State Feedback Controller Design Research Articles

Decentralised state-feedback prescribed performance control for a class of interconnected nonlinear full-state time-delay systems with strong interconnection

This paper investigates the problem of the state-feedback control design for a class of interconnected nonlinear full-state time-delay systems with strong interconnection and prescribed performance. Based on the dynamic gain approach and Lyapunov-Krasovskii method, it overcomes the rigorous restriction that the interconnected time-delay functions should satisfy linear growth condition. Compared with the existing results, the main contribution is that the dynamic gain approach is extended to state-feedback control for interconnected time-delay systems, and it is strictly proved that the closed-loop system is globally bounded stable with the proposed decentralised control strategy. The problem of the strong interconnection terms is solved by combining the backstepping approach and graph theory. Furthermore, the expected transient and steady-state performance of the output can be guaranteed by considering prescribed performance control into such strongly interconnected systems. Finally, simulation is performed and the results show the effectiveness of the proposed method.

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

AbstractRecently, the global robust output regulation problem for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems which may not have well‐defined relative degree and are subject to a nonlinear exosystem has been studied based on a constructive nonlinear internal model. However, the proposed nonlinear internal model‐based control law is applicable to the case where the exogenous signals are reference input and/or measurable disturbance rather than unmeasurable disturbance. For this reason, this paper further studies the same control problem based on a general nonlinear internal model independent of the exogenous signal. It is shown that this control problem can be converted into a global robust stabilization problem of a more complicated MIMO nonlinear system with various uncertainties and well solved by a recursive state feedback controller design. Thus our approach applies to a broader class of output regulation problem of MIMO nonlinear systems.

Pole Placement Based State Feedback for DC Motor Position Control

The paper proposes DC Motor position controller by applying state feedback control which is tuned by pole placement method. DC motor is one of most widely-used industrial and robotics actuators. Hence, DC Motor controller is supposed to have good performance with high efficiency. The research designed state feedback controller which functions to set position of DC motor with best pole parameter value. DC Motor simulation with pole placement is made in MATLAB. Based on test results, best pole values for the DC Motor is [-10+j10-10-10-j10] with system response performance as: 0% overshoot, 0.4459 second in settling time, and 0.2558 second in rise time.

Nonlinear state feedback control design for port-Hamiltonian systems with unstructured component

Abstract This paper considers the problem of state feedback controller design to stabilize generalized Hamiltonian systems with an unstructured component. This class of models enable one to exploit the structure of port-Hamiltonian systems for feedback control design while relaxing the constraint of deriving an exact structured port-Hamiltonian representation. For a given stabilizable nonlinear system, and with some assumptions on the unstructured part of the dynamics, a stabilizing control law is designed and asymptotic stability of a desired equilibrium of the system is demonstrated. A numerical illustration of the proposed approach is presented to demonstrate the design method.

A hybrid state feedback controller design for two different dynamic systems

This paper deals the application of error recursive reduction computational (ERRC) technique to improve the performance of state feedback (SF) with integral control design. To highlight the performance of the proposed method is tested on second order and third order system. A second order system is framed based on general assumptions and the third order system is a model of the aircraft pitch control system. The proportional and integral control gain values are obtained using Ackermann's method. Results of with and without ERRC in state feedback design are compared. The controller performance was verified in terms of rise time, settling time, overshoot and tolerance limits.

Rapid Nonovershooting Control for Simultaneous Infusion of Anesthetics and Analgesics

We propose a rapid nonovershooting tracking controller for the continuous infusion of anesthetics and analgesics to prevent overdosing and other harmful side effects on patients. The controller utilizes a state feedback control design methodology for multi-input multi-output systems to achieve a closed-loop eigenstructure that yields a nonovershooting transient response. The method is combined with a global optimization method to achieve a rapid nonovershooting response. The controller uses an extended Kalman filter to estimate system states from measurable outputs, and integral control is added to achieve robust tracking. The performance of the method is simulated on 20 patient models in two groups, and the results are compared against another recent study from the biomedical control literature.

