Multi-objective design of finite word-length controller structures

Feedback controller implementations with fixed-point arithmetic offer the advantages of speed, memory space, cost and simplicity compared to floating-point arithmetic. Thus, to date, fixed-point processors dedicated for digital controller implementations are still the dominant architecture in many modern digital control engineering applications, particularly for automotive, consumer, military and medical applications. However, most control design methodologies assume that the designed controller will be implemented with infinite precision. Thus, when the controller is implemented on a fixed-point platform, rounding errors can cause a performance degradation and even instability. Hence, there is a trade-off between the cost of the controller in terms of word-length, memory and computation requirements (the controller compactness) and the performance of the system. This paper presents an approach to designing finite word-length feedback controller structures by means of a multi-objective genetic algorithm. The approach provides a set of solutions that are (near) Pareto optimal with respect to minimal word-length and memory requirements and to closed-loop performance. The method is applied to the design of finite word-length controller structures for two examples, a PID controller for a rolling strip mill, and a controller for the IFAC93 benchmark problem