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978-3-8439-2320-0, Reihe Mathematik

Carsten Schäfer Optimization approaches for actuator and sensor placement and its application to model predictive control of dynamical systems

181 Seiten, Dissertation Technische Universität Darmstadt (2015), Softcover, B5

This thesis deals with the vibration reduction of dynamical systems. Vibrations occur in many areas of industry and generate noise or reduce the efficiency of the systems. These vibrations can be superimposed destructively by active application of force and thus vibration reduction can be achieved.

The placement of actuators and sensors and the design of the controller plays an important role. In this thesis, a truss structure and a clamped plate are examples of oscillatory structures. In cooperation with the colleagues of the LOEWE-Centre AdRIA, the models of the two demonstrators were developed and validated.

The optimal placement of actuators and sensors can be considered as mixed-integer nonlinear optimization problem. Controllability and observability measures are used as cost function, which are based on the input and output energy of the system. The controllability and observability gramian form the basis for the definition of the measures. The maximization of these nonlinear cost functions can be formulated as an equivalent semidefinite program (SDP).

Model predictive control (MPC) is used to integrate control and state constraints in the controller design. In each sampling interval, an optimization problem must be solved in order to calculate the control law. For small sampling intervals, this time is not enough in general to solve the optimization problem. Explicit MPC offer the possibility to represent the control law as an affine function of the system state. Thus, only the evaluation of an affine function is required online.

Optimal actuator positions were calculated for both demonstrators and compared with heuristic methods for actuator placement when using an MPC controller.