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Based on the existing research work on the modeling and control of cyclically operated high-throughput screening systems, this paper presents the scheduling and control of high-throughput screening systems with uncertainties and disturbances. Different definitions of disturbance decoupling problems are considered in order to achieve the optimal scheduling of high-throughput screening systems. Online scheduling was achieved by computing optimal prefilters and output feedback controllers, which can be computed using residuation theory. The control strategies achieved by the controllers are optimal in the sense of the just-in-time criterion commonly used in industrial schedule practice.

Based on the existing research work on the modeling and control of cyclically operated high-throughput screening systems, this paper presents the scheduling and control of high-throughput screening systems with uncertainties and disturbances. Different definitions of disturbance decoupling problems are considered in order to achieve the optimal scheduling of high-throughput screening systems. Online scheduling was achieved by computing optimal prefilters and output feedback controllers, which can be computed using residuation theory. The control strategies achieved by the controllers are optimal in the sense of the just-in-time criterion commonly used in industrial schedule practice. [ABSTRACT FROM AUTHOR]

This paper presents a reliable algebraic method for fault detection and identification for rigid robots considering additive faults and external forces. The presented method is based on the reconstruction of a residual or the fault by nonlinear differential algebraic expressions using the polynomial approximation operator. Furthermore, it is shown how the filter parameters and the noise suppression properties of the resulting filter can be parameterized for reliable fault diagnosis according to the characteristics of the fault signals in the frequency domain. The presented method provides an evaluable expression that can be used to explicitly estimate the influence of measurement noise, quantization, numerical errors, and parameter uncertainties in terms of computable error bounds, thus ensuring reliable fault diagnosis. Based on a SCARA robot, a comparison of the method with the generalized momentum observer is performed, highlighting the advantages of the presented approach. Furthermore, it is applied to a real-world application of a delta robot with parallel kinematics for the identification of additive faults while considering interactions due to the application. For this purpose, the appropriate parameterization of the filter is determined and then the feasibility of the method is verified by the implementation on a real-time controller. Note to Practitioners—Especially in human-robot collaboration or similar safety-critical industrial applications of robots, real-time capable monitoring of faults or contact forces is essential. The diagnosis must be both precise and provide reliable information within a specified time. The present concept enables this real-time capable fault diagnosis and can be easily evaluated on a controller using FIR filters and simple algebraic equations. The parameterization can be used as a basis for the evaluation of boundaries and guarantees. [ABSTRACT FROM AUTHOR]

This paper addresses an augmented nonlinear lateral vehicle and lane keeping dynamics in the presence of some unknown disturbances. In a geometric basin, considering unobservable spaces, their orthogonal complements, and using control invariant properties, a disturbance decoupling mechanism is designed for the mentioned dynamics. Afterward, a nonlinear tracking controller is designed to steer the vehicle on a reference path. The obtained disturbance decoupling and tracking controllers are implemented on a typical passenger car in a simulation environment to demonstrate the effectiveness and performance of the proposed method. It is shown that the controller decouples both the uniformly distributed and exponentially attenuated disturbances from the output.

The problem of making the output of a linear system with polytopic uncertainties and discontinuities in the state evolution totally insensitive to an unknown disturbance input by state feedback is investigated. Suitable geometric notions are introduced and used to provide a structural, constructive solvability condition. The requirement of achieving global robust asymptotic stability of the compensated dynamics is then added and further solvability conditions are provided by requiring that the time instants at which discontinuities in the state evolution, or jumps, occur are sufficiently far from each other. [ABSTRACT FROM AUTHOR]

This paper investigates the theoretical requirements for conformable fractional-order linear systems to satisfy the fundamental principles of invariant subspaces, which are the foundation of geometric control theory, for the first time. The problem of exact disturbance decoupling in conformable fractional linear systems is tackled using newly developed geometric tools. Moreover, a set of necessary and sufficient conditions has been established to address this problem, which, at the same time, stabilizes the compensated system for any initial condition in the presence of unknown disturbances. We also show that employing the conformable fractional model as a synthesis model for geometric geometric decoupling control provides a better understanding of the structural system-theoretic characteristics of fractional systems, while upholding the fundamental properties of integer systems. To illustrate the applicability and effectiveness of the theoretical findings, two numerical simulations, including an application to an active suspension system, were carried out and compared with those of the Caputo derivative. [ABSTRACT FROM AUTHOR]

