Robust State Feedback Controller Research Articles

Robust partial sampled-data state feedback control of Markov jump linear systems

This paper proposes new conditions for the design of a robust partial sampled-data state feedback control law for Markov jump linear systems (MJLS). Although, as usual, the control structure depends on the Markov mode, only the state variable is sampled in order to cope with a specific network control structure. For analysis, an equivalent hybrid system is proposed and a two-point boundary value problem (TPBVP) that ensures minimum or cost is defined. For control synthesis, it is rewritten as a convex set of sufficient conditions leading to minimum guaranteed cost of the mentioned performance classes. The optimality conditions are expressed through differential linear matrix inequalities (DLMIs), a useful mathematical device that can be handled by means of any available LMI solver. Examples are included for illustration.

Model reference resilient control for the helicopter with time‐varying disturbance

SummaryIn this paper, the problem of model reference resilient control is investigated for the helicopter system with the time‐varying disturbance and unmeasurable states. Firstly, a disturbance observer and a state observer are built to estimate the time‐varying disturbance and unmeasurable states. Then, combining the methods of model reference control and disturbance observer–based control, the state feedback robust resilient control scheme and the dynamic output feedback robust resilient control method are proposed, respectively. Under the two developed robust resilient control schemes, sufficient conditions are obtained to guarantee that the helicopter system asymptotically tracks the reference model with H∞ performance. Finally, simulation results are presented to show the effectiveness of the model reference resilient control method.

Robust Nonlinear State Feedback Control of Bidirectional Interlink Power Converters in Grid-Connected Hybrid Microgrids

In this paper, a new scheme based on state feedback control concept is presented for robust control of bidirectional interlink power converters (BILPCs) in hybrid microgrids (HMGs). The studied grid-connected HMG contains one dc and one ac microgrid, interconnected by BILPCs. To consider uncertainties, the nonlinear uncertain model of the BILPC is derived and linearized based on Lie derivative concept. As a new point of view for dynamic modeling of BILPC, it is indicated that each nonlinear uncertain BILPC model can be represented by two decoupled subsystems. Then, a virtual robust state feedback controller is designed to independently control each of these subsystems with disturbance rejection capability. The gains of the state feedback controllers are obtained using Ackerman pole placement method. To approximate the unknown inputs/unmodeled dynamics, which are needed in the design process of the state feedback controllers, a high-gain proportional-integral (PI) observer is designed. The high gains of this PI observer are determined using linear quadratic regulation method. Simulation results and comparative studies support the efficacy of the proposed control approach.

Non-fragile control protocol for finite-time consensus of stochastic multi-agent systems with input time-varying delay

The existence of gain variations in control design often disrupts most of the control system performance. By considering this point, as a first attempt in the literature, a robust non-fragile state feedback control design is proposed in this paper for achieving finite-time consensus in a class of stochastic nonlinear multi-agent systems with randomly occurring uncertainty and randomly occurring nonlinearity. Specifically, the randomness phenomena are characterized with the aid of stochastic variables that satisfy the Bernoulli distribution properties. To design the non-fragile control protocol, the communication graph is chosen to be directed and connected subject to switching topologies. On the basis of the Lyapunov–Krasovskii stability theory and stochastic analysis techniques, a new set of sufficient conditions is established to guarantee that the states of all agents can reach an agreement over a given finite-time period via the proposed non-fragile switched control law. The effectiveness of the designed consensus protocol is demonstrated through an academic example.

Observer-based state-feedback robust control for path following of autonomous ground vehicles

In this article, a robust [Formula: see text] observer-based static state-feedback controller is designed for the path following of autonomous ground vehicles. The Takagi–Sugeno fuzzy modeling technique is used for modeling of vehicle dynamics with varying longitudinal velocity first. Then considering the high cost of direct lateral velocity measurement, an observer is designed to estimate the value of lateral velocity. Meanwhile, a robust controller is proposed to deal with the parameter uncertainties and external disturbances simultaneously, including the variation of the tire-cornering stiffness of both front and rear tires. Afterward, the condition of designing such an observer-based controller is transformed into the feasible problem of linear matrix inequalities. Numerical simulations using a high-fidelity and full vehicle model are performed based on a Carsim–Simulink joint platform. Simulation results under different conditions and comparison with other controller show that the proposed controller is effective irrespective of the variation in the road condition, the change in the vehicle longitudinal velocity and the external disturbances.

Robust state-feedback control for discrete-time descriptor systems with norm-bounded parametric uncertainties

ABSTRACTThis paper deals with a state feedback control problem for linear time-invariant discrete-time descriptor systems with norm-bounded parametric uncertainties. To this end, bounded real lemma (BRL) is extended on the class of uncertain descriptor systems. The control design procedure based on the conditions of BRL for uncertain descriptor systems is proposed. Numerical examples are included to illustrate the effectiveness of the present result.

