Dynamic Output Controller Research Articles

‘Adequate amount of data’‐driven system design theory: how far can we know/control/protect?

In contrast to the natural tendency of many researchers to focus on collecting as much data as possible, Assistant Professor Tomonori Sadamoto, from the Department of Mechanical Engineering and Intelligent Systems at the University of Electro-Communications in Japan, believes that the pursuit of big data is not always desirable. He is promoting a shift towards the acceptance of a “adequate amount of data”-driven system design theory. Sadamoto is concentrating on data-driven methodologies and their application in social systems. Through key international collaborations with colleagues at leading institutions, he is advancing his research. His work on data-driven methodologies focuses on interdisciplinary studies that combine machine learning and control theory. His more applied work primarily falls within the realm of smart grids. In his projects, he formulates his questions mathematically from the perspective of control theory. For instance, Sadamoto has developed a novel mathematical tool known as the VARX (vector autoregressive with exogenous input) framework, which facilitates the tractable analysis of dynamic systems. Using this new tool, he has developed data-dependent system identification analyses when only an “insufficient amount of data” is available. Furthermore, for the first time, Sadamoto was able to demonstrate that the informativeness of data in a certain class of dynamic output controller design is equivalent to the identification of the target system. His efforts are aimed at expanding the horizons of these novel control theories into the field of smart grids.

Admissible H$_\infty$ Control of Fuzzy Singular Fractional Order Multi-Agent Systems With External Disturbances

This brief consider the problem about admissible consensus of fuzzy singular fractional order multi agent systems (FSFOMAS). By designing a new distributed fuzzy dynamic output control strategy, the coupled system achieves admissible while satisfying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> performance. Then, when the fuzzy models reduce to ordinary fractional order multi agent systems (FOMAS), a new sufficient condition for determining system consensus is given. The above results all depend only on the eigenvalues of the Laplace matrix and the state matrix of the system and consist of linear matrix inequalities (LMIs). Finally, a numerical example and a practical circuit example can demonstrate the feasibility and validity of the theorems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Due to the unique memorability of fractional orders, their application to fuzzy multi-agent systems will bring system performance metrics closer to reality. This paper investigates the stabilization of singular fuzzy fractional-order multi-agent systems with the perturbation case, the pulse case. We know that in practical applications a single variable does not accurately describe the phenomenon. Therefore we have introduced the concepts of multi-agent, fuzzy, singular and fractional orders in order to describe the system model more accurately. The main objective is to bring the system into equilibrium in the closest possible approximation to reality. The performance metrics of the system are optimised to bring the system to an optimal state. Finally, two examples are used to illustrate the validity of our theorems.

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

This paper studies the global control problem, in the sense of “almost stabilization” or state regulation, for a class of time-delay minimum-phase nonlinear systems via delay-free dynamic compensation. Both dynamic state and output feedback control schemes are developed. By taking advantage of dynamic rather than static feedback, we design delay-independent dynamic state and output feedback compensators, respectively, to achieve asymptotic state regulation with global stability. In the case of dynamic state feedback, a structural condition is imposed on the inverse dynamics that are nonlinear yet imply linear zero dynamics. In the case of dynamic output feedback, more strict conditions on the nonlinearity are characterized to guarantee the existence of a dynamic output controller. In both cases, it is proved by the Lyapunov–Krasovskii functional method, combined with the Barbalat’s lemma, that all the states of the time-delay minimum-phase systems are regulated to zero and boundedness of the closed-loop system is ensured. Two examples are given to validate the proposed delay-free dynamic compensators.

Lateral string stabilization of connected vehicles with time-varying longitude velocity based on gain-scheduling approach