Two types of high-order fully actuated (HOFA) system models subject to external disturbances are firstly introduced. For the type of HOFA systems with deterministic disturbances, the problem of disturbance attenuation via state feedback is treated. While for the type of HOFA systems with dynamical disturbances, the problem of asymptotic disturbance decoupling via output feedback is considered. Utilising the full-actuation feature of the HOFA systems, disturbance attenuation and decoupling controllers for the corresponding systems are conveniently designed such that constant linear closed-loop systems with designed disturbance rejection properties are resulted in. Parametric designs for both controllers are provided, and disturbance attenuation is achieved by establishing a parametric form of the closed-loop transfer function from the disturbance to the output, while the parametric form of the disturbance decoupling controller is derived based on a complete parametric solution to a type of generalised Sylvester equations (GSEs). As a consequence of the parameter approaches, additional performance requirements on the closed-loop systems can be also easily handled. An illustrative example demonstrates the effect of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a new parametric approach is developed for disturbance attenuation in observer design of linear time-invariant systems. First, based on the general solution to a type of generalised Sylvester equations, a complete parametric form of the observer gain matrix is established. Secondly, a new disturbance attenuation index is introduced, and the parameters are further optimised to minimise the index. Under certain conditions, the optimal solution of this optimisation problem is obtained. Finally, the proposed method is used to design the robust observer for the yaw/roll channel attitude control system of a nonrotating missile. It is verified from the simulation results that the proposed method shows a stronger tolerance to disturbances compared with the traditional robust pole assignment method. [ABSTRACT FROM AUTHOR]

This paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven.

Summary: In this article, we investigate the almost output consensus problem for nonlinear multiagent systems under the influence of external disturbances. The problem of almost output consensus of nonlinear multiagent systems is formulated. Conditions on the nonlinear systems are established under which distributed consensus protocols are designed in a recursive manner. These protocols are shown to achieve almost output consensus, that is, output consensus of the system is achieved in the absence of the disturbances and the L2‐gain from the disturbances to the output consensus error of agents when the system is operating in output consensus can be made arbitrarily small. A simulation example is shown to verify the theoretical results. [ABSTRACT FROM AUTHOR]

We develop a geometric approach for fractional linear time-invariant systems with Caputo-type derivatives. In particular, we generalize the fundamental notions of invariance and controlled invariance to the fractional setting. We then exploit this new geometric framework to address the disturbance decoupling problem via static pseudostate feedback, with and without stability. Our main contribution is a set of necessary and sufficient conditions for the disturbance decoupling problem that are related to the input-output properties of the closed-loop system, and hence they are applicable not just to Caputo-type derivatives but, more broadly, to any type of fractional system. These results show that, while the conditions for guaranteeing the existence of a decoupling pseudostate feedback remain essentially unchanged, the underlying theoretical framework is substantially different, because the fractional derivative is a nonlocal operator and this property plays a major role in the characterization of the evolution of the pseudostate trajectory. In particular, we show that, unlike the integer case, the infinite-dimensional nature of fractional systems means that feedback control is insufficient to maintain the pseudostate trajectory on a controlled invariant subspace, unless the entire past history of the pseudostate has evolved on that subspace. However, feedforward control can achieve this task under certain necessary and sufficient geometric conditions. [ABSTRACT FROM AUTHOR]

This paper presents a new disturbance decoupling and rejection method for a multi-connected system, and introduces the composite controller based on disturbance compensator and the state feedback control. While in action, a developed dynamic model of a 2DOF robot system was studied and analyzed. The movement of one joint affects the motion of the other, which brings the control performance down. In order to compensate and keep the desired control performances, we designed a double active control system which can effectively reject the direct mutual disturbances. These disturbances are considered the known uncertainties and can be experimentally determined. The designed control system consists of two controllers, the first one is an inner loop controller and works as a disturbance compensator that attenuates the known disturbances. And the second one, on the other hand, is an outer loop controller, which was designed based on H∞ control theory to maintain the system stability and a robust control performance under the unpredictable uncertainties. In this paper, simulation and experiments were conducted using a PID controller, and the designed control system, as well as changing the payload attached to the end-effector in order to test the control performance. Finally, the results show that the proposed system suppresses and rejects the mutual disturbances effectively with enhanced tracking performances. [ABSTRACT FROM AUTHOR]