Synchronization of complex dynamical networks with random coupling delay and actuator faults

This paper addresses the issue of passivity-based synchronization problem for a family of Markovian jump neutral complex dynamical networks (NCDNs) with coupling delay and actuator faults. Also, by considering the effect of random fluctuation in complex dynamical network systems, the occurrence of coupling delay are taken in terms of a stochastic distribution, which obeys the Bernoulli distribution. To handle the fault effects in actuators of proposed complex network systems, an actuator fault model is considered. The main objective of this paper is to develop a robust state feedback controller such that for all possible actuator failures and random coupling delays, all nodes of the proposed Markovian jump NCDNs is globally asymptotically synchronized to the reference node in mean square sense and guarantee the output strict passivity performance. By developing a suitable Lyapunov–Krasovskii functional and utilizing the Wirtinger-based integral inequality, the required a set of sufficient conditions for the synchronization of proposed system is established in form of linear matrix inequalities. Finally, three numerical examples including a 3-dimensional Lorenz chaotic model are provided to demonstrate the correctness and superiority of the proposed control scheme.

Optimal robust state-feedback control of nonlinear systems: minimal time to target

The design of optimal robust state-feedback controllers that guide a system to a target in minimal time is considered under constraints on the maximal input amplitude and the maximal overshoot of the controlled system. It is shown that such robust feedback controllers exist for a rather broad family of nonlinear systems. It is also shown that optimal performance can be approximated by state-feedback controllers that are relatively easy to design and implement.

Iterative LMI Approach to Robust State-feedback Control of Polynomial Systems with Bounded Actuators

This paper presents a novel approach to state-feedback stabilization of polynomial systems with bounded actuators. To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the Lyapunov matrices. Therefore, parameterization of the state-feedback controllers is independent of the Lyapunov matrices. The proposed design condition is bilinear in the decision variables, and hence we provide an iterative algorithm to solve the design problem. At each iteration, the design condition is cast as convex optimization using the sum-of-squares technique and can be efficiently solved. In addition, the novel parameter-dependent Lyapunov functions are readily applied to robust state-feedback stabilization of polynomial systems subject to parametric uncertainty. Effectiveness of the proposed approach is demonstrated by numerical examples.

Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H∞ and generalized H2 performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.

A proportional–integral-based robust state-feedback control method for linear parameter-varying systems and its application to aircraft

The integration of advanced linear parameter-varying and classical proportional–integral–derivative control methods has attracted great attention in control of nonlinear dynamic systems. However, linear parameter-varying proportional–integral–derivative control synthesis is a nonconvex bilinear matrix inequality problem. Although the synthesis conditions can be convexified in the case of proportional–integral control, a strong constraint on the structure of matrix variables usually leads to infeasible solutions. In this paper, a linear parameter-varying proportional–integral control design method is proposed to remove that constraint. The approach is based on the assumption of state-feedback proportional–integral control to guarantee the linear matrix inequality variables to be full matrices instead of block diagonal matrices, and extended linear matrix inequalities are proposed to synthesize the controller. This increases the likelihood of finding feasible linear matrix inequality solutions and reduces the conservatism. The proposed method is applied to control longitudinal and lateral dynamics of an F-16 aircraft and promising simulation results are obtained.

Active vibration control of motorized spindle based on mixed /Kalman filter robust state feedback control

In its working process, a high-speed motorized spindle bearing-rotor system is affected by a variety of vibration excitations, which severely affect the machining precision and reliability. In view of the problems in the active vibration control of current smart-material-based bearing-rotor systems and based on the structural layout of a piezoelectric device and a controlled bearing-rotor system, a bearing was directly connected to a piezoelectric actuator via a sleeve, which improved the working efficiency of the piezoelectric stack actuator. Furthermore, to improve the robustness of the system’s vibration control performance under different external excitations (e.g., cutting force and mass unbalance), uncertainties in internal parameters (changes in bearing stiffness and stiffness nonlinearity of piezoelectric materials), process and measure noises, a mixed state feedback algorithm based on norm optimization and a Kalman filter observer with state disturbance estimation was established. The dynamic and robust performance of the proposed method was compared with that of the linear quadratic Gaussian optimal control methods and output feedback control method through both simulation and experiment by changing the piezoelectric stacks without changing the control program.

Synchronization Control Design Based on Wirtinger Inequality for Uncertain Coronary Artery Time-Delay System With Input Saturation

This paper focuses on the synchronization of uncertain coronary artery chaos systems (CACSs) with the state and input time-varying delays under input saturation. First, the stability of the closed-loop system is established to ensure the synchronization between the diseased and healthy CACSs under input saturation by utilizing the local sector condition and the Lyapunov–Krasovskii functional (LKF) method. The use of Wirtinger inequality and the reciprocally convex method further reduces the conservatism. Second, by making use of the cone complementary linearization approach to deal with nonlinear terms, we obtained a state feedback controller. Finally, a robust state feedback controller is formulated to achieve the synchronization of the CACS under disturbances bounded by $L_{2}$ norm. The simulation results of the CACS synchronization are presented to demonstrate the effectiveness of the derived results, which provides a certain theoretical basis for curing diseases related to the coronary artery vessel.

