Robust Feedback Control Research Articles

Active disturbance rejection control of flexible industrial manipulator: A MIMO benchmark problem

Robotic manipulators are widely used in modern industry. In order for robot manipulators to achieve trajectory tracking control, the end-effectors must move precisely along the given trajectories. The nonlinearity, strong coupling, and uncertainty of the system make trajectory tracking very complicated and difficult. An approach for robust feedback control is presented in this paper as a solution to this problem. The design relies on active disturbance rejection control to estimate unknown disturbances affecting the plant. The controlled system is an uncertain two-link manipulator with elastic gear transmissions, described by nonlinear friction and elasticity. It is based on an industrial benchmark problem. The model has two significant uncertainties: parametric uncertainty as well as external disturbances that affect tools and motors. A simulation-based evaluation of the proposed control method and a comparison of its performance, considering specific robustness requirements and trajectory tracking, are presented. The comparison includes the baseline controller, the QFD (Quality Function Deployment) method, and PD-CNN (PD Control Compensation based on the Cascade Neural Network). Computer simulations of the proposed controller are carried out to validate the ABB (Asea Brown Boveri) industrial benchmark. The simulation results demonstrate superiority in meeting stability and target value requirements. The stability and ultimate boundedness of the tracking error of ADRC (Active Disturbance Rejection Control) are demonstrated.

Kalman state estimator for aircraft structural load alleviation using eigenpair assignment

Process of finding the “best estimate” from noisy signals amounts to “filtering out” the noise. Many methods exist to filter the unwanted noise. A tried and tested method is to use a Kalman Filter which not only cleans up the signals but can also be used to provide signal estimates, for use in reduced order feedback control. Typically, Kalman filter gains are computed using the Linear Quadratic Regulator theory. Reduced order feedback control has been applied in aircraft control problems. One such application area is in synthetic load alleviation, structural loads that arise due to gusts and or control surface deflections. Aircraft structural load alleviation necessitates the use of robust feedback control. The controllers are required to provide load alleviation in cases where the feedback signals are contaminated with noise or missing due to sensor failures. In this paper a method of computing the Kalman gains for the purposes of reduced order feedback is presented, which completely specifies the error dynamics of the estimator in terms of its eigenvalues and associated eigenvectors. The state estimator synthesized using the proposed approach has excellent noise rejection properties and shown to be robust and can be successfully used in reduced order state feedback control, specifically in Aircraft Structural Load Alleviation control schemes. The proposed scheme demonstrates reduction in structural loads.

High bandwidth control of slow sampling rate nonlinear systems using alternating predictive GPIOs

This paper investigates the problem of robust output feedback control tracking for a class of nonlinear dual-rate sample-data systems subject to time-varying disturbances. These dual-rate systems, known as slow measurement fast control (SMFC) systems, are characterised by a slow sampling rate of the sensor and a fast updating rate of the controller. To facilitate high-frequency signal tracking, this paper introduces an alternating predictive generalised proportional integral observer (APGPIO). The proposed control method not only effectively restores the system state and captures disturbance changes between samples but also enhances the control bandwidth and anti-disturbance ability, enabling effective tracking of high-frequency reference outputs. By combining it with a fast updating sample-data feedback controller, APGPIO utilises predictive methods to increase the sampling rate of the system's sensors, matching the update frequency of the controller. Stability analysis demonstrates that the tracking error of this hybrid nonlinear system converges to a bounded region centred at the origin. Finally, the designed method's high control bandwidth and anti-disturbance ability are demonstrated through multiple sets of simulations using a real system.

Robust data-driven feedback control with pole placement constraints

We consider the problem of designing feedback controllers, using measured data, such that the eigenvalues of the closed-loop system lie in a predefined stability region D of the complex plane. We consider a general convex region D defined by a quadratic matrix inequality (QMI). First, considering the case of noise-free input/state data we provide non-conservative design conditions in terms of data-based linear matrix inequalities. For the case when the input/state data are affected by noise, the data-based design conditions are only sufficient. We further discuss the case of noise-free input/output data. We illustrate our results with a numerical example.

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.

