Robust State Feedback Controller Research Articles

Robust control design of uncertain nonlinear systems: a self-compensating and self-tuning approach

ABSTRACT The problem of robust stabilisation is considered for a class of uncertain nonlinear systems with linear control term. It is not required that the unforced nominal (nonlinear) system has to be stable and/or has to be known, which means that its Lyapunov function need not be known and/or found for designing a stabilising control scheme to compensate the effect of uncertainty on the systems like some traditional control design approaches. For such a class of uncertain nonlinear systems, a design approach, called a self-compensating and self-tuning one, is presented whereby some robust state feedback control schemes can be easily synthesised. The proposed design approach can result in a linear state feedback control scheme with a time-varying control gain for such a class of uncertain nonlinear systems, which implies the simplicity of the design approach and control results. In addition, the system uncertainty is also not required to have to satisfy the matching conditions.

Concurrent Learning Robust Adaptive Fault Tolerant Boundary Regulation of Hyperbolic Distributed Parameter Systems.

This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.

Tracking control of robot manipulators actuated by brushless DC motors: Elimination of joint velocity measurements with a robust observer

AbstractThis work introduces an innovative robust partial state feedback controller designed for robotic manipulators actuated by brushless DC motors. The proposed controller/observer structure relies solely on actuator current and robot joint position measurements, while effectively compensating for dynamic uncertainties in both the electrical (actuator dynamics) and mechanical (robot's dynamical terms) subsystems. Specifically, a model–based robust observer, eliminating the need of joint velocity measurements, is combined with a backstepping‐type controller design. As opposed to the previous model based observers that depend on the actual model parameters, the proposed observer structure utilizes the best guest estimates of the system parameters supported with a robust compensation term. This approach eliminates the need for precise knowledge of system parameters of the observer design which is a significant improvement over most of the previous results. This approach ensures the semi‐global, uniformly ultimately bounded joint tracking error signal. The overall stability of the closed‐loop system is affirmed through Lyapunov‐based arguments. Experimental studies conducted on an in‐house‐built two‐link robotic manipulator, actuated by brushless DC motors, are presented to demonstrate the effectiveness and feasibility of the proposed method.

On global feedback control of unknown nonlinear systems

The construction of robust state-feedback controllers for unknown nonlinear systems is addressed through the derivation of robust bang-bang state-feedback controllers that lead to global asymptotic stabilisation. It is shown that a relatively simple testing process can provide sufficient information about an unknown system to facilitate the construction of bang-bang state-feedback controllers that guide the system toward global robust asymptotic stabilisation. The methodology presented in the paper applies to a broad class of nonlinear systems.

A vector decomposition approach to F–M model realization and its application to robust observed-state feedback control

This work presents a novel approach based on vector decomposition for realizing the Fornasini–Marchesini (F–M) model in multidimensional (n-D) systems. The primary focus is on resolving coefficient dependencies within the n-D rational transfer function matrix (TFM) of a multiple-input multiple-output (MIMO) system, aiming to generate a lower-order F–M model. The proposed method is further extended to robust observational state feedback control. To achieve this, we introduce innovative sufficient conditions for designing a low-dimensional resolvent invariant space (RIS) and outline the corresponding low-order F–M model realization process. By incorporating the polynomial vector dependency technique, we comprehensively address coefficient dependencies, leading to the construction of an even lower-order F–M model and contributing to the simplification of analytical complexity. To accommodate generic rational TFMs, we propose a matrix fractional description (MFD)-based process. Finally, we apply the developed F–M model implementation method to derive descriptor multiple affine representations (DMARs). This application proves instrumental in the robust observed-state feedback control design for rationally uncertain systems, enhancing the overall effectiveness of the robust observed-state feedback control design.

An LMI-based robust state-feedback controller design for the position control of a knee rehabilitation exoskeleton robot: Comparative analysis

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

Model validation and Robust State Feedback control for nonlinear subway traffic networks

This paper develops a nonlinear Discrete-Event (DE) model for Intersecting Lines (ILs) of a Subway Network (SN). A class of Monte Carlo (MC) methods based on repeated random values is employed to validate the model. Model validation is performed by generating random values for delay rates and external disturbances. After model validation, a Robust State Feedback (RSF) controller is designed to compensate the delays caused by disturbances. Simulations are performed based on the characteristics and actual data of lines 2 and 4 of the Tehran subway to demonstrate the effectiveness of the proposed approach. Simulation results show the accuracy and proper performance of the proposed model. In addition, the closed-loop responses demonstrate the effectiveness of the proposed RSF controller for centralized and decentralized control configurations.

