劉 康志

In the ordinary H_∞ control, weighting functions are assumed not to have unstable poles so that the stabilizability of (A, B₂) and the detectability of (A, C₂) are satisfied. However we sometimes face a problem where the weighting functions have jω poles when we want to design a servo system. In this paper, we solve this problem and show when and how H_∞ control system is designed by the conventional H_∞ control theory.

The purpose of the head positioning control of hard disk drives is to move the magnetic head onto the desired track swiftly and to keep it on track precisely against various disturbances and plant uncertainty at high frequency. In this paper, we apply H^∞ control to the head positioning of hard disk drives. The advantage of H^∞ control is that it yields robust feedback system and the trade-off between various specs is easily incorporated into the design. Further, to obtain a good transient response, we adopt the two-degree freedom control scheme. Experimental results are presented to demonstrate the control effects.

Although there are many studies on the H^∞ control, little is known about structures of H^∞ state feedback controllers. In this paper we first correct the parametrization of H^∞ controllers of the FI problem derived by DGKF since they has not parametrized a null space of T₃. At the same time we also show an elementary proof of the necessary condition of the FI problem which only use the Nehari Theorem rather than the Hankel-Toeplitz operator. Using the result, we next parametrize the H^∞ state feedback controllers and explain how dynamical free parameters implied in the H^∞ controller are related with constant feedback gains which are different from the central solution F_∞. Finally we derive some property of the Riccati equation associated with the central solution.

This paper deals with the steady-state performance of lumped LTI feedback systems in the face of plant uncertainty. The plant uncertainty considered here is the multiplicative perturbation at the output port. The necessary and sufficient conditions for various robust steady-state performances are obtained. Internal model principle like results on the structure of controllers achieving various robust steady-state performances are derived from these necessary and sufficient conditions. More importantly, these conditions are transformed into the measure of μ, thus enables the synthesis of controllers achieving robust steady-state performance in the framework of μ synthesis and the generalized H^∞ control theory.

The state feedback H control problem is considered in this paper. It is shown that under mild conditions this problem can be solved simply by using the conjugation approach proposed by Kimura and Kawatani with some extended treatment to the case that T3(S) is tall and strictly proper. A partial parametrization of state feedback controllers achieving the prescribed norm bound is obtained. This is an eminent difference from previous work on the state feedback H control problem where only a static feedback control law (the central solution of our result) is provided. Both four block and one block problems are solved in this paper. The results of this paper embrace those of Doyle et al. and Petersen. © 1990 Taylor and Francis Group, LLC.

We establish conjugation notion in discrete-time systems, first introduced into the HOO control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid of J-Iossless conjugation (conjugation by a J-Iossless system), it is shown that the parametrization of sub-optimal solutions of HOO model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that the J-Iossless conjugation of the HOO model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems. © 1989 Taylor and Francis Group, LLC.

Design of an optimal series compensator for MIMO systems is considered in this paper using the DARMA form. The main purpose is to show how to find the smallest number of samples in each output channel to yield an optimal series compensator which is of the smallest possible order. © 1987.

A new design method for an optimal digital series compensator is considered that is not produced by an optimal regulator incorporated with a state observer, but employs a new idea that assures total closed system optimality in one design step. However, the compensator so designed is not always stable, i.e. strong stability of the closed-loop system is not always guaranteed. For this case, the authors propose to use the inter-sample response to realize an optimal stable compensator and/or optimal output feedback control system. Especially when the given plant is a linearized mechanical system, such a strongly stable system can always be designed using only output data two samples prior to the current sample regardless of the system order and the parity interlacing property condition. © 1987 Taylor &amp Francis Group, LLC.

Today, microprocessors are easily obtained, and many digital control methods can be considered and realized. In this paper, at first, we propose a new optimal control method using only input/output data. The result coincides with the series compensator which can be constructed by optimal regulator incorporated with minimal order observer. However, in the proposed method, the total optimality of closed loop system is derived directly from modified optimal regulator theory.<br>However, in the above case, there are some cases where the strong stability are not guaranteed. So, we reformulate the method so that it uses the intersample output data as well, then the strong stability is assured for almost all plants with mild restrictions. Further, the final compensator form is given by an optimal output feedback control.<br>Especially, in the case where the plant is given by the linearlized mechanical system, the above optimal output feedback is always realizable using only 2 samples output data prior to current sample. Therefore, it is a very attractive method for the control of robots, for example.