Multirate Sampled-data Control Research Articles

Improved stability and stabilization criteria for multi-rate sampled-data control systems via novel delay-dependent states

This paper aims to obtain less conservative stability and stabilization conditions for sampled-data linear systems with multiple sampling rates. To this end, three novel delay-dependent states resulting from sampling are introduced in the augmented state, enabling the exploitation of the sawtooth-type characteristics of the sampling-induced delay in both stability and stabilization processes. Additionally, a novel discontinuous function is included in Lyapunov–Krasovskii-based functional to enhance the capacity to extract more information from specific sampling pattern for each state. Especially, to strengthen the interdependence among the components of the augmented state, supplementary zero equalities are incorporated into the stability analysis conditions. Furthermore, by including a novel weighted state derivative in the augmented state, this paper proposes an effective method that can transform the parameter-dependent stability conditions into stabilization conditions formulated in terms of linear matrix inequalities. Finally, the validity and practicality of the proposed method are demonstrated through two illustrative examples.

Exponential stabilisation of delayed Lur'e systems with multi-rate sampled-data control

In this paper, we focus on the multi-rate sampled-data based exponential stabilisation problem of delayed Lur'e systems. First, a merging time sequence is constructed from the sampling instants of multiple sensors to form the so-called analysis interval and the closed-loop system is represented by a system with multiple time-varying delays over the constructed analysis interval. Then, a useful estimation about the norm of the system state is established. On this basis, a stabilisation criterion is proposed by constructing a two-sided looped-functional. The proposed functional drops positive definite restrictions over the whole analysis interval . Therefore, it can reduce the conservatism of the derived criterion. And, the feasible solution of the multi-rate sampled-data controller gain can be provided by solving a set of LMIs. Finally, the given example shows the advantage of the main results.

Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm

In this paper, the problem of global sampled-data stabilization is investigated for high-order nonlinear systems with arbitrarily long input delays. Based on the Lie algebra technique in nonlinear control theory, a discrete-time predictor-based multi-rate sampled-data state feedback control law with a series expansion form is proposed to ensure that the resulting system is globally asymptotically stable under some conditions. Compared with the existing methods, the proposed control algorithm just needs to know the approximate prediction of state variables, and the faster decrease of Lyapunov function may be provided for each subsystem. Performance of approximate versions of the proposed controller is given by theoretical analyses. It is showed that the approximate controllers achieve practical stability of the sampled-data closed-loop system. Finally, the obtained stabilization results are applied to a trajectory tracking problem for a high-order planar system.

Multi-rate sampled-data composite control of linear singularly perturbed systems

This paper addresses the multi-rate stabilization problem for linear singularly perturbed systems. The proposed multi-rate sampled-data control law is based on the discretization in multi-rate fashion on the continuous-time composite control law obtained from the singular perturbation theory. The sampling times of the slow and fast state variables are allowed to be asynchronous and nonuniformly spaced. A new time-dependent Lyapunov functional is introduced to analyze the closed-loop stability of the considered system with the multi-rate feedback. With the use of the Lyapunov functional, a sufficient condition for exponential stability of the closed-loop system is derived in terms of linear matrix inequalities. Further, a robust stabilizability condition of the proposed multi-rate control law with respect to uncertain singular perturbation parameter is also obtained. Three numerical examples are presented to show the effectiveness of the developed methodology.

Sampled-data stabilization of a class of lower-order nonlinear systems with input delays based on a multi-rate control scheme

This paper focuses on the problem of sampled-data stabilization for a class of low-order lower-triangular nonlinear systems with large input delays. A new predictor-based multi-rate sampled-data control scheme is proposed to guarantee that the resulting system is globally strongly stable under some assumptions. Compared with the existing methods, the present strategy just needs to know the approximate prediction of state variables, and the stabilizing performance of a given continuous-time feedback controller can be preserved at the sampling instants. It is noted that the proposed controller takes the form of a power series. Its truncation at a finite order is regarded as approximate controller which is proved to be effective in the practical implementation. Two simulation examples are finally given to illustrate the advantages and effectiveness of the proposed control scheme.

