Linear Parameter Varying Research Articles

High-precision control of a robotic arm using frequency-based data-driven methods

Next-generation motion control systems require fast and precise control. However, advanced control strategies often rely on complex and costly system models. Data-driven methods have been proposed to design high-performance controllers without requiring a parametric model of the system. In particular, methods using frequency response functions (FRFs) have been widely applied to mechatronic systems due to their good performance, and the industry’s familiarity with obtaining FRFs. This paper applies a recently developed method to design a controller for an industrial robotic arm with three translational degrees of freedom, using only the FRF of the robot around different operating points. Focused on motion control, the objective is to attain the desired reference tracking performance through the design of a linear-parameter-varying (LPV) two-degree-of-freedom (2DoF) controller. Performance is further improved by tuning an additional filter to compensate for inaccuracies in the transmission.

Switched LPV resilient tracking control for rigid-body with defective actuators and sensors

In this paper, a switched linear parameter-varying (LPV) resilient tracking controller is designed for rigid-body under actuator faults, uncertainties in measurement of scheduling parameters and time-delay in detection of system modes. The nonlinear attitude dynamics of rigid-body is constructed as a switched LPV system in which persistent dwell-time switching rule is used to regulate the switches caused by abrupt and intermittent actuator failures. Thereafter, by constructing a class of both parameter-dependent and time-dependent multiple Lyapunov functions (MLFs), a switched LPV resilient tracking controller is developed in order that the global uniform exponential stability and desired L∞ performance of the underlying system are achieved even with uncertain scheduling parameters, mismatched modes and persistent external disturbances. Furthermore, the nonconvex conditions of control synthesis are converted into parameterized linear matrix inequalities that can be readily resolved via gridding technique. Finally, the availability of the provided approach is evaluated with a numerical simulation.

Real-time Actuator Fault Detection and Isolation for Quadrotor UAV via Directional Residuals

Abstract Fault diagnosis is critical for the safe and reliable operation of quadrotor unmanned aerial vehicles (UAVs), so that timely remedial measures can be taken to reduce its negative impact. This paper presents a real-time actuator fault detection and isolation (FDI) method for quadrotor UAV flight process. First, a linear parameter-varying (LPV) model is established to describe quadrotor UAV dynamics, which considers measurement noise and external disturbance. Then, an FDI strategy is developed based on directional residuals, in which only one observer-based residual generator is required and Η_/L∞ indices are incorporated to balance fault sensitivity and disturbance robustness. A threshold is derived from the L∞ performance condition, and actuator fault is detected through residual evaluation. Furthermore, by introducing fault feature vectors associated with the system model, the faulty actuator is isolated promptly by analyzing directional correlations between generated residuals and the defined fault feature vectors. Finally, based on a quadrotor UAV platform, the effectiveness and superiority of the proposed FDI method are verified through online trajectory tracking processes.

Linear parameter varying μ synthesis robust control of CDC semi‐active suspension system for nonlinearity and uncertainty

AbstractBecause the continuous damping control (CDC) semi‐active suspension system has complex nonlinear and uncertain characteristics that can significantly affect the performance of the system. And in the controller design process, achieving a balance of multiple performance objectives is often difficult. Therefore, this paper designs a linear parameter varying (LPV) μ synthesis robust controller for the vibration suppression and multi‐objective control of a 7‐degree‐of‐freedom (7‐DOF) vehicle suspension system equipped with CDC dampers. Firstly, the nonlinear force model of the solenoid valve CDC damper is developed based on the actual damping variation. Considering the nonlinear forces of the coil springs, the nonlinear model of the 7‐DOF suspension system is expressed as LPV form. Further, the linear fractional transformation (LFT) method is used to analyze and reconstruct the system model for multiple parameter uncertainties of the suspension. The actuator time delays are also simulated through a frequency domain transfer function, which is considered to be an unmodeled dynamic at the input of the system. Finally, an LPV‐μ synthesis robust controller based on nonlinearity and mixed uncertainty is designed to improve car ride comfort and achieve the best relationship between comfort and handling stability. Simulation and experimental results under random disturbance conditions show that the LPV‐μ synthesis controller has better anti‐jamming performance and controllability compared to the H∞ controller and μ synthesis controller.

