitude a. For a relay with hysteresis, -1/N(a) is a horizontal line. The intersection of the Nyquist diagram with -1/N(a) gives an approximation of the limit cycle. The line -1/N(a) can be manipulated.

Settings

System

The system can be edited in a dialog box. It is given by the numerator and denominator of a continuous-time transfer function.

Hysteresis

The hysteresis level can be edited in a dialog box.