Mituhiko Araki

Design of a stable state feedback controller based on the multirate sampling of the plant output

A new type of controller is proposed which detects the ith plant output N/sub i/ times during a period of T/sub 0/ and changes the plant inputs once during T/sub 0/. It is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable. This implies, for instance, that arbitrary symmetric pole assignment is possible if the plant is controllable. It is also shown that, if the plant has no zeros at the origin, the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized. That is to say, inversely expressed, any state feedback can be equivalently realized by a controller with any prescribed degree of stability. >

Application of M-matrices to the stability problems of composite dynamical systems

The construction of a Lyapunov function for a nonlinear system has been one of the most awkward problems in the study of dynamical systems. Especially in the case of large scale systems, the required effort can be enormous. To reduce the effort involved, it is helpful to utilize the fact that in engineering problems a large scale system is often a composite system (i.e., interconnection of subsystems). In such a case, we can first construct a Lyapunov function vi for each subsystem and then use the weighted sum u of the W~‘S v = WOVE + w2v2 + ... + w&z& (Wi > 0) (1)

Stability of the limiting zeros of sampled-data systems with zero- and first-order holds

This paper is concerned with the zeros of sampled-data systems resulting from continuous-time systems preceded by a hold and followed by a sampler. The holds we shall consider are a zero-order hold and a first-order hold. For sufficiently small or large sampling periods, such zeros are called limiting zeros. For sufficiently small sampling periods, they are known to consist of two different types of zeros: the zeros of the first type correspond to the zeros of the original continuous-time system, while those of the second type have no continuous-time counterparts. We first show basic properties of the zeros of sample-data systems for sufficiently small sampling periods. Next, we clarify, in more detail, the correspondence between the former-type zeros of the sampled-data systems and the zeros of the original continuous-time system, including the stability property of these zeros. We also study stability properties of the latter-type zeros. In addition, we study limiting zeros for sufficiently large sampli...

Frequency response of sampled-data systems

This paper develops a frequency-domain theory that provides a method to analyze and design sampled-data control systems, including their intersample behaviors. The key idea is to consider the signal space Xϑ

Stability and transient behavior of composite nonlinear systems

= {x(t) ¦x(t) = ∑n∞ = −x xn exp (jϑt + jnωst), ∑n = −x ∥xn∥2 < ∞}, where ωs is the sampling angular frequency. It is shown that a stable sampled-data system equipped with a strictly-proper pre-filter before the sampler maps Xϑ into Xϑ (≡l2) in the steady state. That mapping is denoted by Q(jϑ) and is referred to as an ‘FR operator’. It is proved that the norm of the sampled-data system as an operator from L2 to L2 is given by maxϑ ∥Q(jϑ)∥/2//2, where 12ωs < ϑ ≤ 12ωs. A set of equations relating outputs of a closed-loop system to its inputs in the frequency domain is derived, and their solution is given in an explicit form. Based on that solution, the sensitivity FR operator Y(jϑ) and the complementary sensitivity FR operator T(jϑ) are defined for feedback control systems, and it is shown that Y(jϑ) gives the improvement of the sensitivity of the transfer characteristics from the reference to the controlled output and also represents the ability of rejecting disturbances, and that T(jϑ) represents the degree of robust stability and, at the same time, gives the effect of detection noises. It is also shown that Y(jϑ) + T(jϑ) = I, and thus a frequency-domain paradigm for the design of sampled-data control systems, which is exactly parallel to the continuous-time case, is established.

FR-operator approach to the H/sub 2/ analysis and synthesis of sampled-data systems

A sufficient condition for asymptotic stability in the large is proposed for nonlinear systems. It is applicable if the system in question can be decomposed into subsystems, if appropriate Lyapunov functions are obtained for the subsystems, and if the connections between subsystems have bounded dc gains. It is generally less restrictive than the condition previously presented by Bailey for similar systems. An estimate of transient behavior, together with the stability condition, is also given.

Recent Developments in Digital Control Theory

Recently, a frequency-domain operator called frequency response (FR) operator was defined and shown to represent the transfer characteristics of a stable sampled-data system. Using this novel frequency-domain notion and introducing its extended notion called hybrid FR-operator, we define an H/sub 2/-norm for sampled-data systems in this paper. Then, sampled-data H/sub 2/ control problems are formulated and solved, whereby the usefulness of these frequency-domain notions is demonstrated both in the analysis and synthesis aspects of sampled-data systems. For the case of sampled-data systems with hybrid (i.e., both continuous-time and discrete-time) input and output signals, the H/sub 2/-norm defined by a hybrid FR-operator turns out to be slightly different from that defined in previous studies. The source of the discrepancy is also identified. >

Frequency responses for sampled-data systems—their equivalence and relationships

Abstract Recent, reasearches on application of nonconventional digital controllers are surveyed, Here, nonconventional digital controllers mean digital controllers equipped with general hold circuits, general samplers or periodically time-varying discribe-time compensators, and include multirate digital controllers as a spcial case, First, their basic features ane studied. Then, their advantages pitfalls, and limitation are explained. After that, the problem: “when and how to use nonconventional digital controllers?” is considered. The scope is limited to the control problems of time-invariant continuous-time plants, emphasis is placedon explaining the basic aspects of reasearches and clarifying their interrelations.

A Model-Predictive Hypnosis Control System Under Total Intravenous Anesthesia

Abstract There are two ways to introduce the notion of frequency response for sampled-data systems. One is based on the so-called lifting, and the other based on an interpretation of steady-state response in terms of impulse modulation. This paper proves the equivalence of these two notions; in particular, it establishes a more direct link of the second approach to the H∞ norm, and also provides the first approach with a natural interpretation of steady-state response as an infinite sum of sinusoidal signals. This study also leads to a comprehensive account of impulse modulation from the lifting viewpoint.

Bounds for closed-loop transfer functions of multivariable systems

In ambulatory surgery, anesthetic drugs must be administered at a suitable rate to prevent adverse reactions after discharge from the hospital. To realize more appropriate anesthesia, we have developed a hypnosis control system, which administers propofol as an anesthetic drug to regulate the bispectral index (BIS), an electroencephalography (EEG)-derived index reflecting the hypnosis of a patient. This system consists of three functions: 1) a feedback controller using a model-predictive control method, which can adequately accommodate the effects of time delays; 2) a parameter estimation function of individual differences; and 3) a risk control function for preventing undesirable states such as drug overinfusion or intraoperative arousal. With the approval of the ethics committee of our institute, 79 clinical trials took place since July 2002. The results show that our system can reduce the total amount of propofol infusion and maintain the BIS more accurately than anesthesiologists manual adjustment.