This paper presents an attitude active fault tolerant control for a satellite simulated model. The proposed fault tolerant controller consists of two main parts: a nominal controller, designed assuming that the system is healthy, and a fault diagnosis module which aims at detecting, isolating and estimating the fault affecting the system. The fault diagnosis module is designed by using the non-linear geometric approach tool which allows to obtain detection residuals and estimation filter decoupled from the aerodynamic disturbance representing the main uncertainty in low Earth orbits. The simulation results show the advantages, in terms of attitude tracking accuracy, obtainable when implementing the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an optimization-based perspective for incorporating disturbance decoupling constraints into controller synthesis, which paves the way for utilizing numerical optimization tools. We consider the constraints arising from the following sets of static state feedback: (i) The set of all disturbance decoupling controllers; (ii) The set of all disturbance decoupling and stabilizing controllers. To inner approximate these sets by means of matrix equations or inequalities, we provide a unifying review of the relevant results of the geometric control theory. The approximations build on the characterization of controlled invariant subspaces in terms of the solvability of a linear matrix equation (LME) involving the state feedback. The set (i) is inner approximated through the LME associated with any element of an upper semilattice generated by controlled invariant subspaces. The set (ii) is inner approximated through a bilinear matrix inequality (BMI) and the LME associated with any element of a different upper semilattice generated by internally stabilizable controlled invariant subspaces. However, the resulting inner approximations depend on the subspaces chosen from the semilattices. It is shown that a specific (internally stabilizable) self-bounded controlled invariant subspace, which is the best choice regarding eigenvalue assignment, yields the largest inner approximation for both of the sets among (internally stabilizable) self-bounded controlled invariant subspaces. The inner approximations exactly characterize the controller sets under particular structural conditions. We have been driven by two primary motivations in investigating inner approximations for the sets above: (i) Enable the formulation of a variety of equality (and inequality) constrained optimization problems, where cost functions, such as a norm of the state feedback, can be minimized over a large subset of the set of all disturbance decoupling (and stabilizing) controllers; (ii) Introduce the disturbance decoupling constraints to members of the control systems community who might not be quite familiar with the elegant geometric state-space theory, similar to the authors themselves. This can add another dimension to research endeavors in resilient control of networked multi-agent systems. [ABSTRACT FROM AUTHOR]

The integrity and transparency of a haptic feedback in a bilateral control is crucial for precise and accurate operators’ sensation during human–machine interactions. Conventional master and slave bilateral control systems are often subject to unknown or unwanted disturbances and dynamics in the actuators and powertrain linkages that hamper the haptic feedback integrity and transparency. Force sensor torque sensing and feedback control are required to mitigate these effects. In contrast to the conventional approach of introducing torque sensing using a mechanical spring, this paper introduces a magnetic coupling as a torque sensor to detect reaction torque between the human input and the master actuator. Disturbance observer-based torque feedback control is designed to suppress the disturbances and tailor the haptic transparency dynamics. Experimental results on a virtual reality interaction system, which involves the steering wheel bilateral control in a cyber-physical driving simulator system, demonstrate the feasibility and effectiveness of the proposed method with improved haptic integrity and transparency.

In this paper, we consider the problem of disturbance decoupling for a class of non-minimum-phase nonlinear systems. Based on the notion of partially minimum phaseness, we shall characterize all actions of disturbances which can be decoupled via a static state feedback while preserving stability of the internal residual dynamics. The proposed methodology is then extended to the sampled-data framework via multi-rate design to cope with the rising of the so-called sampling zero dynamics intrinsically induced by classical single-rate sampling. [ABSTRACT FROM AUTHOR]

• The reduced state transition matrix of Boolean (control) networks is introduced to analyze the disturbance decoupling problem. • The relationship between three types of disturbance decoupling and robust indistinguishability is revealed. • Algebraic conditions with lower computational complexity are given for disturbance decoupling. Disturbances are ubiquitous and affect the normal operation of systems. This paper investigates the disturbance decoupling problem of Boolean networks (BNs) and Boolean control networks (BCNs) by a robust indistinguishability method. Utilizing a new method based on the reduced state transition matrix, the relationship between three types of disturbance decoupling and robust indistinguishability is revealed, which also builds a link between robust observability and disturbance decoupling. Based on a parameter extraction mapping, several feasible criteria are presented for original and weak disturbance decoupling of BNs and BCNs. Additionally, our approach is more concise and has a lower computational complexity than the existing methods. Finally, two examples are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The paper studies the problem of disturbance decoupling of nonlinear hybrid systems. The hybrid systems under consideration are switched systems that consist of finite automaton, which defines the switching rule, a set of nonlinear discrete-time systems and the so-called mode activator, that defines an input for the automaton. Such systems allow to handle more complex switching rules than just time- or state-dependent switchings. The goal of the paper is to achieve the disturbance decoupling by dynamic measurement feedback. The advantage of such feedback is that it does not require estimations of state variables. Sufficient conditions are found under which there exists a dynamic measurement feedback, such that in the closed-loop system the controlled output of the hybrid system does not depend on the disturbance. An algebraic approach called functions’ algebra is used, which can address in a similar manner both discrete-time systems and discrete-event systems (finite automaton). [ABSTRACT FROM AUTHOR]