This paper deals with the controller design for lateral string stabilization and vehicle following in connected vehicles with time-varying longitude velocity. The platoon of the vehicles is modeled based on LPV systems by considering the longitude velocity as scheduling parameter. To derive results less conservative than existing methods, polynomial functions are suggested to approximate various nonlinear functions of the scheduling parameter in the lateral dynamics. Approximation errors are considered as bounded uncertain parameters. Moreover, H∞ gain-scheduling dynamic output controller is designed by defining appropriate weighting functions and considering uncertain parameters in order to suppress the disturbances along the platoon. Towards this, new change of variables is proposed to derive sufficient conditions that guarantee H∞ performance in the form of parameter-dependent Linear Matrix Inequalities (LMIs). Since the measurements are available in sampling times and are transmitted through network with delay or packet dropouts, new method is proposed to determine the maximum sampling interval that guarantee the stability of the closed-loop LPV system. This method is derived based on modeling sampling process by delay operator with bounded L2 gain. The performance of the proposed gain-scheduling controller is investigated by numerical simulations. By considering real situations in which velocity in the longitude direction is variable in time, the prosperity of the proposed controller for tracking the proceeding vehicle in the platoon and attenuating of disturbances is validated.

Partially Parameter-Dependent Dynamic Output Controller with Event-Triggered for Discrete-Time Saturated LPV Systems

Partially Parameter-Dependent Dynamic Output Controller with Event-Triggered for Discrete-Time Saturated LPV Systems

Synthesis of Dynamic Output Feedback Controller Using Functions of Matrix Root-Clustering in D-Regions

This article considers an algorithm for the synthesis of dynamic output controller, where the eigenvalues of a closed control system should be located in a given region (D-region) of the complex plane. The main direction of the research is to synthesize dynamic controllers of minimal order when there is no complete controllability at the output. For this purpose, a brief excursion into the external Grassmann algebra is made with the purpose of determining the external product of vectors, on the basis of which the operation of the bialternate product of matrices is explained. The use of the bialternate product of matrices made it possible to introduce the functions of matrix root-clustering of complex eigenvalues located in separate transformable D-regions. For the usual product of matrices, the functions of matrix root-clustering of real eigenvalues located in separate transformable D-domains are introduced. The functions of matrix root-clustering are transforming, respectively, complex or real points of a given bounded or unbounded D-region of the complex plane into a left half-plane. The article considers the main D-domains most widely used in practice (disk, cone, stability margin), presents their matrix root-clustering and functions of matrix root-clustering of real and complex modes. An algorithm for parametric optimization of dynamic output feedback controller over D-domains has been developed. Practical examples of synthesis are considered. For a fourth-order object (a two-mass weakly damped system with two integrators and parametric uncertainty), a secondorder dynamic controller providing robust quality has been synthesized.

Intermittent Cluster Consensus Control of Multiagent Systems From a Static/Dynamic Output Approach

This article is concerned with the cluster consensus control problem for multiagent linear systems with a directed communication topology, where only relative output measurements of neighboring agents are available to each agent. Motivated by the pinning control technique, both static and dynamic intermittent output control strategies are proposed. Using Lyapunov functions, sufficient conditions are developed to ensure cluster consensus with existence-guaranteed control parameters. Both periodic and nonperiodic operations of intermittent controllers are investigated. Finally, the effectiveness of the theoretical results is demonstrated by a simulation example.

On the Separation Principle in Dynamic Output Controller Design for Uncertain Linear Systems

In this paper, the problem of designing the improper dynamic output controllers for uncertain linear multi-input/multi-output continuous-time systems is considered. In the principal part, the system state coordinate transform is outlined and matrix variable structures are found, defining the solution based on the structured linear matrix inequalities and linear matrix equality. Of principal novelty is the framework related to the system uncertainties with newly introduced inequality structures and their partial factorization. The main results are shown in detail by the example to characterize potential application of the method for quadratic stabilization of uncertain linear systems by the improper dynamic output controllers.

Dynamic anti-windup controller design for Takagi-Sugeno fuzzy systems under saturations

Abstract This paper presents a new H∞ anti-windup dynamic output control developed for a class of nonlinear systems subject to both sensors and actuators saturations. First, the nonlinear system under consideration is represented by a Takagi-Sugeno (T-S) fuzzy model. Then, a dynamic output feedback (DOF) control strategy is proposed and the saturation constraints are transformed into dead-zone nonlinearities. Based on this transformation and by using the sector condition, the H∞ dynamic output stabilization conditions of the closed-loop system are given in terms of linear matrix inequalities (LMI). Finally, a numerical example is simulated to demonstrate the efficiency of the proposed design method.