Delay-Dependent State-Feedback Dissipative Control for Suspension Systems With Constraints Using a Generalized Free-Weighting-Matrix Method

This paper presents a novel delay-dependent dissipative control synthesis technique with a state-feedback structure for input-delayed suspension systems using a tighter bounding technique. By more accurately estimating the derivative of the LKF, we focus on reducing the conservatism of the state-feedback control synthesis for suspension systems with strict design constraints. New LMI conditions for a desired state-feedback controller are developed by employing a generalized free-weighting-matrix (GFWM) method. By solving the LMIs, the proposed controller for active suspension systems is obtained such that the closed-loop systems have asymptotic stability with guaranteed $(\mathcal {Q},\mathcal {S},\mathcal {R})$ -dissipative performances, while also satisfying the design constraint conditions. Numerical simulations effectively confirm the benefits of the proposed control synthesis technique for the design of state-feedback control.

A Hybrid State Feedback Controller Design for Two Different Dynamic Systems

This paper deals the application of error recursive reduction computational (ERRC) technique to improve the performance of state feedback (SF) with integral control design. To highlight the performance of the proposed method is tested on second order and third order system. A second order system is framed based on general assumptions and the third order system is a model of the aircraft pitch control system. The proportional and integral control gain values are obtained using Ackermann's method. Results of with and without ERRC in state feedback design are compared. The controller performance was verified in terms of rise time, settling time, overshoot and tolerance limits.

Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities (LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.

이산시간 불확실 특이시스템의 새로운 강인 유한시간 상태궤환 제어

In this paper, we consider the problem of robust finite-time singular stability(RFSS) and state feedback controller design method for discrete–time linear singular systems with norm-bounded parameter uncertainties. First, the FSS sufficient condition is derived by equivalently transformed closed-loop system. Second, a state feedback controller design method satisfying regular, causal, and RFSS is proposed by LMI(linear matrix inequality) technique on the basis of the obtained FSS condition and equivalent properties of the considering system. The presented conditions are strict LMI conditions in terms of finding all variables compared with previous results. Finally, a numerical example is given to illustrate the validity of the proposed method.

Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems

This paper addresses the guaranteed cost control problem of a class of uncertain fractional-order (FO) delayed linear systems with norm-bounded time-varying parametric uncertainty. The study is focused on the design of state feedback controllers with delay such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Stemming from the linear matrix inequality (LMI) approach and the FO Razumikhin theorem, a delay- and order-dependent design method is proposed with guaranteed closed-loop stability and cost for admissible uncertainties. Examples illustrate the effectiveness of the proposed method.

Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

AbstractIn this study, the finite‐time control for uncertain positive systems with impulses using a hybrid state feedback control mechanism is investigated. The hybrid state feedback double control strategy is utilized, which includes impulsive state control scheme and continuous state feedback control scheme. A type of time‐varying Lyapunov copositive function is constructed. Considering different impulsive effects, the finite‐time boundedness criterion is obtained by applying the average impulsive interval approach. In addition, sufficient conditions are proposed for finite‐time characterization analysis and the hybrid state feedback controller design. All the criteria can be checked by the linear programming approach succinctly. The relationships among the upper bound of the finite‐time interval, the frequency and intensity of impulses, and the minimum allowable ‐gain level are revealed. Numerical examples are used to illustrate the usefulness of the theoretical results.

State feedback controllers based finite-time and fixed-time stabilisation of high order BAM with reaction–diffusion term

ABSTRACT In this paper, we are interested in the finite time and fixed-time stabilisation of high order bidirectional associative memory neural networks (HOBAMNNs) with time delays and reaction–diffusion terms. Via the theory of topological degree, a set of sufficient conditions are obtained to guarantee the existence of the equilibrium point of HOBAMNNs. The finite time and fixed time stabilisation are introduced based on Lyapunov functional, new designing state feedback controllers and inequality techniques. At the end, some numerical simulations are carried out to support the theoretical results.

Observer-based finite-time control of linear fractional-order systems with interval time-varying delay

In this paper, the problem of finite-time observer-based control for linear fractional-order systems with interval time-varying delay is studied. The delay is assumed to vary within an interval with known lower and upper bounds. A new proposition on estimating Caputo derivatives of quadratic functions is given. Based on the proposed result, delay-dependent sufficient conditions for finite-time stability and for designing state feedback controllers and observer gains for observer-based control problem are established in terms of a tractable linear matrix inequality and Mittag–Leffler function. A numerical example with simulation is given to demonstrate the effectiveness of the proposed method.

