Multirate Sampled-data Systems 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.

Data-driven NODE based multirate sampled data state feedback control

In control systems, multirate sampled data systems are widely used because they improve system performance and adaptability, especially when systems deal with both continuous and discrete signals or entirely asynchronous sampling signals. This paper addresses the challenges of system stability and optimization in these multirate systems, specifically for a certain class of nonlinear systems. Existing controllers, though capable in certain contexts, tend to be overly complex and often lack guidance on appropriate sampling interval selection for these intricate systems. Our approach takes into account both system stability and practical considerations, providing a criterion for selecting multiple sample periods that guarantees system stability, as well as an optimal choice of parameters by Neural Ordinary Differential Equation (NODE) for the linear practical controller that maximizes performance according to a predefined performance index. With the construction of a set of linear stabilizers that are implemented using multirate sampled data, the stability and controller design at three different sampling levels are studied. To demonstrate the effectiveness of our proposed strategy, the simulations and real world application of a single-link robot system are presented.

Data-Driven Multimodel Predictive Control for Multirate Sampled-Data Nonlinear Systems

This paper is concerned with the asynchronous control problem of multi-rate sampled-data nonlinear systems. To solve this problem, the data-driven multi-model predictive control (DMMPC) strategy is proposed. First, a multi-model predictive control structure is designed such that each state variable of the multi-rate sampled-data nonlinear system can be controlled synchronously at all sampling instants. In this structure, the fuzzy neural network (FNN) is introduced to build the multi-model. Then, the prediction outputs of each state variable at all sampling instants are obtained to provide control information for the controller. Specially, the objective function with adaptive weight matrix (AWM) is designed to reduce the influence of the prediction error caused by nonlinear fitting on control performance. Then, the optimal control laws are calculated to improve the control precision. Finally, the convergence and stability of DMMPC are proved in detail. The numerical example and industrial application reveal that the proposed DMMPC can obtain considerable control performance for the multi-rate sampled-data nonlinear systems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The asynchronous control problem of the multi-rate sampled-data nonlinear system (MRSNS) may degrade the operation performance of closed-loop system. In this paper, a data-driven multi-model predictive control (DMMPC) strategy is designed for MRSNS without mechanism model. The strategy mainly consists of three parts: First, a multi-model prediction structure based on fuzzy neural network (FNN) is established to obtain the prediction output of all variables at each sampling point. The parameters of FNNs are corrected at each sampling point to ensure prediction accuracy. Second, an objective function with an adaptive weight matrix (AWM) is designed to compute the control law, in which AWM is used to reduce the influence of prediction error on control performance. Third, the effectiveness of DMMPC is verified by a numerical example and an industrial application of the wastewater treatment process. The experimental results show that DMMPC can achieve satisfied operation performance in control accuracy.

Fuzzy dynamic output feedback control for nonlinear networked multirate sampled-data systems: An integral inequality method

This paper is devoted to fuzzy dynamic output feedback control for nonlinear networked multirate sampled-data systems based on T-S fuzzy systems. Using asynchronous multirate sampled-data, a multirate fuzzy controller is designed. The resultant closed-loop system is modeled as a perturbed system with two perturbed terms which include multirate sampling and the asynchronous membership functions between the controlled plant and the controller. A novel refined integral inequality is developed, and it improves Jensen's inequality and extends Wirtinger's inequalities by considering the sawtooth structure of time-varying delays. By applying the inequality to the perturbed system and constructing a new storage function, a stability criterion and two fuzzy dynamic output feedback controller design methods are presented for the nonlinear networked multirate sampled-data systems. Finally, three illustrative examples show the effectiveness of the proposed method.

Sensors Allocation and Observer Design for Discrete Bilateral Teleoperation Systems with Multi-Rate Sampling.

This study addresses sensor allocation by analyzing exponential stability for discrete-time teleoperation systems. Previous studies mostly concentrate on the continuous-time teleoperation systems and neglect the management of significant practical phenomena, such as data-swap, the effect of sampling rates of samplers, and refresh rates of actuators on the system’s stability. A multi-rate sampling approach is proposed in this study, given the isolation of the master and slave robots in teleoperation systems which may have different hardware restrictions. This architecture collects data through numerous sensors with various sampling rates, assuming that a continuous-time controller stabilizes a linear teleoperation system. The aim is to assign each position and velocity signals to sensors with different sampling rates and divide the state vector between sensors to guarantee the stability of the resulting multi-rate sampled-data teleoperation system. Sufficient Krasovskii-based conditions will be provided to preserve the exponential stability of the system. This problem will be transformed into a mixed-integer program with LMIs (linear matrix inequalities). These conditions are also used to design the observers for the multi-rate teleoperation systems whose estimation errors converge exponentially to the origin. The results are validated by numerical simulations which are useful in designing sensor networks for teleoperation systems.