A New Approach to Model Predictive Control Based on Two Degrees of Freedom Control and B-Splines Input Shaping

The purpose of this article is to reduce some technical difficulties related to the complexity of stability and feasibility analysis of Model Predictive Control (MPC) as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom control scheme where the output $r(k)$ of a feedforward input estimator is used as input forcing the closed-loop system $\Sigma _f$ . This latter is given by the feedback connection of a Linear Time Invariant (LTI) plant with a dynamic output controller. The task of the controller is to guarantee the stability of $\Sigma _f$ , as well as the fulfillment of hard constraints for any $r(k)$ satisfying an “ a priori ” determined admissibility condition. The input $r(k)$ is computed through the online minimization of a quadratic cost functional and is applied to $\Sigma _f$ according to the usual MPC strategy. To simplify the constrained optimization problem, the input $r(k)$ forcing $\Sigma _f$ is assumed to be given by a B-spline function. This greatly decreases the number of decision variables of the online optimization procedure because B-splines are universal approximators which admit a parsimonious parametric representation. Moreover such parameterization allows us to reformulate the minimization of the cost functional as a box Constrained Least Squares (CLS) problem. It is shown that stability and recursive feasibility of the adopted MPC strategy are guaranteed in advance, regardless the chosen prediction horizon.

A Dynamic Feedback Framework for Control of Time-Delay Nonlinear Systems With Unstable Zero Dynamics

This paper presents a dynamic feedback framework for the control of time-delay cascade systems with unstable zero dynamics. Both dynamic state and output feedback control strategies are studied. Recognizing the difficulty of controlling time-delay systems via static feedback, we develop a systematic method, by taking advantage of dynamic feedback, for the design of delay-free, dynamic state and output feedback compensators that achieve global state regulation with stability. The controlled plants under consideration not only cover time-delay nonlinear systems in the normal form, but also include a class of time-delay cascade systems beyond the normal form. In the case of state feedback, the zero dynamics are not required to be “minimum phase” but satisfy certain regularity conditions. In the output feedback case, appropriate conditions are characterized for the zero dynamics so that the existence of a dynamic output controller is ensured. A key feature of the proposed control strategies is the utilization of dynamic gains to counteract the effect of time-delay nonlinearities and unstable zero dynamics.

Output control design and separation principle for a class of port‐Hamiltonian systems

SummaryUsing a structure preserving observer, a dynamic output controller is proposed for a class of port‐Hamiltonian systems. The core of this method is based on the notion of contractive port‐Hamiltonian systems. The proposed method utilizes an extended form of IDA‐PBC (interconnection and damping assignment passivity‐based control), a well‐known controller design method for port‐Hamiltonian systems and paves the way for using IDA‐PBC in output control design of challenging control objectives, such as output tracking for underactuated mechanical systems. In the line of output control design, a useful separation principle for a class of port‐Hamiltonian systems is achieved, which is valuable in the field of nonlinear systems. Some simulations on magnetic levitation and ball on wheel testbeds show the potency and applicability of the proposed method.

Stability Analysis and Antiwindup Design of Switched Linear Systems with Actuator Saturation

This paper investigates the stability analysis and anti-windup design problem for a class of switched linear systems with input saturation by using the multiple Lyapunov functions method. The premise is that a set of linear dynamic output controllers have been designed to stabilize the closed-loop system without saturation. Then, the anti-windup compensators and the switching law are designed which can enlarge the domain of attraction of the closed-loop system. Finally, the anti-windup compensators and the switching law are presented by solving an optimization problem with constraints. A numerical example is shown to demonstrate the effectiveness of proposed method.

Cascade structures of fault-tolerant control schemes with the static and dynamic output controllers

An enhanced approach to fault-tolerant control design is proposed in the paper for linear systems subject to cascade control strategy, while static and dynamic output controllers are employed to maintain the stability of the overall interconnected control structure. The controller gains are solved simultaneously using two-step linear matrix inequality formulation, conditioned by linear matrix equalities. A simulation example, subject to a system matrix parameter fault, demonstrates the effiectiveness of the proposed method of design and cascade control technique.