An LMI approach to design robust <i>H</i><SUB align="right">∞ controller for 2-D systems with delays

This paper focuses on H∞ controller design for two-dimensional (2-D) discrete state delay systems described by the second Fornasini-Marchesini local state space (FM LSS) model with polytopic uncertainties. The objective is to design a robust state feedback controller such that the corresponding closed-loop system achieves robust asymptotic stability and guarantees a prescribed H∞ performance index for all admissible uncertainties. Based on parameter-dependent Lyapunov functions and Finsler's lemma, a new sufficient condition for H∞ performance analysis of 2-D discrete systems with delays is developed. Then a stabilising state feedback controller is designed. A simulation example is exploited to show the effectiveness of the proposed approach.

Simultaneous Robust Control and Sensor Fault Detection for a Ducted Coaxial-Rotor UAV

This paper addresses the aerodynamic modeling, observer-based state-feedback robust control and sensor fault detection for a laboratory ducted coaxial-rotor UAV (DCUAV). First, by introducing the main model elements of this novel unmanned vehicle, the detailed nonlinear mathematical model of the hovering flight UAV is presented. Second, through introducing a weighting matrix and a new form of change-of-variables, a new method is proposed by designing two different systems simultaneously as detector and controller. An observer-based controller is proposed to achieve the control objective and finite-frequency sensor fault detection objective simultaneously. The observer-based controller design method is derived from a new formulation of linear matrix inequality (LMI), which can achieve the prescribed H ∞ performance, H - performance and the stability of the closed-loop system. By constructing a new matrix decomposition form, the simultaneous design of detector parameters and controller parameters is solved. Finally, simulations are conducted for the hover flight with disturbances and sensor faults, the results show the satisfactory control performance and fault detection performance.

Minimal Time Control of Nonlinear Systems: Optimal Robust State-Feedback

Optimal robust state-feedback controllers for minimal-time control of nonlinear systems are developed under constraints on the input and output signal amplitudes of the controlled system. Simple to design and implement controllers that approximate optimal performance are presented.

On finite time stability with guaranteed cost control of uncertain linear systems

This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example.

Cooperative Robust Output Regulation for Second-Order Nonlinear Multiagent Systems With an Unknown Exosystem

The cooperative robust output regulation problem for a class of second-order nonlinear multiagent systems with an exactly known exosystem has been studied recently. This paper further studies the same problem for the same class of systems subject to an unknown exosystem. We first show that the problem can be converted into the adaptive stabilization problem for an augmented system composed of the given multiagent system and the distributed internal model. Due to the unknown parameters in the exosystem, the augmented system is a nonlinear multi-input system with both linearly parameterized uncertainties and norm-bounded nonlinear uncertainty. By combining the adaptive control technique and the robust control technique, we will solve our problem by a distributed adaptive robust state feedback controller.

H∞ Robust Load Frequency Control for Multi-Area Interconnected Power System with Hybrid Energy Storage System

To enhance the quality of output power from regional interconnected power grid and strengthen the stability of overall system, a hybrid energy storage system (HESS) is applied to traditional multi-area interconnected power system to improve the performance of load frequency control. A novel topology structure of interconnected power system with the HESS is proposed. Considering the external disturbances of the system and the interconnected factors between each control area, the dynamic mathematical model of each area in the new topology is established in the form of state-space equation. Combining the state feedback robust control theory with linear matrix inequality (LMI) theory, the controller is designed to calculate how much power the HESS should provide to power grid in real time, according to the load change of system. Taking the four-area interconnected power system as study object, the simulation results obtained by MATLAB prove that the application of HESS can well improve the frequency stability of multi-area interconnected system and the H∞ robust controller proposed in this paper is effective.

Dynamic analysis, simulation, and control of a 6-DOF IRB-120 robot manipulator using sliding mode control and boundary layer method

Because of its ease of implementation, a linear PID controller is generally used to control robotic manipulators. Linear controllers cannot effectively cope with uncertainties and variations in the parameters; therefore, nonlinear controllers with robust performance which can cope with these are recommended. The sliding mode control (SMC) is a robust state feedback control method for nonlinear systems that, in addition having a simple design, efficiently overcomes uncertainties and disturbances in the system. It also has a very fast transient response that is desirable when controlling robotic manipulators. The most critical drawback to SMC is chattering in the control input signal. To solve this problem, in this study, SMC is used with a boundary layer (SMCBL) to eliminate the chattering and improve the performance of the system. The proposed SMCBL was compared with inverse dynamic control (IDC), a conventional nonlinear control method. The kinematic and dynamic equations of the IRB-120 robot manipulator were initially extracted completely and accurately, and then the control of the robot manipulator using SMC was evaluated. For validation, the proposed control method was implemented on a 6-DOF IRB-120 robot manipulator in the presence of uncertainties. The results were simulated, tested, and compared in the MATLAB/Simulink environment. To further validate our work, the results were tested and confirmed experimentally on an actual IRB-120 robot manipulator.