Control System Verification Using Realtime Execution of Symbolically-Generated Multibody Equations of Motion

The need to verify controller designs has produced a strong interest in real time, hardware-in-the-loop simulations in which the actual controller can be tested against a nonlinear plant model. We will examine the model requirments for a successful hardware-in-the-loop implementation and discover that a tradeoff exists between the time required to develop a plant model and the cost of the equipment required to execute that model in real time. We will look closely at this tradeoff and derive some specific dollars-and-cents figures showing the extent of the problem. The tradeoff is so severe that few analysts today use any automated method of producing the plant dynamic response. Instead, equations of motion are derived and coded by hand to obtain the required performance. The largely overlooked computer science field of Symbolic Mathematics is examined as a possible solution to this dilemma. We discover that it is not much help in its common form, but that a suitable adaptation can be made which eliminates the development time/execution time tradeoff. Special purpose symbolic codes can be constructed which produce plant equations of motion with very little effort and very high performance. A commercially available code of this type is introduced. Finally, we look at a specific example of a symbolic multibody code in actual use to produce a hardware-in-the-loop simulation of a full nonlinear model of a 19 degrees-of-freedom spacecraft.