Moving horizon estimation for multirate systems with time-varying time-delays

This paper presents a moving horizon estimation approach for the multirate sampled-data system with unknown time-delay sequence. To estimate the unknown variables of interest, two main challenging issues need to be addressed: (a) synthesizing the multirate input and output data for state estimation, (b) simultaneously estimating the continuous state and discrete time-delay sequence. In this work a moving horizon estimation based approach is developed to tackle these issues. The proposed approach can simultaneously estimate both the continuous states and discrete time-delay sequence for dynamic systems. The effects of different noise level on the estimation of continuous states and discrete time-delay sequence are analyzed. The effectiveness of this method is illustrated through a simulation study.

Identification and Accommodation of Control Actuator Faults Using Multi-rate Sampled Measurements

Abstract This work presents a model-based approach for the detection, estimation and accommodation of control actuator faults in dynamic processes controlled using multi-rate sampled state measurements. Initially, a model-based state feedback controller that employs an inter-sample model predictor to compensate for the unavailability of continuous state measurements is designed. Characterizations of both the stability and performance properties of the multi-rate sampled-data closed-loop system are obtained and expressed in terms of the measurement sampling rates, the magnitudes of the faults, and the various predictor and controller design parameters. A parameter estimator that estimates the magnitudes of the faults by minimizing the error between the estimated and sampled states over a moving horizon is then introduced and used to determine the fault or health status of the control actuators at the sampling times. The identification of faults triggers a fault accommodation scheme that adjusts selected predictor and controller design parameters to simultaneously preserve closed-loop stability and optimize a pre-defined performance metric. The implementation of the developed approach is illustrated using a simulated model of a solid oxide fuel cell system subject to both stability and performance-degrading actuator faults. A discussion of some of the intricacies of the multi-rate sampling scheme and how they impact the practical implementation of the fault identification and accommodation schemes is presented.

Model-based strategies for sensor fault accommodation in uncertain dynamic processes with multi-rate sampled measurements

This work presents model-based strategies for the accommodation of sensor faults in dynamic processes with multi-rate sampled state measurements. The developed strategies account explicitly for both closed-loop stability and performance considerations. Initially, a model-based feedback control system, in which a model predictor compensates for the unavailability of state measurements between sampling times, is designed. The stability and performance characteristics of the multi-rate sampled-data closed-loop system are analyzed and explicitly characterized in terms of the state sampling rates, the fault parameters, and the various process, model and controller design parameters. The resulting characterizations provide insight into the robustness and margins of tolerable faults that can be accommodated, and are used to develop both stability-based and performance-based fault accommodation schemes that aim to maintain closed-loop stability and minimize the degradation of closed-loop performance in the presence of sensor faults. Two types of sensor faults are considered. These include faults that manifest themselves as improper sensor readings, as well as faults that cause drift in the sensor sampling rate. The first type of fault introduces errors in the model state updates at the sampling times, while the second type of fault alters the rate at which the sensors sample the process states. The developed methods are illustrated through a case study involving a cascade of two non-isothermal continuous-stirred tank reactors with plant-model mismatch and access to full state measurements that are sampled at different rates. The case study gives some insight into the effects of sensor faults on the stability and performance of the sampled-data state feedback control system, and how these effects can be mitigated through use of fault-tolerant control.

An Approach to Fault Detection for Multirate Sampled-Data Systems With Frequency Specifications

This paper is concerned with the design of fault detection for sampled-data systems, which are based on multirate sampling, with frequency specifications. A general multirate system is considered in this paper, where not only the inputs and outputs but also their different channels have different sampling rates. The purpose of this paper is to make this residual system with multirate sampling satisfy a given disturbance attenuation level over a restricted frequency range. With the use of the lifting technique, this paper reformulates a single-rate linear time-invariant system, which is equivalent to the multirate time-varying system. For a given restricted frequency range, convex conditions are obtained in designing a required fault detection filter. Then, the restricted frequency ranges problem are also solved specifically via the generalized Kalman–Yakubovic–Popov lemma. Finally, this paper uses a continuous-stirred tank reactor system to illustrate the effectiveness and advantages of the fault detection filter design method.

