Introduction#

A trolley is driven via two motors on the horizontal plane (one linear axis and one rotation). A mass is attached to the trolley by a cable of variable length. A third motor drives the hoist system.

This system has three control inputs, one for the $x$, $\theta$, and $z$ motor, each. This is a PWM signal corresponding to the velocity. There are five measured outputs: the $x$, $\theta$, and $z$ position of the trolley as well as the $x$ and $y$ angle (local frame) that measure the sway. You may need to calibrate those measurements to correspond to their physical units, e.g., meters and radians.

Control Objective#

Design an anti-sway controller. The controlled system should be able to quickly follow a reference for the trolley position, while minimizing the mass swing. You can start with a constant cable length and only using the $x$ axis. If time permits, design also a controller that additionally includes the cable length or the $\theta$ axis.

Simulink Template#

A Simulink template contains the necessary real-time interface blocks and some scopes. Make your own copy of this file and use it as a starting point for your experiments. Before starting the first simulation, define the sampling period $h$ as a variable in the workspace of Matlab.