Robust State Feedback Control With D-Admissible Assurance for Descriptor Systems Subjected to Perturbed Derivative Matrix

Robust State Feedback Control With D-Admissible Assurance for Descriptor Systems Subjected to Perturbed Derivative Matrix

Trajectory Tracking for Autonomous Vehicles Using Robust Model Predictive Control

This paper proposes a novel trajectory tracking control method using a robust model predictive control (RMPC) design technique based on matrix inequality and the theoretical approach of the hybrid & switched system. Firstly, considering bounded model uncertainties and norm-bounded external disturbances, the system states and control matrices are modified. In addition, vehicle time-varying longitudinal speed is considered, and a vehicle lateral dynamic model based on Linear Parameter Varying (LPV) is established by utilizing a polytope with finite vertices. Then the Min-Max robust MPC state feedback control law is obtained at every timestamp by solving a set of matrix inequalities which are derived from Lyapunov stability and the minimization of the worst-case in infinite-horizon quadratic objective function. The numerical simulation results demonstrated that the proposed robust LPV MPC can effectively track vehicle lateral dynamics on both straight and curved roads with varying longitudinal speeds.

A Robust Control for a Controllable Suspension System with an Input Time Delay

In this study, a state feedback robust control strategy with time delay dependence for the uncertainty, fault, and input time delay of a vehicle’s controllable suspension system is designed. Firstly, based on the working principle of the adjustable damping suspension system, the total damping force of the suspension is divided into “foundation damping force” and “controllable damping force”, taking the adjustable damping interval as the constraint boundary, which varies with the actuating velocity. Furthermore, based on the sensitivity analysis of the input time delay’s relationship with damping force disturbance, it exerts influence on the controllable damping force part. The associated uncertainty and fault are defined through linear fraction transformation and proportional gain, respectively, and the two are decoupled from the control mechanism. Then, based on the Lyapunov stability theory, a robust control law for the time-delay-dependent H∞ state feedback is designed and transformed into a linear matrix inequality convex optimization problem to solve. Finally, the feasibility and effectiveness of the proposed method are verified by designing different combinations of uncertainty and fault tests and by comparing and analyzing these with the time-delay-independent H2/H∞ robust control strategy under random and pulse road excitation.

Optimal robust control of nonlinear systems: inter-sample optimisation in sampled-data control

A methodology is presented for the design and implementation of robust controllers that optimise inter-sample performance for a broad range of nonlinear systems operated within a sampled-data environment. The methodology applies to nonlinear continuous-time systems described by state equations, and it allows for modelling uncertainties and constraints on maximal control effort. It is shown that there exist optimal robust state-feedback controllers that minimise inter-sample tracking errors for such systems, as long as an appropriate controllability requirement is met. A relatively simple design and implementation procedure for such controllers is described.

Parametric uncertain LTI systems: an LMI optimisation formulation for robust feedback control design

This article considers the following problems for a parametric uncertain (affine) linear time-invariant system. The first problem is: Let a feedback gain matrix be designed such that the states of the closed loop system satisfy the specified transient performance bounds. Then, compute a ball in the uncertain parameter space such that for all parameter perturbations within it, the state response continues to satisfy the same transient performance bounds. The second problem is on the synthesis of a robust static state feedback control, which i) minimises the norm of the gain matrix, ii) maximises the radius of the ball in the uncertain parameter space, and iii) ensures achieving specified transient performance in the closed loop. For this, a sub-optimal linear matrix inequality optimisation is formulated. The developed results are demonstrated with numerical examples. It also highlights how the proposed methodology can be applied to design robust static state feedback control for a polytopic uncertain system.

