Architectural Issues in the Implementation of Digital Compensators

Abstract

There are many techniques for designing discrete-time compensators.However, the digital implementation of such designs has not typically been addressed.The nature of digital hardware impacts the computational structure of the compensator and also can affect the original system design parameters.This paper deals with the architectural issues of serialism, parallelism and pipelining in implementing digital feedback compensators.The concepts of serialism and parallelism are shown to involve essentially the same considerationsfor digital compensators as for digital filters.However, the same cannot be said of pipelining, due to the feedback loop.A design technique is proposed for dealing with the problem of compensator pipelining, and several examples of pipelining LQG compensators are presented.* This work was performed in part at the MIT Laboratory for Information and Decision Systems with support provided by NASA Ames under grant The implementation of control algorithms in such digital hardware has raised many new issues. These tend to fall into two categories, one involving the effects of the finite precision and fixed-point arithmetic of small-scale digital systems, and one involving architectural issues. Such questions have not generally been treated in the literature. Therefore some methodology must be established for digital feedback compensator implementation. In other words, we need some way to specify and order the critical computations that must take place in a compensator so that the resulting digital hardware performs as close to the ideal design as is consistent with the expense and speed requirements of the application.We have addressed the issue of finite wordlength due to compensator coefficient rounding and multiplication roundoff in earlier works [1,2].Our general approach has been to examine the concepts already developed for digital signal processing. Then, considering the compensator as a digital filter within a control loop, we can try to apply these ideas. However, the presence of the feedback path itself, and the emphasis on closed-loop performance,has frequently required us to adapt and extend the methods of digital signal processing.In this paper, we will examine the architectural issues involved in -1-compensator implementation, in particular, the notions of serialism, parallelism and pipelining. We will show that the serialism/parallelism concept is essentially identical to that involved in the implementation of any digital system. However, the use of pipelining in digital control systems raises several difficult questions. We will discuss these points in the context of linear-quadratic-Gaussian (LQG) control systems, although they extend easily to maore general cases-.The organization of this paper will be as follows. In Section II, we will briefly review the LQG control problem and describe the resulting ideal compensator equations. The notion of a compensator structure, which is somewhat different than a conventional filter structure, and an adapted notation for describing s...

Roundoff noise and scaling in the digital implementation of control compensators

“…The compensator output u(k) will still depend on inputs up to and including y(k-l), but now y(k-1) is produced only one calculation time before u(k) is needed. This eliminates any inefficiency [16,23]. We will return to the implications of this necessary calculation time in Section 3.…”

“…In a more conventional form, this can be written: A structure for implementing equation (5) is depicted in to all types of filter and compensator structures [16]. In fact,…”

“…The extension of this very useful procedure to low-noise compensator design is presented in [16]. This continuous-time system was discretized at a sample rate of 10 HZ and the optimal regulator and Kalman filter designed.…”

“…We have reported results concerning the coefficient quantization issue in [15] and [16]. In this paper, we will examine the issues of scaling and roundoff quantization in fixed-point controller implementations.…”

“…Also, in this paper we shall deal only with single-input single-output control systems, although our results can be extended to multiple-input multipleoutput systems [16].…”