Convex Synthesis of Robust Controllers for Linear Systems With Polytopic Time-Varying Uncertainty

The design of robust controllers for linear systems with structured time-varying uncertainty is a fundamental problem in control systems. This problem is still open because the available methods for robust analysis lead to nonconvex optimization whenever design variables are present. This paper proposes a novel approach that overcomes this difficulty. Specifically, continuous-time linear systems with polytopic time-varying uncertainty are considered. The basic problem consists of designing a robust static output feedback controller ensuring robust asymptotical stability. A novel approach is proposed through the introduction of robust stabilizability functions (RSFs), i.e., functions able to establish whether a controller is robustly asymptotically stabilizing. In particular, RSFs based on homogeneous polynomial Lyapunov functions (HPLFs) are searched for. The proposed approach requires the solution of two convex optimization problems with constraints expressed as linear matrix inequalities (LMIs). For any size of the LMIs, the proposed approach provides a sufficient condition for the existence of a sought controller. Moreover, this condition is also necessary when the size of the LMIs is large enough. Several extensions of the proposed methodology are presented, which deal with the synthesis of controllers ensuring desired decay rate, fixed-order dynamic output controllers, and controllers with the minimum norm.

Stability Analysis and Design of Uncertain Discrete‐time Switched Systems with Actuator Saturation Using Antiwindup and Multiple Lyapunov Functions Approach

AbstractThe stability analysis and anti‐windup design problem is investigated for a class of discrete‐time switched systems with saturating actuators by using the multiple Lyapunov functions approach. Firstly, we suppose that a set of linear dynamic output controllers have been designed to stabilize the switched system without input saturation. Then, we design anti‐windup compensation gains and a switching law in order to enlarge the domain of attraction of the closed‐loop system. Finally, the anti‐windup compensation gains and the estimation of domain of attraction are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. A numerical example is given to demonstrate the effectiveness of the proposed design method.

Modeling and quadratic stabilization of a class of linear uncertain time‐varying systems

SummaryThis paper considers the quadratic stabilization of a class of uncertain linear time‐varying (LTV) continuous‐time plants. The state‐space representation of each plant is based on the physically meaningful assumption of a dynamical matrix containing uncertain elements whose time trajectories are sufficiently smooth to be well described by interval polynomial functions with arbitrarily time varying coefficients. At some isolated time instants, the parameters trajectories can exhibit some first‐kind discontinuities due for example to sharply varying operating conditions. Using a parameter independent Lyapunov function, a quadratically stabilizing dynamic output controller is directly obtained by the solution of some LMIs. A salient feature of the paper is that, unlike all the other existing methods, quadratic stabilization can be achieved over possibly arbitrarily large uncertain domains of parameters. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Input/Output Decoupling of Square Linear Systems by Dynamic Two‐Parameter Stabilizing Control

AbstractAnalytical expressions of the free parameters of a two‐parameter stabilizing control (TPSC), solving an input/output (I/O) decoupling problem, are presented, and stability conditions are given. Multi‐input‐multi‐output (MIMO), proper, lumped and linear time invariant (LTI) systems are considered. These systems have stabilizable and detectable realizations. The separation principle is applied to design a dynamic output control in a controller‐observer feedback configuration. The I/O relation of the overall system is equivalent to a subsystem, in which the I/O decoupling problem has a solution. Also, if the state dimension of the plant is even, and is double the input dimension of the plant, then coprime factorizations of the plant used for the stabilizing controllers are proposed. The results are illustrated through an example.

Dynamic Output Feedback Robust MPC with Input Saturation Based on Zonotopic Set-Membership Estimation

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

Dynamic Output Feedback Control for a Micro Wind Turbine

Hybrid renewable energy systems are considered as a delightful alternative power supply for isolated rural areas and remote locations. In this paper, only the wind conversion part from hybrid system has been interested. In order to keep our focus on control strategy due to its important advancements in satisfying power in wind turbines, the dynamic output control law is developed such that it can guarantee a certain level of performances especially in the transitory domain besides providing adequate precise in voltage-reference tracking. The sufficient conditions for output feedback stabilizing designed controller are given in terms of solutions to a linear matrix inequality (LMI). The numerical illustrations and some simulation results are presented to visualize the feasibility of the proposed control strategy.