Optimal actuator and sensor placement in flexible structures using closed-loop criteria

A closed-loop optimal location selection method for actuators and sensors in flexible structures is developed. The introduced technique simultaneously designs a computationally simple H ∞ controller and optimizes the location with a gradient-based unconstrained minimization. The H ∞ controller is a modified version of a normalized coprime controller and obtained by solving control and filter algrebraic Riccati equations (CARE and FARE) approximately. Different types of weights (disturbance input, performance output, sensor noise inputs, etc.) are incorporated to the generalized plant. Hence, the approximate ARE solutions take into consideration the signal weightings in the system. Since an iterative gradient search algorithm is used, the partial derivatives of the approximate AREs with respect to the design parameters are taken. Developed method is detailed and illustrated by a Euler–Bernoulli beam example.