Multirate Sampled-data Systems Research Articles

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.

Dissipativity of nonlinear multirate sampled-data systems under emulation design

This paper deals with a common practical problem where the output of a nonlinear sampled-data system is constrained to be measured at a relatively lower sampling rate. Designing a continuous-time controller that satisfies a specific dissipation inequality, it is shown that the closed-loop sampled-data system obtained by digital implementation of the emulated controller in a multirate scheme preserves similar dissipation inequality in a semiglobal practical sense. Moreover, we address multirate nonlinear H∞ control via an emulation method as an important application.

On Semiglobal Stabilization of Discrete-Time Periodic Systems With Bounded Controls

This brief revisits the problem of the semiglobal stabilization of discrete-time linear periodic systems with bounded controls. First, a new state feedback solution based on a parametric periodic Riccati equation is established to solve the problem under the condition that the open-loop characteristic multipliers are strictly inside or on the unit circle. Different from our early solution based on the parametric periodic Lyapunov equation, this new solution does not require any state transformation on the open-loop system and is theoretically more appealing. Second, an output feedback solution is presented in this brief, which complements the two state feedback solutions. Third, as a periodic system model, the multirate sampled-data system is considered, and the problem of semiglobal stabilization for such a system subject to input saturation is solved. In doing so, the connections between the semiglobal stabilizability of the original continuous-time system and of the multirate sampled-data system are established. A numerical example is worked out to illustrate the effectiveness of the proposed design.

Linear Parameter Varying Control for Sampled-data Multi-rate Systems

A new methodology for the design and implementation of linear parameter varying (LVP) controllers for multi-rate sampled-data systems is presented and its stability properties are analyzed. A controller structure is first proposed for the regulation of multi-rate systems with more measured outputs than inputs. This structure is specially suited for a gain-scheduling implementation that verifies an important property known as the linearization property. The proposed solution guarantees local stability of the feedback interconnection of the nonlinear multi-rate system and the LPV controller about individual equilibria, and ultimate boundedness of a conveniently defined closed-loop error in response to slowly varying exogenous inputs. An example is presented that illustrates the applicability of the proposed solution.

Identification of Lifted Models for General Dual-Rate Sampled-Data Systems Using N4SID Algorithm

The technological and the economical reasons often make the researchers and engineers encounter the so-called multirate sampled-data systems which include multiple sampleddata mechanisms with different sampling periods. As a class of multi-rate systems, general dual-rate systems are very attractive because the contributions in the literature of the dual-rate systems can be easily extended to the whole scope of multi-rate sampled system. In this research, we consider the identification problems for the general dual-rate systems. A general dual-rate system is illustrate Fig. 1. In Fig. 1, u(kT1) and y(kT2) are the dual-rate system input and output signals and the sampling period T1 = T2. y(kT2) is corrupted by a stochastic noise v(kT2). The measurement of the output is denoted by z(kT2) . ZOH is a zero order holder with period T1. ADC is a sampler with period T2. Pc is a linear time-invariant(LTI) continuous-time process. Suppose that the samplers and zero order holders are synchronized at time t = 0. Most typical identification algorithms only handle the identification problems of single-rate systems. However, a single-rate LTI isomorphism can be obtained for the dualrate system in Fig.1 by the lifting technique. The isomorhpism is the so-called lifted model, Although there are several contributions in the literature for the identification problems of the lifted models, most of them need detailed prior information about the dual-rate system, e.g. observability structure indexes which cannot be obtained in many cases. In contrast, Subspace State-Space IDentification(4SID) algorithms need no prior information about the systems under investigation. Unfortunately, it is commented that the 4SID type algorithm cannot be used to the lifted models because of the causality constraints.

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.

Observer-Based Fast Rate Fault Detection for a Class of Multirate Sampled-Data Systems

This note deals with the problem of observer-based fast rate fault detection for a class of multirate sampled-data (MSD) systems. Applying a lifting technique, a linear time-invariant (LTI) representation with slow sampling period is firstly obtained for the MSD systems and, based on this, an observer-based fault detection filter is considered as a residual generator. Then an optimization fault detection approach for LTI systems is modified to the residual generation for the MSD systems and, by solving a discrete-time Algebraic Riccati equation, a family of optimal solutions with causality constraint can be obtained. An inverse lifting operation on the generated residual implements its fast rate. The residual evaluation problem is also considered. A numerical example is finally given to illustrate the effectiveness of the proposed design techniques

Multirate sampling and input-to-state stable receding horizon control for nonlinear systems

In this paper, a robust receding horizon control for multirate sampled-data nonlinear systems with bounded disturbances is presented. The proposed receding horizon control is based on the solution of Bolza-type optimal control problems for the approximate discrete-time model of the nominal system. “Low measurement rate” is assumed. It is shown that the multistep receding horizon controller that stabilizes the nominal approximate discrete-time model also practically input-to-state stabilizes the exact discrete-time system with disturbances.

An [formula omitted] approach to fast rate fault detection for multirate sampled-data systems

In this paper the problem of fault detection in multirate sampled-data systems is studied. The lifting technique and direct design approach are used to convert the time-varying multirate design problem into an equivalent time-invariant single-rate discrete-time problem. A performance index is optimized to obtain a set of H ∞ optimal and causal residual generators. The key new feature of such a residual generator is that it operates at a fast rate for prompt fault detection.

