This experiment investigates a digital control scheme using a Linear Quadratic Regulator (LQR) to control a rotary flexible link. The flexible link is a thin steel ruler approximately 20 inches long with a DC motor and a light sensor mounted at one end and a light source mounted on the other end The DC motor allows for rotational motion of the flexible link. The light sensor measures the amount of the tip deflection.

In this experiment, the DC motor end of the flexible link is required to track a desired trajectory, either a step or a sinusoidal reference. An experimental investigation easily reveals that the flexible link tip deflection with a position controller that neglects the flexible link dynamics is quite large. In comparison, a position controller that accounts for the flexible link dynamics significantly reduces the flexible link tip deflection.

The control panel on this page allows 5 LQR control gains for the flexible link system to be manipulated. It essentially consists of a set of PID control gains for the base dynamics and a set of PD control gains for the flexible link tip dynamics.

A switch is provided to change the reference signal from tracking a sinusoidal base trajectory to a step reference (by default, the switch off-light color is the step reference).

Finally, a control switch is provided to change the control design to either include the tip dynamics or to disregard the tip dynamics (default switch off-light color refers to the exclusion of the tip dynamics from the control).