Integrated Optimum Design of Structure-control Combined System by Using Closed Loop System Redesign Based on Feedback Control

This paper aims at proposing an integrated optimum design method of the structure-control combined system by using closed loop system redesign based on feedback control. The proposed method is constructed from two steps: in the rst step, output feedback control system is designed for an initial structure in order to realize the desired closed loop system's characteristics; and in the second step, both structure and its control system are simultaneously optimized to minimize the objective function under the closed loop system's characteristics constraint. Two numerical examples are shown in order to demonstrate the availability of the proposed method. One example is the design of a cantilever beammodel, the other is the design of a exible rotor supported by active magnetic bearings (AMB). Not only structural con guration but also control gain for structural vibration suppression are successfully optimized. INTRODUCTION One of the main di culties encountered in the optimum design process of the mechanical structures equipped with structural vibration control system, such as large space structures, exible robot manipulators, exible rotors and so on, is the strong interaction between structure and its control system. In such structures, the structural dynamic behavior and the control performance depend on both structural con guration and control law (control gain, sensors and actuators locations, etc.). As far as applying the traditional sequential optimum design method, in which the control system is designed after the structure has been designed, above di culties will not be able to avoided. One of the attractive optimum design method for such structures is structure-control integrated optimum design in which both structure and its control system are designed simultaneously [1]-[8]. An integrated optimum design method of the structure-control combined system by using closed loop system redesign based on feedback control is proposed in this paper. Fundamental idea of the redesign had been proposed by Prof. R. E. Skelton of Purdue University (Currently in Univ. of California San Diego, USA), and several practical procedures and illustrative numerical examples had been presented by his research group [9]-[12]. In this paper, the idea of the redesign is incorporated into the optimization process. In the following sections, the design procedure of the proposed method is shown. Then, two numerical examples are shown in order to demonstrate the availability of the proposed method. CLOSED LOOP SYSTEM REDESIGN Design Procedure The proposed method is constructed from two steps. FIGURE 1 shows the block diagram of the design procedure. In the rst step, output feedback control system is designed for the initial structure in order to realize the desired closed loop system's characteristics. The closed loop pole assignment of the lower order model which is constructed by dominant structural vibration modes of the initial structure is taken as the closed loop system's characteristics. The closed loop pole assignment is selected in order to satisfy the design requirement about the dynamic characteristics of the closed loop system. In the second step, both structure and its control system are simultaneously optimized to minimize the objective function under the pole assignment constraint by using numerically iterative optimization process. In this step, modi ed feedback control gain is obtained by subtracting the equivalent feedback gain corresponding to the structural modi cation from the initial feedback gain which is decided in the rst step. That is the pole assignment constraint. According to the proposed method, the closed loop pole assignment of the lower order model is not changed in each iteration of optimization process. It means that the damped natural frequencies and the damping ratios of dominant vibration modes of the closed loop system remain unchanged before and after redesign. Therefore, it is obvious that the selection of the pole assignment is very important. In the following subsections, the procedure of each step is described.