Preview control for linear parameter‐varying discrete‐time systems using a linear fractional representation

AbstractIn order to create a mixed tracking controller for discrete‐time linear parameter‐varying (LPV) systems, this work introduces a unique control strategy employing a linear fractional representation (LFR). Under the premise that the reference signal can be previewable, a design strategy for a controller with preview compensations is suggested. First, a preview tracking control issue is changed into a regulator problem by adding two additional linked auxiliary parameters into the initial system state/input, which further creates more enhanced error systems incorporating future information of reference signals. The suggested conditions then depend on utilizing slack variables with decision matrices related to the LFR approach in order to give innovative preview controller designs. We also construct reduced conservative synthesis situations by taking into account parameter‐dependent Lyapunov functions and full‐block multipliers. In order to create state‐feedback and output‐feedback preview tracking controllers, design requirements are characterized as linear matrix inequalities. Two simulation studies are completed as the last step to highlight how successful the suggested control strategy is.

Performance Optimization with LPV Synthesis for Disturbance Attenuation in Planar Motors

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation.

Q‐learning‐based H∞ control for LPV systems

AbstractIn this paper, a model‐free H∞ control method is developed for discrete‐time linear parameter‐varying (LPV) systems by leveraging Q‐learning, which employs the data encompassing system states, control inputs, exogenous disturbance, and time‐varying convex hull rather than the dynamical model known a priori. A policy iteration algorithm presented via linear matrix inequality formed by such collected data is developed with convergence guarantee. Our analysis demonstrates that, in the presence of sufficiently rich disturbances, the attenuation level converges to a lower value than the traditional H∞ control solution derived from an exact LPV model. A numerical example is demonstrated to verify the stabilization, disturbance attenuation, adaptivity, and convergence of the H∞ attenuation level. Moreover, a continuous stirred tank reactor (CSTR) approximated by a discrete‐time LPV system is employed to show the practical potential of the developed model‐free approach.

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

This paper presents a practical model predictive control (MPC) framework for gust load alleviation of a flexible flying wing. Both the controller solving and state estimation are based on a reduced-order model, which features a linear parameter-varying (LPV) form, avoiding online linearization and reducing the scale of the corresponding quadratic programming problem. An improved modeling and model reduction process is used to enhance modeling efficiency and ensure that the reduced-order model can accurately capture the rigid-flexible coupled characteristics of the flexible flying wing under arbitrary gusts. By reconstructing the output of the control-oriented model to include both rigid-body motion and flexible vibrations, the rigid-flexible coupled multi-objective control is established as an MPC problem for reference tracking. The online optimization is formulated in a sparse fashion and combined with an iterative algorithm based on predicted trajectories, describing the variation of model dynamics within the prediction horizon more accurately. With a time-varying Kalman estimator for state updating, the closed-loop simulations are performed for gust alleviation performance validation. Additionally, the real-time potential of the proposed MPC framework is demonstrated through Monte Carlo simulations.

Learning-based Predictive LPV Control of Atmospheric Pressure Plasma Jets

Abstract Complexity of atmospheric pressure plasma jet dynamics poses a significant challenge for control design, and this letter presents a learning- and Scenario-based Model Predictive Control (ScMPC) method in the Linear Parameter-Varying (LPV) framework to tackle this challenge. By leveraging artificial neural networks, an LPV state-space representation of the system dynamics is first learned. The mismatch between this model and real plant is then estimated using Bayesian neural networks, enabling scenario generation for ScMPC design. Soft constraints are imposed in the control design formulation to ensure the feasibility of the underlying optimization problem. Results from extensive simulations are used to compare the proposed framework with a benchmark LTI-based ScMPC, demonstrating superior performance in both reference tracking and thermal dose delivery. The proposed approach allows for accurate control of plasma jets while reducing conservatism inherent in either LTI-based approaches or other robust control methods.

Stochastic LPV MPC-based path following control for bevel-tip flexible needle with probabilistic constraints

This paper addresses the path-tracking problem for flexible needle control systems using a stochastic linear parameter varying (LPV) and model predictive control (MPC) strategy. Flexible needles operating in dynamic environments with non-uniform tissue density often deviate from ideal assumptions, resulting in non-standard models. The bicycle kinematics model for flexible needle motion control is transformed into an LPV model, improving accuracy and enabling more efficient control. The proposed stochastic LPV MPC approach aims to mitigate uncertainties arising from modelling errors and dynamic environmental factors, ensuring accurate trajectory tracking for the flexible needle. The sample and removal method is utilized to reformulate the probabilistic-constrained optimization problem for implementation. The contributions of this work lie in the application of stochastic LPV MPC to address the trajectory tracking problem in the presence of uncertainties. The simulation results illustrate the superior robustness of the stochastic LPV MPC approach, as evidenced by significantly smaller tracking errors across various scenarios.