Robust sampled‐data control of non‐linear LPV systems: time‐dependent functional approach

This study addresses the problem of robust exponential stability and stabilisation of sampled-data linear parameter varying (LPV) systems with an aperiodic sampling rate. Utilising the input delay approach and taking the distance between real and measured parameters into account, new stability and stabilisation conditions are derived for LPV systems with arbitrary dependence on the parameters. By means of a modified parameter dependent Lyapunov-Krasovskii functional, stability conditions are formulated as a set of parameter-dependent linear matrix inequalities (PLMIs) which are suitable to investigate the effect of the sampling rate on the closed-loop stability. Furthermore, sufficient conditions to guarantee the feasibility of PLMIs over the set of whole parameters are derived that lead to the feasibility of a finite number of linear matrix inequalities. Applying the projection lemma new stability analysis conditions are obtained and shown to be suitable for the stabilisation problem. Under the new stability criteria, an efficient procedure developed for robust sampled-data controller design in the presence of uncertainty on the varying parameters and unknown time varying sampling rate. The proposed method is applied to a sampled-data fuzzy control problem of a non-linear system and multi-rate sampled-data LPV systems. Several examples show the efficiency of the method.

Controllability and stabilizability of multi-rate sampled data systems

This paper gives sufficient conditions for controllability and stabilizability of multi-rate sampled data systems. For this purpose, it is firstly proposed that if the actuator communication sequence of a bandwidth limited networked system is equidistant, then the resulting model is mathematically equivalent to a multi-rate sampled data system. Secondly, recent results on controllability and stabilizability of bandwidth limited networked systems are reduced to the case of equidistant communication sequences. The established conditions enhance existing results on controllability and stabilizability of multi-rate sampled data systems. Also, it is shown that two independently established conditions for controllability and stabilizability of networked systems are equivalent in the special case of equidistant actuator communication sequences.

Output Feedback Control of Multirate Sampled-Data Systems With Frequency Specifications

This paper addresses the problem of $H_{\infty }$ output feedback controller design of multirate sampled-data systems with frequency specifications. The general multirate situation is considered, where not only the inputs and outputs but also different channels of the inputs or the outputs have different sampling rates. The aim of this paper is to design an output feedback controller for multirate sampled-data systems in order to ensure an $H_{\infty }$ performance level over a restricted frequency, which includes the standard $H_{\infty }$ control problem as a special case and can better reflect the requirement of attenuating disturbances over restricted frequency ranges. The problem is solved via reformulating the multirate sampled-data system with an output feedback controller and utilizing the generalized Kalman–Yakubovic–Popov lemma to deal with the restricted frequency specifications. For a given restricted frequency range, convex conditions are derived for the existence of a required controller and cases for low/high/entire frequency ranges are also addressed specifically. Finally, illustrative examples are presented to show the effectiveness and advantage of the proposed controller design methods.

Event-triggered multi-rate fusion estimation for uncertain system with stochastic nonlinearities and colored measurement noises

This paper is concerned with the event-triggered robust fusion estimation problem for uncertain multi-rate sampled-data systems with stochastic nonlinearities and the colored measurement noises. Due to the effects of stochastic nonlinearities and parameter uncertainties, a new augmentation approach is proposed by which the multi-rate sampled-data system under consideration is transformed into the single-rate system. In order to eliminate the effect of the colored measurement noises, a measurement model with uncorrected noises is established. Based on the measurement model established, a set of local event-triggered filters is constructed and the upper bounds of the local filtering error covariances at each sampling instant are obtained. By using the Lagrange multiplier method, the local filter parameters are designed such that the upper bound obtained is minimum. For the local state estimates, a new fusion estimation scheme is proposed with the help of covariance intersection (CI) method and the consistency of the proposed CI-based fusion estimation scheme is shown. Finally, an illustrative example is presented to verify the effectiveness of the fusion estimation scheme proposed.

Multirate Identification of Mechanical Resonances Beyond the Nyquist Frequency in High-Performance Mechatronic Systems

Due to the aliasing effect produced by the sampling operation, mechanical resonant modes beyond the Nyquist frequency are difficult to be identified using conventional system identification techniques. In this paper, a parametric approach is proposed to identify these resonances. Identification is performed in a closed-loop multirate sampled-data system, where the input is sampled integer times faster than the output. First, the polynomial transformation technique-based recursive least-squares algorithm with a dead-zone is designed to identify the mixed-rate model. Next, the identified mixed-rate model is used to compute the fast-rate model, from which the resonant modes beyond the Nyquist frequency can be extracted. The proposed approach is evaluated on the head-positioning servo control system of a hard disk drive during the track-seeking mode and the effectiveness is verified by both simulation and experimental results. As compared to analog sensors, the proposed approach can potentially be implemented to identify mechanical resonances to arbitrarily high frequencies by increasing the sampling rate of the digital-to-analog converter.