On scaling robust feedback control and state estimation problems in power networks

Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of scalability and sensitivity. In particular, Lyapunov-based approaches rely on forming semi-definite programs (SDPs) that are (i) not scalable and (ii) extremely sensitive to the choice of the bounding scalar that ensures the strict feasibility of the linear matrix inequalities (LMIs). This paper addresses these two issues by employing a celebrated non-Lyapunov approach (NLA) from the control theory literature. In lieu of linearized models of power grids, we focus on (the more representative) nonlinear differential algebraic equation (DAE) models and showcase the simplicity, scalability, and parameter-resiliency of NLA. For some power systems, the approach is nearly fifty times faster than solving SDPs via standard solvers with almost no impact on the performance. The case studies also demonstrate that NLA can be applied to more realistic scenarios in which (i) only partial state data is available and (ii) sparsity structures are imposed on the feedback gain. The paper also showcases that virtually no degradation in state estimation quality is experienced when applying NLA.

Decentralized robust adaptive backstepping control for a class of non-minimum phase nonlinear interconnected systems

In this paper, a class of interconnected systems is considered, where the nominal isolated subsystems are fully nonlinear and non-minimum phase. A decentralized Extended Kalman Filter-Extended High Gain Observer (EKF-EHGO) is designed to observe the system states. Then, a systematic backstepping design procedure is employed to develop a novel decentralized robust adaptive output feedback control, in which the adaptive law is designed to counter the effects of the interconnections and uncertainties. The proposed decentralized dynamic output feedback control scheme can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Both interconnections and uncertainties are allowed to be unmatched and bounded by an unknown high-order polynomial, which is a more general form when compared with existing work. Two MATLAB simulation examples are used to demonstrate the effectiveness of the proposed method including a system comprising translational oscillator with rotating actuator (TORA) sub-systems.

Sampled-Data Output Feedback Control for Nonlinear Uncertain Systems Using Predictor-Based Continuous-Discrete Observer.

In this article, we investigate the problem of sampled-data robust output feedback control for a class of nonlinear uncertain systems with time-varying disturbance and measurement delay based on continuous-discrete observer. An augmented system that includes the nonlinear uncertain system and disturbance model is first found, and by using the delayed sampled-data output, we then propose a novel predictor-based continuous-discrete observer to estimate the unknown state and disturbance information. After that, in order to attenuate the undesirable influences of nonlinear uncertainties and disturbance, a sampled-data robust output feedback controller is developed based on disturbance/uncertainty estimation and attenuation technique. It shows that under the proposed control method, the states of overall hybrid nonlinear system can converge to a bounded region centered at the origin. The main benefit of the proposed control method is that in the presence of measurement delay, the influences of time-varying disturbance and nonlinear uncertainties can be effectively attenuated with the help of feedback domination method and prediction technique. Finally, the effectiveness of the proposed control method is demonstrated via the simulation results of a numerical example and a practical example.

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.

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.

The Equivalence Conditions of Optimal Feedback Control-Strategy Operators for Zero-Sum Linear Quadratic Stochastic Differential Game with Random Coefficients

From the previous work, when solving the LQ optimal control problem with random coefficients (SLQ, for short), it is remarkably shown that the solution of the backward stochastic Riccati equations is not regular enough to guarantee the robustness of the feedback control. As a generalization of SLQ, interesting questions are, “how about the situation in the differential game?”, “will the same phenomenon appear in SLQ?”. This paper will provide the answers. In this paper, we consider a closed-loop two-person zero-sum LQ stochastic differential game with random coefficients (SDG, for short) and generalize the results of Lü–Wang–Zhang into the stochastic differential game case. Under some regularity assumptions, we establish the equivalence between the existence of the robust optimal feedback control strategy operators and the solvability of the corresponding backward stochastic Riccati equations, which leads to the existence of the closed-loop saddle points. On the other hand, the problem is not closed-loop solvable if the solution of the corresponding backward stochastic Riccati equations does not have the needed regularity.