Linear Parameter Varying and Reinforcement Learning Approaches for Trajectory Tracking Controller of Autonomous Vehicles

This research focuses on controlling the motion trajectory of autonomous vehicles by using a combination of two high-performance control methods: Linear Parameter Varying (LPV) and Reinforcement Learning (RL). First, a single-track motion model is researched and developed with coordinate systems to determine the car's motion trajectory through signals from GPS. Then, the LPV control method is used to design a controller to control the car's motion trajectory. Reinforcement learning method with detailed training procedures is used to combine with the advantages of LPV controller. Finally, the simulation results are evaluated in the time domain through the use of specialized CarSim software, which clearly demonstrates the superiority of the research method.

TVIE-based fault-tolerant model predictive control for trajectory tracking of mobile robot

This paper investigates the trajectory tracking control issue for a linear parameter-varying (LPV) system of a wheeled mobile robot (WMR) with actuator fault and constraints, where a time-varying intermediate estimator (TVIE)-based fault-tolerant model predictive control (MPC) method is proposed. To obtain the real system with actuator fault, based on the existing traditional IE, an optimized objective function is designed to update its observer gain online, which results in a TVIE. A new estimation-based predictive model in MPC is designed by introducing the estimations of error state and fault from the TVIE. Moreover, compared with the existing IE or extended state observer (ESO), the estimation performance of TVIE is better. Then the MPC optimization strategy is used to design fault-tolerant controllers. To guarantee stability and recursive feasibility, the bimodal MPC strategy is used, where a terminal penalty and a terminal constraint are included. Finally, the effectiveness and superiority of the proposed approach is illustrated in experiment.

LMI-based state observer design for supercavitating vehicles with time delay

Due to the existence of the planing force, the control of the supercavitating vehicle is difficult, and the vertical velocity which has a great influence on the planing force cannot be directly measured. Therefore, considering the time-delay effect of the planing force and the external disturbance, the state observer and controller based on linear matrix inequality (LMI) have been designed. By decomposing the planing force into two parts of time delay and non-time delay, and a longitudinal plane Linear Parameter Varying (LPV) time-delay model for supercavitating vehicles is derived. In addition, the controller and state observer for the supercavitating vehicle system with time-delay characteristics and external disturbances are simultaneously designed. The gains of the controller and observer are obtained by combining the theory of linear matrix inequalities and convex polytopes, ensuring the convergence of estimation error. At the same time, taking into account the possibility of exceeding the physical limits of the actuator when the input value is too large, the compensator has been added. Finally, the simulation results demonstrate that the designed controller exhibits good stability and tracking performance.

Analysis and Controller Design for Parameter Varying T-S Fuzzy Systems with Markov Jump

In this paper, we investigate a novel T-S fuzzy parameter varying system with Markov jump, in which parameters depend not only on a Markov chain but also on linear parameter varying elements that take values in convex polytopic sets. Stable conditions and the gain-scheduling controller design method for this system are obtained. Applying Lyapunov function depending on the operation mode and full block S-procedure lemma, we obtain stochastic stabilization conditions. We find that this novel system has two distinct advantages. On the one hand, it inherits the advantages of traditional T-S fuzzy systems in handling nonlinear objects under the frame of T-S fuzzy systems; on the other, it obtains the advantages of dealing with time-varying characteristics from the point of linear parameter varying (LPV) systems. Finally, the theory results are illustrated via numerical simulation.

Switched Observer Design for a Class of Non-Linear Systems

This paper is concerned with the switched observer design for a class of systems subject to locally Lipschitz non-linearities. By performing a suitable description of the estimation error dynamics into a linear parameter varying (LPV) system representation, sufficient conditions for the existence of a switching output injection gain are proposed such that the asymptotic stability of the estimation error is guaranteed. These conditions can be conveniently expressed by means of linear matrix inequalities (LMIs), which are easily computationally tractable. A numerical example is provided to show the favorable performance achieved by the proposed observer, which can be applied to a large class of non-linear systems.