A Bode-Like Integral for Discrete Linear Time-Periodic Systems

We present a generalization of the Bode integral formula for discrete-time linear periodic systems. It is shown that similar to the classical Bode integral formula, the sensitivity integral for a discrete-time linear periodic system depends only on the open-loop dynamics of the system; in particular, on the open-loop characteristic multipliers outside the unit circle in the complex plane. The integral is derived by using an asymptotic eigenvalue distribution theorem for block Toeplitz matrices, which does not require the open loop system to be stable or the disturbance to be Gaussian. The result is demonstrated through application to a class of multi-rate sampled data systems with commensurate rates.

Sensor allocation with guaranteed exponential stability for linear multi-rate sampled-data systems

This paper addresses sensor allocation with guaranteed exponential stability for linear multi-rate sampled-data systems. It is assumed that a continuous-time linear plant is exponentially stabilized by a continuous-time linear controller. Given sensors with incommensurate sampling rates, the objective is to allocate each state to a sensor such that the resulting multi-rate sampled-data system remains exponentially stable. The main contributions of this paper are twofold. First, we propose sufficient Krasovskii-based conditions to partition the state vector among sensors such that exponential stability of the closed-loop system is guaranteed. Second, the problem of finding a partition that guarantees exponential stability is cast as a mixed integer program subject to linear matrix inequalities. The theoretical results are successfully applied to two robotic problems: path-following in unicycles and hovering in quadrotors. Copyright © 2015 John Wiley & Sons, Ltd.

Design of Consensus Controllers for Multi-rate Sampled-data Strict-Feedback Multi-agent Systems

Design of state feedback consensus controllers is considered for multi-rate sampled-data strict-feedback multi-agent systems. First state feedback consensus controllers are designed for continuous-time strict-feedback multi-agent systems. Then the Euler model is used to estimate the states at input sampling times between successive measurement sampling times. It is shown that emulation controllers of designed continuous-time state feedback controllers with estimated states achieve consensus for multi-rate sampled-data strict-feedback multi-agent systems. The proposed design method is also applied to consensus control of multi-rate sampled-data fully-actuated ships.

Stability and stabilization of linear sampled-data systems with multi-rate samplers and time driven zero order holds

In multi-rate sampled-data systems, a continuous-time plant is controlled by a discrete-time controller which is located in the feedback loop between sensors with different sampling rates and actuators with different refresh rates. The main contribution of this paper is to propose sufficient Krasovskii-based stability and stabilization criteria for linear sampled-data systems, with multi-rate samplers and time driven zero order holds. For stability analysis, it is assumed that an exponentially stabilizing controller is already designed in continuous-time and is implemented as a discrete-time controller. For each sensor (or actuator), the problem of finding an upper bound on the lowest sampling frequency (or refresh rate) that guarantees exponential stability is cast as an optimization problem in terms of linear matrix inequalities (LMIs). Furthermore, sufficient conditions for controller synthesis are formulated as LMIs. It is shown through examples that choosing the right sensors (or actuators) with adequate sampling frequencies (or refresh rates) has a considerable impact on stability of the closed-loop system.

H∞Controller Design for Asynchronous Multirate Sampled-Data Systems

This paper considers the analysis and synthesis of a linear discrete asynchronous multirate sampled-data system. AnH∞controller based on an observer is proposed, which guarantees the stability of the closed system and makes theH∞norm of the closed system less than a given attenuation level. To improve the performance further, a tradeoff strategy is applied. That is, the exogenous signals sampled at different rates are lifted to an appropriate signal rate, while the endogenous signals are not lifted for avoiding the causal constraint and the dimension multiplied again. The controller is obtained by solving the corresponding matrix inequality, which can be calculated by Matlab. Finally, an example is presented to demonstrate the validity of these methods.

Predictive Control of a Reactive Distillation Column using Multi-rate DAE EKF

Control of product purity is of paramount importance in effective control of tightly integrated process such as reactive distillation. In practice, however, measurements of product concentrations may be unavailable or may be available at slower sampling rates when compared with other measurements. A cost effective approach to improve control of such systems is to develop a state estimator that can accommodate measurements at multiple rates and use it in controller development. In this work, DAE EKF formulation developed by Mandela et al. (2010) is modified to accommodate measurements available at multiple sampling rates. A successive linearization based nonlinear MPC scheme is then developed for controlling a system modeled as DAEs. Observer error feedback approach developed by Hunag et al. (2012) has been extended to achieve offset reduction and to improve regulatory control of a multi-rate sampled data system. The efficacy of the proposed approach is demonstrated by conducting simulation studies on an ideal reactive distillation system. Analysis of the simulation results reveals that the feedback introduced using the multi-rate concentration measurements reduces the offset significantly in the face of unmeasured disturbances of moderate magnitude.