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

A novel condition for fixed-time stability and its application in controller design for robust fixed-time chaos stabilization against Hölder continuous uncertainties

This paper presents a new nonlinear state-feedback controller design for robust fixed-time chaos stabilization of chaotic systems in the presence of a relatively large class of uncertainties known as Holder continuous uncertainties. Based on Lyapunov's second method, a novel sufficient condition for fixed-time stability is derived. The spectacular property of the proposed controller is that the upper bound of the convergence time exists as an explicit parameter in the control's law, thus the true fixed stabilization time can be set in advance. To show the effectiveness of the proposed controller, two scenarios are provided, and the simulation results are reported.

Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales

In this article, we study the finite-time stability (FTS) and finite time stabilization problems for a class of switched impulsive systems evolving on an arbitrary time domain. This problem is formulated using time scale theory where the time domain can be continuous, discrete, union of disjoint intervals with variable gaps and variable lengths or any combination of these. Using common Lyapunov-quadratic and Lyapunov-like functions, we establish sufficient conditions to ensure the FTS results. Further, to solve the stabilization problem, we design state feedback controllers. We have illustrated the effectiveness of the obtained analytical results though numerical examples.

Hardware in the Loop Testing of Adaptive Inertia Weight PSO-Tuned LQR Applied to Vehicle Suspension Control

This paper presents an adaptive inertia weight particle swarm optimization (AIWPSO) employed for solving the multiobjective weight optimization problem of LQR applied for the vehicle active suspension system (ASS). To meet the competing control objectives of ASS including the ride comfort, road handling, and suspension travel, the state feedback controller design for ASS is formulated as an optimization problem and an improved PSO is employed for finding the optimal weights of the linear-quadratic regulator (LQR). Specifically, for solving the premature convergence of the particles and imbalance between exploration and exploitation capabilities of PSO, an adaptive inertia weight that updates the velocity of the particles based on the success rate is used. The efficacy of the AIWPSO-tuned LQR is experimentally tested on a quarter-car ASS plant using the hardware in loop (HIL) testing for an uneven road surface. Experimental results highlight that, compared to conventional PSO-tuned LQR, the proposed scheme can significantly minimize the vehicle body acceleration due to irregular road profile while guaranteeing the minimum tire friction for passenger safety. The ISO 2361-1 standards adopted to evaluate the ride and health criteria substantiate that the proposed scheme reduces the vibration dose value by 25.34% for a bumpy road profile. Moreover, the cumulative power spectral density (CPSD) of vehicle body acceleration assessed in both low- and high-frequency regions manifests the significant improvement in the ride comfort.

State-Feedback Filtering for Delayed Discrete-Time Complex-Valued Neural Networks.

This article explores a new filtering problem for the class of delayed discrete-time complex-valued neural networks (CVNNs) via state-feedback control design. The novelty of this article comes from the consideration of the newly developed complex-valued reciprocal convex matrix inequality as well as the complex-valued Jensen-based summation inequalities (JSIs). By employing an appropriate Lyapunov-Krasovskii functional (LKF) and by using newly proposed complex-valued inequalities, attention is concentrated on the design of a state-feedback filter such that the associated filtering error system is asymptotically stable with prescribed filter and control gain matrices. The proposed theoretical results are presented in terms of complex-valued linear matrix inequalities (LMIs) that can be solved numerically by using the YALMIP toolbox in MATLAB software. Additionally, one numerical example is given to confirm the validity of the resulting sufficient conditions with the availability of the suitable control and filter design.

Design of an adaptive state feedback controller for a magnetic levitation system

This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controller in terms of the operating point. The results of the simulation show that the operating point has significant effect on the performance of nonadaptive SFC, and this performance may degrade as the operating point deviates from the equilibrium point, while the ASFC achieves the required design specification for any operating point and outperforms the state feedback controller from this point of view.