Reference tracking via output feedback for constrained uncertain linear systems

In this paper we propose a robust output feedback control scheme for constant reference tracking in uncertain linear systems subject to state and control constraints. First, we establish conditions under which a polyhedral set is Output Feedback Controlled Invariant with respect to a linear system subject to polytopic uncertainties, i.e. a set guaranteeing robust constraint satisfaction via output feedback. Then, we build a dynamic output feedback controller for the uncertain model based on set-membership observers, allowing the reduction of the set of possible states consistent with the measurements. Finally, to reduce the tracking error, we propose a model update procedure that adjusts the nominal model used for tracking to the output measurements. Numerical experiments illustrate the ability of the proposed controller to achieve reference tracking with reduced offset for the uncertain systems under consideration. To the best of our knowledge, it is one of the first works that addresses constant reference tracking in uncertain linear systems under constraints with output feedback.

Robust integral controller design based on composite nonlinear feedback in uncertain systems with constrained inputs and external disturbances

AbstractIn this article, to enhance the transient performances in constrained uncertain systems, a control technique based on linear matrix inequality (LMI) is characterized to the robust integral composite nonlinear feedback (CNF) controller design. To achieve this aim, considering the inputs limitations and the uncertainties, the regulation is transformed into a minimization subjected to several LMIs. Solving an optimization in real‐time, the gains of the controller are calculated. So, the regulation and the disturbance rejection are effectively handled employing the presented control law. Compared with the existing integral methodology, the provided simulations validate the applicability of the robust integral CNF control law in uncertain systems.

Dynamic output feedback model predictive control for asynchronous Markovian jump systems under try‐once‐discard protocol

AbstractThis paper is concerned with the dynamic output feedback robust model predictive control (RMPC) problem for a class of discrete‐time asynchronous Markovian jump systems (MJSs) subject to polytopic parameter uncertainties and hard constraints on states and inputs. A hidden Markov model is employed to describe the asynchronous phenomenon between the detected modes and the system modes. For the purpose of improving the network utilization as well as reducing the transmission burden and avoiding data collisions, the try‐once‐discard (TOD) protocol is deployed in the shared communication network between sensor nodes and the controller node. Considering the difficulty of obtaining the system state in the practice, the dynamic output‐feedback control in the framework of RMPC is adopted, and the worst‐case optimization problem over the infinite moving horizon is formulated for the performance analysis and control synthesis. By means of the Lyapunov‐like function approach, free weighting matrices and inequality techniques such as the ‐procedure are introduced to deal with the non‐convexity caused by couplings between decisive variables and the negative influence resulting from the data orchestration is mitigated. Based on the delicate establishments, a certain upper bound of the objective function is employed to construct an auxiliary optimization problem with solvability to find the desired controllers, and sufficient conditions are obtained to guarantee that the MJSs under the proposed RMPC‐based controllers are mean‐square stable. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.

Robust Output Feedback Position Control of Hydraulic Support with Neural Network Compensator

Hydraulic support is important equipment in the fully mechanized mining face, and the control performance of the hydraulic support multi-cylinder system directly affects the smooth progress of coal mining process, which is the basis for the continuous advancement of the coal face. However, the friction force of the hydraulic support in the process of pulling the frame is complex due to the underground environmental load. Moreover, the parameters of the moving cylinder are uncertain, and the state of the system cannot be fully measured, which increases the difficulty of control. A proportional-integral-derivative controller is usually used in electro-hydraulic closed-loop control systems because of its computational complexity, but its robustness is poorly adapted to variable load conditions in the coal mine. Therefore, a robust output feedback position controller is proposed in this paper to improve control accuracy and system robustness with only position signal. The multi-cylinder system of hydraulic support is modeled as a standard type, and then a high-order differentiator is proposed to estimate the immeasurable system states using the output position signal. A neural network compensator is applied to estimate and compensate for the external disturbance of the moving cylinder. Furthermore, the parameters of the ZY3200/08/18D hydraulic support are adopted to analyze the effectiveness of the designed controller in simulations. Finally, a real-time control system of hydraulic support is built, and the experimental results show that the novel robust output feedback controller has improved by 47.2% and 30.6% in tracking accuracy compared to PI controller.

