State-derivative Feedback Control Research Articles

PD Control-Based Reachable Set Synthesis for Singular Takagi-Sugeno Fuzzy Systems With Time-Varying Delay.

This article focuses on the reachable set synthesis problem for singular Takagi-Sugeno fuzzy systems with time-varying delay. The main contribution is that we design a proportional plus derivative state feedback controller to ensure that the singular fuzzy system is normal and the system states are bounded by a derived ellipsoid. In the light of the Lyapunov stability theory and the parallel distributed compensation method, the sufficient criteria are shown in the format of linear matrix inequalities. Furthermore, we investigate another case of reachable set synthesis, where the reachable set to be found is contained in a given ellipsoid. Finally, we use two examples to exhibit the usefulness of the proposed method.

Robust fault estimation and proportional derivative fault tolerant control for a class of singular systems with interval time‐varying delay and disturbance

SummaryThis paper deals with observer‐based fault estimation (FE) and proportional derivative state feedback fault tolerant control (FTC) schemes for singular systems affected by actuator fault, interval time‐varying delay and external disturbance. Firstly, the system transformation method of constructing the derivative matrix into a full‐rank matrix is adopted to transform the singular system into a normal system, which effectively eliminates the impulse characteristic of the singular system. Secondly, in the design of the dynamic observer, fault estimation utilizes the real‐time output error and its derivative simultaneously, which can achieve better estimation performance when the fault change frequently. Most importantly, the observer‐based FTC adopts a proportional derivative state feedback control, considers disturbance and interval time‐varying delay, and the introduction of state estimation derivative term can eliminate the impulse property of the closed‐loop system, which optimizes the design scheme of the fault‐tolerant controller. The obtained sufficient conditions for stability can be solved by the strict linear matrix inequality (LMI), and the superiority of the conclusions will be further verified by the simulations.

Robust normalization and stabilization of descriptor fractional‐order systems with polytopic uncertainties in all matrices

AbstractThis paper addresses the robust normalization and stabilization problems for descriptor fractional‐order systems with polytopic uncertainties in all system coefficient matrices, including the state derivative coefficient matrix. Firstly, novel sufficient conditions for the robust normality and stability of polytopic uncertain descriptor fractional‐order systems are presented based on linear matrix inequalities. Then, for the cases when the uncertain parameters are known and unknown, the proportional and derivative state feedback control with constant feedback gain and parameter‐dependent feedback gain are introduced to normalize and stabilize such systems, respectively. Finally, numerical examples are provided to show that the proposed approach is effective and less conservative than the results obtained by other researchers.

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

AbstractThis paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network‐induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network‐induced delay and uncertain sampling periods can be incorporated from the original continuous‐time state‐space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete‐time model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.

Design of a mixed ℋ2/ℋ∞ gain scheduling state derivative feedback controller for linear parameter-varying systems

In this paper, the mixed guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed guaranteed cost minimisation.

Reliable induced [formula omitted] control for polytopic uncertain continuous-time singular systems with dynamic quantization

This paper considers the problem of state feedback control for a class of polytopic uncertain continuous-time singular systems with input quantization and actuator faults. The aim of this paper is to design the reliable controller and dynamic quantizer that ensure the considered closed-loop system is asymptotically stable and satisfies the prescribed induced L∞ performance constraint. The introduced proportional plus derivative state feedback controller can eliminate the structural restrictions of the system matrices, thus a more general sufficient condition is obtained for the problem. Finally, the four-mesh circuit is provided to demonstrate the effectiveness of the proposed induced L∞ control approach.

State and static output feedback control of singular Takagi–Sugeno fuzzy systems with time-varying delay via proportional plus derivative feedback

This paper investigates the problems of state and static output feedback control for a class of singular Takagi–Sugeno fuzzy systems with time-varying delay. Two kinds of controllers are considered: one is the proportional plus derivative state feedback controller, the other is the proportional plus derivative static output feedback controller. The augmented Lyapunov–Krasovskii functional is chosen to analyze the stabilization of the considered system and the sufficient conditions are proposed based on the Lyapunov stability theory. In order to solve the controller gains, two iterative algorithms are built. Two persuasive examples are given to show the effectiveness of our methods.

