Comparison of linear-quadratic and controllability criteria for actuator placement on a beam

For control of a distributed parameter system, the performance of the controlled system is known to be dependent on the placement of the control actuator, and thus actuator location can be viewed as an additional variable in the controller design. The most common criterion in the engineering literature is to maximize a measure of the controllability. However, as shown here, this approach yields predictions that depend on the order of the model used for the calculations. Furthermore, minimizing the linear-quadratic cost is a common objective in controller design. It is reasonable then to choose the actuator location, as well as the controller itself, to minimize the linear-quadratic cost. In this paper, the performance of a controlled beam with the actuator chosen using these different criteria is examined. The effect of different weights in the cost function on the optimal actuator location is also examined. The control signal is calculated for a number of a different cases. It appears that optimal location of the actuator can improve performance without a corresponding increase in control effort, although possible saturation of control signals may be a concern in some applications.