This paper considers the disturbance decoupling problem by the dynamic measurement feedback for discrete-time nonlinear control systems. To solve this problem, the algebraic approach, called the logic-dynamic approach, is used. Such an approach assumes that the system description may contain non-smooth functions. Necessary and sufficient conditions are obtained in terms of matrices similar to controlled and ( h , f ) -invariant functions. Furthermore, procedures are developed to determine the corresponding matrices and the dynamic measurement feedback.

This paper investigates the disturbance decoupling problem for Boolean control networks. Firstly, using the matrix semi‐tensor product, the logical dynamic equations of Boolean control networks are converted into discrete time linear equations. Secondly, the solvability of the disturbance decoupling problem is analyzed based on the structure matrices of BCNs, and a method for design state‐feedback controllers is put forward to deal with this problem. Two necessary and sufficient conditions for the disturbance decoupling problem of BCNs are obtained. Then an algorithm is provided to design controllers for calculating the disturbance decoupling forms of Boolean control networks. Finally, an illustrative example is given to describe the proposed algorithm. [ABSTRACT FROM AUTHOR]

This study presents a detailed survey on recent development of logical networks and its applications, including the background of logical networks, the theory of a new matrix product called semi‐tensor product (STP) of matrices, some fundamental works on logical networks, and some current research works. Particularly, some fundamental works on logical networks are presented for the past years, including controllability, stability and stabilisation, synchronisation, disturbance decoupling and so on. Due to the great potential of STP in dealing with logical networks, a surge of attraction from overseas is paid on the study of STP and its applications. Currently, some new research areas are widely studied including pinning control, function perturbations, system decomposition, trajectory control, output tracking issues, symbolic dynamics and so on. The main concern of this study is to present a comprehensive introduction to logical networks and some other applications under the framework of STP of matrices. [ABSTRACT FROM AUTHOR]

We study disturbance decoupling for linear differential–algebraic systems which are not necessarily regular. Compared to previous approaches, where state feedback is used, we use the concept of behavioral feedback which allows to study a larger class of systems. We derive geometric characterizations for solvability of the disturbance decoupling problem following the classical approach. Exploiting the freedom in the choice of the behavioral feedback we show that whenever disturbance decoupling can be achieved by behavioral feedback we may additionally achieve autonomous zero dynamics. Finally we solve Lebret’s twenty year old open problem concerning disturbance decoupling with output uniqueness using behavioral feedback. [ABSTRACT FROM AUTHOR]

The design and the experimental validation of a continuous‐time model predictive control (CTMPC) for a permanent magnet synchronous motor (PMSM) drive with disturbance decoupling is discussed. The CTMPC approach uses Taylor series expansion to derive a closed‐form solution to the problem of model predictive control even though the system behaviour is described by a non‐linear model. This type of controller requires an exact knowledge of the system model to guarantee an accurate prediction of the system behaviour, while the PMSM is usually subjected to model uncertainties and external disturbances such as the load torque. Moreover, in the proposed approach, the predicted speed tracking error is directly used to determine the required voltage command without the need for a cascaded control scheme. As a result, the load torque is seen as unmatched disturbance which makes exact disturbance decoupling more challenging. To overcome such a problem, a non‐linear disturbance observer is designed and combined with the CTMPC method to enhance the prediction accuracy under parameter variation and unknown load torque. The feasibility of the proposed approach is experimentally investigated, and good transient and steady‐state performances are obtained. [ABSTRACT FROM AUTHOR]

