Multirate Output Sampling Research Articles

Output feedback based event-triggered sliding mode control for delta operator systems

In this paper, we present an output feedback based design of event-triggered sliding mode control for delta operator systems. For discrete-time systems, multi-rate output sampling based state estimation technique is very useful if the output information is available. But at high sampling rates, the discrete-time representation of the system using shift operator becomes numerically ill-conditioned and as a result, the observability matrix becomes singular as the sampling period tends to zero. Here, a new formulation of multi-rate state estimation (MRSE) for a small sampling period is presented. We first propose a new observability matrix and then discuss its relationship with the observability matrix defined in the conventional sense. For the delta operator system with matched uncertainty, we have presented the design of MRSE based sliding mode control (SMC). Additionally, to make the control efficient in terms of resource utilization, MRSE based event-triggered SMC is proposed. The absence of Zeno phenomenon is guaranteed as the control input is inherently discrete in nature. Finally, the effectiveness of the proposed method is illustrated through numerical simulations, considering a ball and beam system and a general linear system as a numerical example.

Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

This paper studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.

Multirate output sampling linear functional observer-based state feedback for systems with delay in state variables

In this paper the design of functional observer-based state feedback controller for linear time-invariant (LTI) systems with time-delay in state variables is addressed. To illustrate the approach we consider a dual-rate system with fast output measurements and slow control actions. Necessary and sufficient conditions are given for existence of proposed controller with minimal number of output samples than those already employed multirate output sampling (MROS) and full state observability is not a necessary condition. By the so-called lifting method, time-delay systems are transformed into delay-free systems such that simple conditions have been developed for the stability and stabilisation. Design example is given to illustrate the procedure for the design of proposed controller and to demonstrate the advantages.

State Based Functional Observer Design for Linear Uncertain Systems Using Multirate Output Sampling

In this paper a design of controller has been proposed for linear uncertain systems based on multirate output sampling for the purpose of state feedback and nullification of disturbance effect on system response. If certain conditions are satisfied, construction of proposed functional type controller require less number of output samples than any other method based on fast output sampling. The advantage of proposed method is that it can be extended to unobservable systems and avoids the boundedness constraint on disturbance. A numerical exam- ple demonstrates the procedure, superiority in terms number of required output samplings and application to unobservable systems.

Computationally Efficient Functional Observer for LTI System Based on a Multirate Output Sampling Algorithm

This paper proposes a technique for computing a vector linear functional of the system states of a linear time invariant (LTI) system. The concept of multirate output observations has been used to design the observer. The paper also proves that the complete state observability of a system is not a necessary condition for the existence of a functional observer. The proposed technique reduces the computational time and complexity of the hardware and software of the observer system considerably due to static structure of observer as well as involvement of reduced dimension matrices in computation of the functional. The proposed technique has been validated using numerical examples.

Multirate Implementation of a Quasi-Sliding Mode Control

In this paper a discrete time sliding-mode type controller is proposed and it is implemented by using a multirate output sampling scheme. This strategy avoids the use of state observers, the uncertainty in the model parameters and disturbances being counteracted by the robustness of the sliding mode control structure. This controller does not involve switching, and it is applied to control stable and unstable systems. Also by simulations, the controller has shown to be robust against changes in the plant model parameters.

Design of reduced-order multirate output linear functional observer-based compensators

Often in control system design, it is only necessary to estimate a single (but prespecified) linear function of the system's state for the purpose of implementing a feedback control law. This can be achieved by a linear functional observer which may have order one less than the observability index of the plant, but generically cannot have smaller order. In this paper, we explore the concept of multirate output sampling and show that a linear functional observer-based compensator employing multirate sampling of the plant output can be designed with dimension much smaller than that of the linear functional observer-based compensator employing single-rate sampling of the plant output. Necessary and sufficient conditions for the existence of the single-rate and multirate output linear functional observer-based compensators are found. Design procedures for constructing these observer-based compensators are also outlined. Furthermore, both types of compensators are strictly causal and open-loop stable for sufficiently small frame period, T0.

Generalized multirate-output controllers

This paper studies controllers employing multirate sampling of the plant output (Hagiwara and Araki 1988 a). Specifically, it is shown that arbitrary pole assignment is possible by a multirate output sampling mechanism with smaller output multiplicities if a multiframe control law is introduced. We refer to the new control law as the generalized multirate-output controller. It is also shown that type-1 robust servo controllers with two degrees of freedom can be designed and strong stabilization with loop transfer reovery is possible. The relation of the generalized multirate-output controllers to the two-delay output controllers (Mita et al. 1987, Mita and Chida 1988) is also discussed.