Robust normalization and stabilization of descriptor fractional-order systems with uncertainties in all matrices

This paper focuses on the robust normalization and stabilization problems for descriptor fractional-order systems with norm-bounded uncertainties in all system coefficient matrices, including the state derivative coefficient matrix. The proportional and derivative state feedback control is introduced simultaneously to normalize and stabilize such systems. Novel sufficient conditions for the robust normalization and stabilization of such closed-loop systems are presented. Then, both the proportional feedback gain and the derivative feedback gain are obtained simultaneously by solving linear matrix inequalities. Finally, numerical examples are provided to show that the proposed approach is applicable and less conservative than the existing results.

Proportional Plus Derivative State Feedback Control of Takagi-Sugeno Fuzzy Singular Fractional Order Systems

Proportional Plus Derivative State Feedback Control of Takagi-Sugeno Fuzzy Singular Fractional Order Systems

Design of an gain scheduling state derivative feedback controller for linear parameter-varying systems

ABSTRACT This paper is devoted to the guaranteed cost of continuous-time linear parameter-varying (LPV) systems, considering the gain scheduling (GS) strategy and the state derivative feedback (SDF). The main contribution of the paper is to derive linear matrix inequalities (LMIs) conditions for the -SDF problem for LPV systems, taking into account the GS controller. For the good behaviour of the controller, we assume that the time-varying parameters are available for online measurement. In some cases, the -GS-SDF controller obtained high control signals, and as we intend to apply the proposed method in practical situations, we introduce the concept of -stability in the problem approach. Examples and a practical implementation show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and guaranteed cost minimisation.

Pole placement LMI constraints for stability and transient performance of LPV systems with incomplete state measurement

In this paper, new conditions for the stabilisation and transient performance improvement of linear parameter-varying (LPV) systems considering the gain-scheduling (GS) strategy are proposed. Our work is focused on dealing with LPV systems under the major practical constraint of incomplete state measurement. In that sense, we propose two new control design strategies based on linear matrix inequalities (LMI). First, for coping with the general case where only a subset of the state variables is measured, we propose a new static output feedback (SOF) strategy. Second, for dealing with the particular case where only accelerometers signals are available, we bring new synthesis conditions for the design of state derivative feedback (SDF) controllers. Further from stability, our proposed methods are able to induce better transient response by including pole placement LMI constraints in the control design. For illustrating our contribution efficacy, we present a couple of design examples.

Inverse Optimal Control in State Derivative Space System with Applications in Motor Control

This paper mathematically explains how state derivative space (SDS) system form with state derivative related feedback can supplement standard state space system with state related feedback in control designs. Practically, inverse optimal control is attractive because it can construct a stable closed-loop system while optimal control may not have exact solution. Unlike the previous algorithms which mainly applied state feedback, in this paper inverse optimal control are carried out utilizing state derivative alone in SDS system. The effectiveness of proposed algorithms are verified by design examples of DC motor tracking control without tachometer and very challenging control problem of singular system with impulse mode. Feedback of direct measurement of state derivatives without integrations can simplify implementation and reduce cost. In addition, the proposed design methods in SDS system with state derivative feedback are analogous to those in state space system with state feedback. Furthermore, with state derivative feedback control in SDS system, wider range of problems such as singular system control can be handled effectively. These are main advantages of carrying out control designs in SDS system.

Reachable set synthesis of singular Markovian jump systems

The reachable set synthesis problem of singular Markovian jump systems (SMJSs) is investigated in this paper. Both state reachable set and output reachable set are considered for SMJSs without delay and with distributed delay. By utilizing proportional and derivative state feedback control technique, sufficient conditions for delay-free SMJSs are proposed to guarantee the reachable set of closed-loop systems to be mean-square bounded by a prescribed ellipsoid firstly. Then the result is extended to SMJSs with distributed delay. Numerical examples are given to demonstrate the effectiveness of the obtained result.

Bounded Derivative Feedback Control with Application to Magnetic Levitation

In this paper, we study the stabilization of dynamic systems with uncertain equilibrium states and in the presence of bounded control. We propose state and output derivative feedback control schemes to stabilize the dynamic system, and to drive the system states to its true equilibrium state even when the location of such equilibrium is uncertain. Control bounds in the feedback control are also considered in this paper, and stability conditions are derived for the cases when the control energy is bounded, and when the maximum control is bounded. Stability conditions are derived in the form of matrix inequalities for both cases of control bounds, and numerical methods are discussed to synthesize feasible control solutions. The effectiveness of the proposed method is illustrated by an experimental implementation.