In this paper we study the question under which conditions a linear multi-modal system is disturbance decoupled. We establish necessary and sufficient geometric conditions from which the existing results on switched linear systems and conewise linear systems can be recovered as special cases. Also, we apply these conditions to a class of linear complementarity systems in order to obtain a more crisp characterization. [ABSTRACT FROM AUTHOR]

In this paper, the sliding mode dynamic disturbance decoupling tracking control method based on the linear extended state observer (LESO) is proposed for a class of square multivariable nonlinear uncertain system. The model plant contains the known linear dynamics, the unknown nonlinear dynamics and the internal and external disturbances, and the various input-output pairs are interacted. The system states are not available for measurement. An improved LESO is developed. The leading feature which is different from the typical ESO lies in that its extended state does not contain the known linear dynamics. The improved LESO can guarantee the error variables to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. So this ball radius can be arbitrarily as small as desired by tuning design parameters. And we give a simple method by which the gain parameters of LESO can be computed easily. This estimation to the total disturbance of the original system is introduced into the sliding mode control design to complete disturbance rejection and decoupling. Rigorous stability analysis shows that the system output can track the desired signal closely. Finally, a class of mass-spring-damper system is taken to make the numerical simulation analysis to illustrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In multi-sensor fusion, it is hard to guarantee that all sensors have an identical sampling rate, especially in the distributive and/or heterogeneous case. Meanwhile, stochastic noise, unknown inputs (UIs), and faults may coexist in complex environment. To this end, we propose the problem of joint optimal filtering and fault detection (FD) for multi-rate sensor fusion subject to UIs, stochastic noise with known covariance, and faults imposed on the actuator and sensors. Furthermore, the new scheme of optimal multi-rate observer (MRO) is presented and applied to detect faults. The observer parameters are determined optimally in pursuit of the UI decoupling and maximizing noise attenuation under the causality constraint due to multi-rate nature. Finally, the output estimation error of the MRO is used as a residual signal for FD via a hypothesis test in which the threshold is adaptively designed according to the MRO parameters. One numerical example is given to show the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition is derived for the solvability of the disturbance decoupling problem by a pure shift dynamic compensator. It corrects previously obtained results for multi-input multi-output (MIMO) systems. Also, necessary and sufficient conditions are given for the solvability of the problem by a dynamic compensator for single input single output (SISO) systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of leader-following almost output consensus for discrete-time multi-agent systems with heterogeneous follower agents. Conditions on agent dynamics, the communication topology and how the disturbance enters the agent dynamics are established under which leader-following almost output consensus can be achieved, that is, the leader-following output consensus can be reached with any pre-specified level of accuracy and the effect of the disturbance on the leader-following consensus can be attenuated to any pre-specified level. A family of state feedback consensus protocols are constructed by using the low gain feedback design technique and a modified discrete-time Riccati equation. These consensus protocols are shown to achieve leader-following almost output consensus. Additional conditions are identified under which output feedback results are established. Simulation results demonstrate the effectiveness of the proposed consensus protocols. [ABSTRACT FROM AUTHOR]

The paper addresses the disturbance decoupling problem by dynamic measurement feedback for discrete event systems. The mathematical technique called the pair algebra of partitions is used. The paper gives sufficient solvability conditions and a procedure to compute the required feedback. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The disturbance decoupling problems via measurement feedback for switched linear systems are studied in the framework of the so-called geometric approach. At first, the robust ( C i ∈ I , A i ∈ I , B i ∈ I ) -pair which incorporates both the concepts of robust controlled ( A i ∈ I , B i ∈ I ) -invariant and its dual robust conditioned ( C i ∈ I , A i ∈ I ) -invariant subspaces for a family of linear systems is investigated. Next, disturbance decoupling problems via dynamic and/or static measurement feedback under arbitrary switching for switched linear systems are formulated, and necessary and sufficient conditions for the problems to be solvable are presented. After that the stabilization for disturbance decoupled systems under arbitrary switching is also discussed. Finally, an illustrative numerical example is given. [ABSTRACT FROM AUTHOR]

This paper studies the disturbance decoupling problem for multi-agent systems with single integrator dynamics and a directed communication graph. We are interested in topological conditions that imply the disturbance decoupling of the network, and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled. In particular, we will develop a class of graph partitions, which can be described as a “topological translation” of controlled invariant subspaces in the context of dynamical networks. Then, we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled, as well as conditions guaranteeing solvability of the disturbance decoupling problem. The proposed results are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]