A novel robust extended dissipativity state feedback control system design for interval type-2 fuzzy Takagi-Sugeno large-scale systems

Recently, systems have become large in their model and dynamic. To apply control algorithms, serious problems appear that need to be solved. Two significant problems are modelling the dynamics of the large-scale system and reducing effects of perturbations. In this paper, we use the advantage of large-scale systems modelling based on the type-2 fuzzy Takagi–Sugeno model to cover the uncertainties caused by large-scale systems modelling. The advantage of using membership function information is the reduction of conservatism resulting from stability analysis. Also, this paper uses the extended dissipativity robust control performance index to reduce the effect of external perturbations on the large-scale system, which is a generalization of , , passive and dissipativity performance indexes and control gains can be achieved through solving linear matrix inequalities (LMIs). Hence, the whole closed-loop system is asymptotically stable. Finally, the effectiveness of the proposed method is demonstrated by two practical examples.

Evaluation of Ride Performance of Active Inerter-Based Vehicle Suspension System with Parameter Uncertainties and Input Constraint via Robust H∞ Control

In this study, we investigate a robust H∞ controller for a quarter-car model of an active inerter-based suspension system under parameter uncertainties and road disturbance. Its main objective is to improve the inherent compromises between ride quality, handling performance, suspension stroke, and energy consumption. Inerters have been extensively used to suppress unwanted vibrations from various kinds of mechanical structures. The advantage of inerter is that the realized ratio of equivalent mass (inertance relative to the mass of the primary structure) is greater than its actual mass ratio, resulting in higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system were achieved for the quarter-car model with parameter uncertainties. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the robust H∞ criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the robust state-feedback controller. According to numerical simulations, the active inerter-based suspension system in the presence of parameter uncertainties and external disturbance performs much better than both a passive suspension with inerter and active suspension without inerter.

Robust stabilization for a class of complex production process systems based on multi-dimensional moving pattern

This paper studies robust stabilization problem and state feedback controller design problem for a class of complex production process systems by pattern class variable instead of state variable or output variable. Firstly, the maximum entropy clustering method is introduced and modeling method based on multi-dimensional moving pattern is given. Nonlinear state space models of systems with input-delay are established by using the trajectories of pattern class variable. Then sufficient conditions for robust stabilization of the system are obtained by Linear Matrix Inequality. In addition, a state feedback controller is designed based on this condition. Finally, the effectiveness of the methods is illustrated by taking the actual working conditions data as an example.

Robust Control Based on Observed States Designed by Means of Linear Matrix Inequalities for Grid-Connected Converters

This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results.

Non-fragile robust model predictive controller design for uncertain time-delay systems with input constraints

ABSTRACT This paper addresses a non-fragile robust model predictive control design for a class of continuous-time uncertain systems with multiple state-delay and constrained control signals. The parameters of the system and the control gain are assumed to have perturbation in the additive form. The Lyapunov–Krasovskii functional approach is employed to derive sufficient conditions for determining a non-fragile robust state-feedback controller for all admissible uncertainties by minimising the upper bound of the defined quadratic cost function with respect to some linear matrix inequalities (LMIs). An additional inequality condition is imposed to address the constraint associated with the control signals. Numerical simulations are provided to assess the performance of the proposed controller.

On Robust Stabilization of Discrete-Time LPV/LFR Systems

This technical article presents novel robust stabilization conditions for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). The proposed conditions rely on the use of slack variables and decision matrices associated with the LFR approach to provide new controller designs. In addition, we address parameter-dependent Lyapunov functions and full-block multipliers to obtain less conservative synthesis conditions for discrete-time LPV/LFR systems. Design conditions are cast in the form of linear matrix inequalities to generate robust state-feedback and output-feedback controllers. Numerical examples demonstrate the effectiveness of the proposed method.

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

Robust Tracking Control of a Three-Phase Bidirectional Charger for Electric Vehicle

This paper presents a robust control strategy for an electric vehicle's three-phase off-board bidirectional AC-DC battery charger. The conventional constant current (CC) and constant voltage (CV) charging mode are considered to provide a fast-charging performance for the batteries. The bidirectional charger also allows using of the vehicle as an energy storage system for the grid i.e., charging during the peak-off times and delivering the energy back to the grid during peak times of electrical consumption. In discharging mode, the bidirectional charger maintains constant active power flow to the grid with a given reference. For both cases, user of a robust state feedback controller with integral action is made in the DQ-synchronous frame. The set of stabilizing gains of this controller are determined by a linear matrix inequality (LMI)-based optimization so that the convergence time to steady stead is minimized in the occurrence of the parametric uncertainties of the L-filter. The efficacy of the proposed controller is verified through simulation and experimental results on 102.4 V Lithium iron phosphate (LiFePO4) batteries.