FAST RATE FAULT DETECTION FOR MULTIRATE SAMPLED-DATA SYSTEMS WITH TIME-DELAYS

This paper deals with the fast rate residual generation problem for a class of multirate sampled-data (MSD) systems with multiple data transfer time-delays. By using the l2-induced gain to measure the robustness of residual with respect to unknown input and sensitivity to fault, the design of residual generator for such MSD systems is formulated as an H∞ optimization problem. A solution of the optimization problem is then presented via a discrete-time algebraic Riccati equation by applying some recent results of fault detection of single rate SD system. The fast rate of residual generator can be implemented when its causality is guaranteed. The main contribution of this paper lies in the treatment of residual generation problem for such an MSD system as that of linear time-invariant system without time-delays and, further, the implement of its fast rate. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.

Multirate versions of sampled-data stabilization of nonlinear systems

The problem of state feedback sampled-data stabilization of nonlinear systems is considered under the “low measurement rate” constraint and in the presence of (not necessarily small) time delay in the measurement channel. A multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the delayed measurements. For both the controller emulation approach and the approach based on approximate discrete-time model of the system, we show that under standard assumptions the closed-loop multirate sampled data system is asymptotically stable in the semiglobal practical sense. An illustrative example of sampled-data control of vertical take off and landing aircraft is discussed.

Identification of Multirate Sampled-Data Systems

Abstract This paper studies identification of a general single-input and single-output (SISO) multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant lifted system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discllssed. The effectiveness is demonstrated through simulation and a real-time implementation.

System Identification from Multi-Rate Data

In this paper, we provide a novel iterative identification algorithm for multi-rate sampled data systems. The procedure involves, as a first step, identifying a simple initial model from multi-rate data. Based on this model, the "missing" data points in the slow sampled measurements are estimated following the expectation maximization approach. Using the estimated missing data points and the original data set, a new model is obtained and this procedure is repeated until the models converge. An attractive feature of the proposed method lies in its applicability to irregularly sampled data. An application of the proposed method to an industrial data set is also included.

Multirate sampled-data systems: computing fast-rate models

Abstract This paper studies identification of a general multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discussed. The effectiveness is demonstrated through simulation and real-time implementation.

Optimal control of multirate sampled-data feedback systems via a polynomial approach

The linear quadratic Gaussian design of multirate-sampled multivariable feedback systems using input-output models is described. The theoretical emphasis is placed upon the formulation of augmented representations in which each variable is specified at its associated sample instants throughout one cycle of the sequence of sampling operations. The structures of the polynomial matrices utilised illuminate the causality issues involved and facilitate the acquisition of the optimal control solution from coupled diophantine equations.

A distributed state estimation and control algorithm for plantwide processes

A multirate distributed and decentralized approach to state estimation and control is developed for large-scale processes. The decentralized and scalable form of the Kalman filter algorithm is formulated for multirate sampled-data systems. The multirate formulation is necessitated by differing sample times for distributed computation and process measurement availability. The distributed linear quadratic Gaussian control methodology is implemented in a simulation environment using appropriate tools for distributed computation. The issues involved in the model decomposition for employing the distributed control algorithm are examined. Heuristic guidelines are proposed to balance the computational load and communication overhead across the distributed control network. This methodology is demonstrated in a case study involving a simulated large-scale industrial reaction-separation system.

Observer-based robust fault detection of multirate linear system using a lift reformulation

This paper presents observer-based robust fault detection for multirate sampled-data linear system. It is assumed that all plant inputs are updated with a unique sampling period and that the plant outputs are sampled uniformly at integer multiples of the input sampling period. A state observer is constructed, as in the single-rate case, and a residual generator is derived. The paper shows that the residual signals can be decoupled from noise and disturbances. An illustrative numerical example is provided.

개루프 상태에서 플랜트가 불안정한 경우에 대한 멀티레이트 표본 데이터 제어 시스템의 안정화

This paper proposes a stabilizing controller for the multirate sampled-data systems, which have a periodic output measurement scheme, in case of the open-loop unstable plant. A sufficient condition for maintaining observability in the multirate sampled-data systems is derived and a design strategy for filtered disturbance rejection is proposed. We also propose a design method for the plant output estimator. It is shown that the proposed pre-stabilizing controllers can stabilize the plant through the simulations. The proposed controller has IMC structure, and can be decomposed into the pre-stabilizing controller, the plant output estimator, the filtered disturbance estimator and the inverse of the fast pre-stabilized plant model. We assume that the plant is open-loop unstable and the disturbance consists of a sum of finite number of sinusoids with different frequencies. Some examples are presented for illustrations.

Generalized predictive control for non-uniformly sampled systems

In this paper, we study digital control systems with non-uniform updating and sampling patterns, which include multirate sampled-data systems as special cases. We derive lifted models in the state-space domain. The main obstacle for generalized predictive control (GPC) design using the lifted models is the so-called causality constraint. Taking into account this design constraint, we propose a new GPC algorithm, which results in optimal causal control laws for the non-uniformly sampled systems. The solution applies immediately to multirate sampled-data systems where rates are integer multiples of some base period.

Fault detection for multirate sampled-data systems with time delays

In this paper, problems of fault detection in multirate sampled-data (MSD) systems with time delays are studied. The background of our study is the increasing demands for fault detection in complex, distributed process control systems, where the plant, controllers, sensors and actuators are networked by standardized bus systems. The basic idea behand the problem solutions is to derive the parity relations of the MSD system with time delays by taking into account the multirate nature and the multiple time delays. Having introduced two operators, the fault detection problem can be formulated as an optimization problem in the framework of the well-known parity space method. Application and advantages of the approaches proposed in this paper are finally illustrated by simulation examples and by comparison with other indirect design approaches.