Global stabilization of high-order nonlinear systems under multi-rate sampled-data control

This paper studies the sampled-data control problem for a class of high-order nonlinear systems. Based on exact discrete-time equivalent model of the sampled-data system, a multi-rate sampled-data controller with the form of a power series expansion is designed to achieve the global asymptotic stability of the closed-loop system under some assumptions. Approximate solutions of the proposed controller are proved to be effective by a theoretical analysis. The results show that, compared with the emulated control scheme, the approximate controllers allow considering larger sampling periods and enlarge the domain of attraction for a given sampling period. Finally, a simulation example is given to show the effectiveness of the proposed control scheme.

Frequency-domain estimates of the sampling interval in multirate nonlinear systems by time-delay approach

ABSTRACTA class of nonlinear hybrid systems consisting of a continuous plant and a multirate sampled-data controller is considered. Applying the time-delay approach, the system is transformed to the system with a time-varying sawtooth delay. Then, the value of the sampling intervals ensuring stability of the closed-loop system is estimated based on the frequency-domain circle-like criterion for systems with time-varying delay. Such a criterion for multirate MIMO systems is established based on the previous result for SISO systems proposed by M.Churilova in 1995. Efficiency and advantages of the method are illustrated by numerical examples. The key advantage of the proposed approach is that it is applicable to multirate systems nonaffine in control. It allows one to use a nonlinear feedback for stabilisation. Particularly, the case of nonsmooth or discontinuous nonlinear systems can be treated.

Design of One Sampling Period Delay Stabilizing Controllers for Nonlinear Sampled-data Strict-feedback Systems

We consider the design of one sampling period delay state feedback and output feedback controllers that semiglobally practically uniformly asymptotically (SPUA) stabilize nonlinear sampled-data strict-feedback systems. First we apply nonlinear multi-rate sampled-data control to design one sampling period delay state feedback controllers. Then we derive one sampling period delay output feedback controllers by combining the designed state feedback controllers and reduced-order observers. A numerical example is given to illustrate the proposed design methods.

Multiloop controller design for a fly-by-wireless UAV quadrotor based on a multirate sampled-data model

This paper presents a novel approach for multirate sampled-data control of a fly-by-wireless quadrotor using three feedback loops: attitude control loop, velocity control loop, and position control loop. The proposed multiloop controller operates over a network of sensors. Each sensor corresponds to one of the control loops and is dedicated to sampling the attitude, the velocity, or the position of the quadrotor. The sensors operate at different sampling frequencies that are assumed to be lower bounded. The control signals in each loop are computed at different rates, which are dictated by the corresponding sensor of the control loop. Two formal results are proved. Given the controller gains, the first result provides sufficient conditions for finding the lowest allowable sampling frequency for each control loop such that stability of the closed-loop system is guaranteed. The second result provides a controller synthesis algorithm and sufficient conditions guaranteeing the stability of the closed-loop system. Simulation results show the effectiveness of the proposed multiloop controller when compared to the single-loop, single-rate case. In particular, the results show that increasing the sampling frequency of a control loop allows a designer to decrease the sampling frequency of the other control loops below the limit imposed by the single-rate case. Using the technique proposed in this paper, an engineer can thus select the proper combination of sampling frequencies for a specific application, based on the price, availability, performance, power requirements, weight, maintenance costs, and other characteristics of the sensors.

Multi-rate digital redesign of cascaded and dynamic output feedback systems

In this paper, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analogue controllers are often pre-designed based on desirable frequency specifications, such as bandwidth, natural angular frequency, etc. To take advantage of the digital controller over the analogue controller, digital implementation of these analogue controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilised to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analogue controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.

Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems

We consider multirate sampled-data output feedback control of a class of nonlinear systems using high-gain observers where the measurement sampling rate is made faster than the control update rate. We show that, in the presence of bounded disturbances, given a sampled data state feedback controller that achieves stabilization with respect to a closed set, the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast. As an application we consider the control of smart material actuated systems. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

Adaptive output feedback control of general MIMO systems using multirate sampling and its application to a cart–crane system

In adaptive output feedback control based on almost strictly positive real conditions, a technical difficulty arises when the multi-input multi-output (MIMO) system under consideration is non-square, and in particular, has less inputs than outputs. To overcome this, we propose the idea of multirate sampled-data control—by carefully choosing faster input sampling rates, we obtain a lifted discrete-time system, which has the same number of inputs and outputs and does not give rise to the causality constraint. The adaptive control strategy is then applied to the lifted system, resulting in a multirate adaptive output feedback controller which is implementable digitally and provides closed-loop stability under certain conditions. The results reported here are validated on an experimental cart–crane system.

