Self-tuning regulator for reducing disturbance in H/sub infinity /-norm

Abstract

This paper proposes a design method of a self-tuning regulator (STR) for reducing disturbance in the minimum H,-norm, when the plant is described by a SISO discrete-time linear stochastic model with colored noise. Taking into account o j estimating parameters of the plant and the noise structure, the STR is designed to be suitable for adaptive algorithm, using the optimal interpolation theory in H, control study. This theory produces an improper controller, so an STR with a predictor to realize the controller is discussed. h t r o d u c t ionThe reduction problem of additive disturbance on the plant output is important in the design of the feedback system. For this problem, h t r o m presented a useful design method of selftuning regulator ( STR) to minimize the plant output in the sense of mean square'. This work considers the following a singleinput single-output discrete-time linear time-invariant stochastic plant with colored noise A(z-')y(k) = z-'B(z-')u(k) + C(z-')w(k)(1)where y(k) and u(k) denote the output and input respectively, and {w(k)} is a white random sequence with zero mean and variance c :. A(z-') , B(z-') and C(z-') are scalar polynomials in the unit delay operator z-' , and are of forms A = ~+ o~z " + * * -+~z -" B = bo+b1z"+**.+bnz-" c = l+clz-'+...+C,z-"For simplicity the arguments of polynomials are often omitted.The following assumption will be made about the plant (A-1) The degree n is known.(A-2) A , B and C are coprime.The reason why Astrom's STR requires (A-4) is that the characteristic equation of the feedback system is C. In the design, the optimal output is given by y(k) = w(k). The problems inAstriim's STR are that (A-4) is required and the output is a white noise. The former is not general condition, and the latter, which is caused by the control strategy based on the minimal variance of the plant output, often leads to the satulation or chattering of the feedback controller.Up to now, the control strategy based on H,-norm theory is studied, and some usefule results to calculate the optimal controller in H,-norm are presented. It is expected that a design method of the STR using H,control theory overcome the problems pointed out in Astrom's STR Unfortunately, the recent remarkable results studied by Zamesl, Francis3 and Doyle ' are not designed for on-line control calculation as required in adaptive system. Thus, it is need to apply H,control theory to a design of STR in a suitable formulation. The resemblant works to a p ply H,theory to a adaptive control are shown in references[5], [6]. These works, however, consider the output tracking problem, not the reducing disturbance one.In the proposed design, taking into accout the transfer function from w(k) to y(k) where the adaptive algoritm estimates A , B and also C , the authors consider the usual model matching problem in Hacontrol study; the optimal interporation theory, with the specified transfer function from w(k) to y(k). It is shown that the proposed STR overcomes the problems in Astrom's STR. This design method produces an ...

Velocity and pressure profiles for Newtonian creeping flow in regular packed beds of spheres

“…Velocity profiles in regular arrays of spheres have been calculated approximately by Uchida ( 6 ) , Brenner (7), and Hasimoto (8). Uchida and Brenner included packed (dense) arrays, whereas Hasimoto considered only dilute arrays.…”