Ellipsoidal tube‐based output feedback robust MPC for linear systems with bounded disturbances and noises

AbstractThis paper designs an ellipsoidal tube‐based output feedback robust model predictive control approach for linear systems with bounded disturbances and noises subject to physical constraints. The ellipsoidal tube‐based output feedback robust model predictive control approach combines the off‐line optimization to compute controller parameters and deal with system uncertainties, and the on‐line optimization to stabilize the nominal system with time‐varying tightened constraints. In the off‐line optimization, the state observer gain, ancillary feedback controller gain, and tightened constraint sets on the nominal system are synthesized in one optimization. Then, an ellipsoidal terminal constraint set with terminal controller gain and terminal cost matrix, and tightened constraint sets related to different sizes of estimation error bounds are computed. In the on‐line model predictive control optimization with time‐varying tightened constraints, a sequence of nominal control inputs is receding horizon optimized to steer the nominal system state to the ellipsoidal terminal constraint set. When the current nominal system state is bounded within the ellipsoidal terminal constraint set, the nominal control inputs are switched to the feedbacks on the closed‐loop nominal system states. Recursive feasibility of the proposed algorithm and robust stability of the controlled system are guaranteed.

Robust stabilization of uncertain nonlinear systems with infinite distributed input delays

This paper studies the robust stabilization problem of a class of uncertain Lipschitz nonlinear systems with infinite distributed input delays. A novel robust predictor feedback controller is developed and the controller gain can be obtained via solving a linear matrix inequality. It is shown that the proposed robust predictor feedback controller can globally exponentially stabilize the concerned uncertain nonlinear system with infinite distributed input delays. The key to the proposed approach is the development of several new quadratic Lyapunov functionals. The obtained results are extended to the case of systems with both multiple constant input delays and infinite distributed input delays. It is noted that the obtained results include some existing results on systems with constant input delays or bounded distributed input delays as special cases. Finally, two examples of Chua’s circuit and spacecraft rendezvous system are presented to illustrate the effectiveness of the proposed robust controllers.

High precision structured H∞ control of a piezoelectric nanopositioning platform.

The inherent weakly damped resonant modes of the piezoelectric nanopositioning platform and the presence of model uncertainty seriously affect the performance of the system. A structured H∞ design is used in this paper to solve the accuracy and robustness problems respectively using a two-loop control structure. The multiple performance requirements of the system are constituted into an H∞ optimization matrix containing multi-dimensional performance diagonal decoupling outputs, and an inner damping controller d is set according to the damping of the resonant modes; the second-order robust feedback controller is preset in the inner loop to improve the robustness of the system; the tracking controller is connected in series in the outer loop to achieve high accuracy scanning; finally, the structured H∞ controller is designed to meet the multiple performance requirements. To verify the effectiveness of the proposed structured H∞ control, simulation comparison experiments are done with the integral resonant control (IRC) and H∞ controller. The results demonstrate that the designed structured H∞ controller achieves higher tracking accuracy compared to the IRC and H∞ controllers under grating input signals of 5, 10, and 20 Hz. Moreover, it has good robustness under 600g and 1000g loads and high frequency disturbances close to the resonant frequency of the system, meeting multiple performance requirements. Compared with the traditional H∞ control, yet with lower complexity and transparency, which is more suitable for engineering practice applications.

Optimal Robust Tracking Control of Injection Velocity in an Injection Molding Machine

Injection molding is a critical component of modern industrial operations, and achieving fast and stable control of injection molding machines (IMMs) is essential for producing high-quality plastic products. This paper focuses on solving an optimal tracking control problem of the injection velocity that arises in a typical nonlinear IMM. To this end, an efficient optimal robust controller is proposed and designed. The nonlinear injection velocity servo system is first approximately linearized at iteration points using the first-order Taylor expansion approach. Then, at each time node in the optimization process, the relevant algebraic Riccati equation is introduced, and the solution is used to construct an optimal robust feedback controller. Furthermore, a rigorous Lyapunov theorem analysis is employed to demonstrate the global stability properties of the proposed feedback controller. The results from numerical simulations show that the proposed optimal robust control strategy can successfully and rapidly achieve the best tracking of the intended injection velocity trajectory within a given time.