A MODERN CONTROL APPROACH TO THE DESIGN OF THE SPS CONTROL SYSTEM Richard Gran Research Department, Grumman Aerospace Corporation, Bethpage, New York The Problem The structural dynamics of the solar power satellite are complex. There are many low frequency vibration modes with frequencies that are closely clustered. In addition, the requirements on the vibraton of the microwave antenna are very severe. Lastly, the possibility of thermal induced vibration is such that severe structura1-therma1 interactions are possible. One way of eliminating these problems is to design the structure stiff enough and with low coefficient of thermal expansion material so that the vibrations do not create a problem, and the thermal interactions can not occur. A second possibility is to use the active control system to mitigate the structural problems. A cautionary note must be sounded. The first approach might actually exacerbate the structural problem if the control system were designed without consideration of the structural dynamics. This comes from the interaction of the control actuators and the sensors with the vibration of the structure. The so called "control and observation spill-over" problem is so important that it must be kept in view as one goes about developing the control system. Since the detailed structural, thermal and control models are required to guarantee that spill-over does not occur, it makes sense to evaluate other advantages that a complex control system may provide. One possibility is that the control system will permit lighter structural material with lower stiffness, the loss of structural stiffness being overcome by the active control system. Figure 1 shows the spill-over problem and the potential solutions to the problem. The Approach There are several distinct avenues that one may follow if the control system is designed using modern control methods. These are: • Design of an optimal controller with an estimator (Kalman Filter) to reconstruct the missing measurements of the structural motion. • Design of a control system that uses only measurements, that is with no estimation of the missing dynamic states. This is sometimes called direct output feedback. • Design of a control system on a very limited set of models and then adaptively modify the control system during its operation. Fig. 1 illustrates the first two of these techniques. The emphasis in this presentation is on the second of the approaches, since this seems the most robust method. In the context of modern control, the term robust has a very specific meaning. A control system is robust if the variations in the parameters of the system being controlled do not alter the stability, and if the expected parameter variations do not dramaticly alter the response. The robustness results that are available from the modern optimal control techniques are the following: • A control system that uses "full state feedback" (i.e. for each state in the system their is a feedback gain to each control), has infinite gain margin when used in the system whose model was used for the design. • A control system that is optimal has at least 60° of phase margin. • A control system that is optimal and that is designed with an integral compensation in each control channel, is more robust than one without
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