Proportional plus derivative state feedback controller design for a class of fuzzy descriptor systems

ABSTRACTThis study focuses on the proportional plus derivative state feedback (PDSF) control problem for continuous-time nonlinear descriptor systems described by Takagi–Sugeno fuzzy models with distinct fuzzy rules appearing in both sides of the considered system. Without using any additional transformations, some new conditions are developed by means of the free-weighting matrix technique and presented in terms of linear matrix inequalities to ensure that the resultant closed-loop system is normal and stable. Explicit expression of the desired PDSF controller is also given. Furthermore, the obtained result is extended to a class of uncertain nonlinear descriptor systems with norm-bounded perturbations. Finally, three examples are presented to show the effectiveness of the proposed method.

Control of Nonlinear Markovian Jump System with Time Varying Delay via Robust $$\mathcal{H}_\infty$$ Fuzzy State Feedback Plus State-derivative Feedback Controller

This paper investigates the problem of designing a robust $$\mathcal{H}_\infty$$ state feedback plus state-derivative feedback control mechanism for a class of uncertain nonlinear markovian jump systems with time varying delay described by a Takagi-Sugeno (T-S) fuzzy model. The linear matrix inequalities (LMIs) approach is applied to derive a robust controller for such a system. The proposed controller satisfies design requirements that ensure that the closed-loop system is asymptotically stable and meets pre-prescribed $$\mathcal{H}_\infty$$ performance index values. Finally, to illustrate the effectiveness of the design developed in this paper, a numerical example is also provided.

Robust non-fragile proportional plus derivative state feedback control for a class of uncertain Takagi–Sugeno fuzzy singular systems

This paper proposes a novel robust non-fragile proportional plus derivative state feedback (PDSF) control scheme for a class of uncertain nonlinear singular systems. The Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear singular system with parameter uncertainties appearing not only in distinct state matrices, but also in distinct derivative matrices. By using the free-weighting matrix technique, some sufficient conditions, which guarantee the resulting closed-loop system to be normal and stable (NS), are presented. With these conditions, the problems of non-fragile PDSF controllers design with additive and multiplicative uncertainties are respectively solved in terms of linear matrix inequalities (LMIs), which can be conveniently solved via the convex optimization technique. Finally, two examples are provided to illustrate the validity of the presented results.

Direct parametric attitude tracking control for generic hypersonic vehicle

ABSTRACTThis paper considers the attitude tracking problem for the generic hypersonic vehicle (GHV). First, the second-order nonlinear GHV attitude model is introduced. Second, by utilising the direct parametric approach, a modified parametric controller composed of the parametric state proportional plus derivative feedback controller and the feedforward controller is proposed. With application of the first part, the closed-loop system is a constant linear system with desired eigenstructures, and the second part is used to ensure the asymptotic tracking property of the outputs of the GHV attitude system. Since the control input of the established GHV attitude model is moment command, an algorithm that transforms the moment commands into the fins deflection command is proposed. Finally, the effectiveness of the proposed parametric controller and transform algorithm is illustrated by the numerical simulation results.

A novel robust $$H_{\infty }$$ H ∞ fuzzy state feedback plus state-derivative feedback controller design for nonlinear time-varying delay systems

This paper investigates the problem of designing a robust $$H_{\infty }$$ state feedback plus state-derivative feedback control mechanism for a class of uncertain nonlinear time-varying delay systems described by a Takagi–Sugeno fuzzy model. A linear matrix inequality approach is applied to derive a robust controller for such a system. The proposed controller satisfies design requirements that ensure that the closed-loop system is asymptotically stable and meets pre-prescribed $$H_{\infty }$$ performance index values. Finally, the illustrative examples are simulated to illustrate the effectiveness of the proposed methodology.

Robust normalisation and P–D state feedback control for uncertain singular Markovian jump systems with time‐varying delays

This study is concerned with the problem of robust normalisation and stabilisation of singular Markovian jump systems (SMJSs) with time-varying delays and parameter uncertainties. The main aim is to design a proportional and derivative state feedback controller to realise the normalisation and stabilisation of the delayed SMJSs. Based on the constructed Lyapunov–Krasovskii functional, sufficient conditions are presented in terms of linear matrix inequalities via utilising the free-weighting matrix method. Illustrative examples including an resistor inductor capacitor (RLC) circuit network are employed to demonstrate the effectiveness and usefulness of the obtained results.