Floating quantization effects on multirate sampled-data% nonlinear control systems

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.

Simultaneous Stabilization and Pole Assignment by Two Level Controllers Consisting of a Gain Feedback and a Multirate Input Controller

A method of simultaneous pole assignment of a finite number of plant models is studied. Extending the idea of multi-structured multirate sampled-data controllers proposed in our previous work, this paper proposes a new method where a continuous-time gain feedback controller instead of a multirate sampled-data controller is used as the “internal structure.” By the proposed method, the plants precompensated by the internal structure can generally be made to satisfy an existing sufficient condition for simultaneous pole-assignability, and hence the class of the plant models for which simultaneous pole assignment can be attained becomes wider than that by the previous results. In particular, simultaneous pole assignment becomes possible for any finite number of plant models, provided that each model is controllable and observable.

Linear periodically time-varying discrete-time systems: Aliasing and LTI approximations

Linear periodically time-varying (LPTV) systems are abundant in control and signal processing; examples include multirate sampled-data control systems and multirate filter-bank systems. In this paper, several ways are proposed to quantify aliasing effect in discrete-time LPTV systems; these are associated with optimal time-invariant approximations of LPTV systems using operator norms.

Simultaneous pole assignment by multi-structured multirate sampled-data controllers—orthogonality consideration

A new method of simultaneous pole assignment and simultaneous stabilization of h plant models Pj (j = 1, …, h) by multirate sampled-data controllers is presented. The method is based upon two key ideas. The first is the introduction of the ‘perturbation structure’ assumption on the plant models; i.e., it is assumed that a part of Pj is fixed for all j and the rest is changed completely. This assumption seems fairly feasible if Pjs are the models of a single object under different conditions or the models of many objects which perform the same function. The second key idea is the use of multi-structured multirate sampled-data controllers, which might offer a new horizon for a wide class of control problems other than simultaneous stabilization. The significance and feature of the proposed method in contrast with a previous method are clarified from the viewpoint of ‘controller-plant orthogonality’. Namely, we show that the resulting controller can be regarded as consisting of h subcontrollers each of which controls its target plant model but causes no feedback effect at sampling instants on other h—1 plant models.

Frequency Analysis for Continuous-Time Systems Under Multirate Sampled-Data Control

Performance analysis in the frequency domain is presented for single and multirate sampled-data control systems. The main idea is to compute the input to output power gain for a single sinusoidal input with a specific frequency. This method is therefore closely related to the maximum principal gain for continuous-time MIMO systems. However, in contrast to the continuous-time case, we observe that the maximum gain of a single sinusoidal input does not equal the H∞-norm for sampled-data systems. This implies that robust stability and performance can not be determined by the same kind of frequency analysis. The suggested method for performance analysis, is illustrated on a multirate sampled-data controlled packed-bed distillation column.

Simultaneous Pole Assignment and Stabilization by a Time-Sharing Multirate Output Controller

In this paper, we study the simultaneous stabilization problem and siniultaneois pole assignment problem by a multirate sampled-data controller. We propose a multirate output controller in which the control action and the observation action are carried out alternately, and introduce a method of simultaneous pole assignment by this type of controllers. Furthermore, based on the LQG control theory, we propose a method to determine the feedback gain of the proposed controller so as to attain simultaneous stabilization. Effectiveness of the proposed method is shown through simulations.

Discrete model reference adaptive control of continuous-time linear multi-input multi-output systems via multirate sampled-data controllers

The use of multirate sampled-data controllers for linear multivariable time-invariant systems with unknown parameters is investigated. Such controllers contain periodically time-varying elements and a multirate sampling mechanism with different sampling periods at each system input. Their application to unknown continuous-time linear multi-input, multi-output systems results in a sampled closedloop system for which an arbitrary discrete-time transfer function matrix can be assigned, as is shown in the present paper. The contribution of the present paper is twofold: the use of multirate sampled-data controllers in the area of model reference adaptive control; and the application, for the first time, of periodically varying controllers for model reference adaptive control of multi-input, multi-output systems.