Stability and Robustness Analysis and Optimization for Gain-Scheduled Control of Aero-Engines

Abstract Gainscheduled control is widely applied in the aerospace domain, yet the selection of design points for gainscheduling controllers to ensure stability and robustness throughout the range of scheduling variables remains theoretically unguided. Therefore, this paper introduces an analysis and optimization method for the stability and robustness of gain-scheduled control, aimed at providing a theoretical framework for design points selection. Initially, the method characterizes the gainscheduled control system as a polytopic Linear Parameter Varying (LPV) system, wherein the design points of the gainscheduled control system correspond to the vertices of the polytopic LPV system. Subsequently, the method utilizes Linear Matrix Inequality techniques to demonstrate the stability of a polytopic LPV system with a corresponding number of vertices, and by assessing the approximation degree between the polytopic LPV system and the gainscheduled control system with an identical number of design points, it evaluates and ensures the stability of the latter, thereby establishing the minimal requirements for the number of design points. After ensuring stability, the method further refines the number of design points within the gainscheduled control system to meet additional robustness and performance considerations. A case study on turbofan engine controls validates the proposed method. New design points, selected via stability and robustness analysis, enhance the system's steadystate phase margin and robustness against model uncertainties. Moreover, compared to a vgap metric-based method, the two methods exhibit similar performance in terms of stability, robustness, and tracking control. However, the proposed method requires fewer design points, resulting in less conservatism.

Sampled-data static output feedback robust MPC for LPV systems with bounded disturbances

This paper investigates a sampled-data static output feedback robust model predictive control (MPC) approach for continuous-time linear parameter varying (LPV) systems with unknown system states and bounded disturbances. Between two successive sampling time instants, it is assumed that the controlled LPV systems evolve in continuous-time, and the control inputs are piecewise constant. The robust stability conditions and control input constraints on the closed-loop system are considered in the formulated robust MPC optimization. The constraints in the formulated robust MPC optimizations are formulated as linear matrix inequalities (LMIs) and solved as convex optimization. The designed sampled-data static output feedback robust MPC optimization has a simple structure and directly optimizes output feedback controller. Furthermore, the system state constraint sets are on-line updated over the sampling interval. The designed sampled-data static output feedback robust MPC approach has the property of recursive feasibility, and can guarantee robust stability of the controlled continuous-time LPV systems. A simulation example is given to illustrate the effectiveness of the approach.

Switching LPV approach for analysis and control of TCP-based cyber-physical systems under DoS attack

Cyber-physical systems (CPSs) integrate controllers, sensors, actuators, and communication networks. Tight integration with communication networks makes CPSs vulnerable to cyberattacks. In this paper, the impact of denial of service (DoS) attacks on the stability of cyber physical systems is investigated, with a focus on the transmission control protocol (TCP). A sufficient stability condition is extracted in linear matrix inequality (LMI) form. The TCP-CPS under DoS attack is modeled as a switching linear parameter-varying (LPV) time-delay system using the Markov jump model. Subsequently, a parameter-dependent stabilizing controller is designed for CPSs under DoS attacks, taking into account network parameters. Finally, the efficiency and feasibility of the findings are demonstrated through a well-known case study in the networked control systems literature.

Event-triggered dynamic output-feedback control for LPV systems

This paper addresses the co-design of event-triggered dynamic output-feedback (DOF) control for discrete-time linear parameter-varying (LPV) systems. Two independent event-triggering schemes are introduced to determine when to transmit data from the sensor to the controller and from the controller to the actuator channels. Enhanced conditions employing linear matrix inequalities (LMIs) are derived to establish constructive criteria for simultaneously designing the gain-scheduled DOF controller and the triggering mechanisms, ensuring the asymptotic stability of the closed-loop LPV system's origin. Additionally, a convex optimisation problem is proposed to enlarge the inter-event sampling on the independent channels of sensor-to-controller and controller-to-actuator. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Enhancement of Yaw Moment Control for Drivers with Excessive Steering in Emergency Lane Changes

When a ground vehicle runs at high speeds, even a slight excess in the wheel steering angle can immediately cause the vehicle to slide sideways and lose control. In this study, we propose an active safety control system designed to address emergency situations where the driver applies excessive steering input and the vehicle speed varies significantly during control. The system combines the direct yaw moment (DYM) method with a steering saturation scheme that prevents excessive driver steering input from adversely influencing the front-wheel steering. Consequently, the control system allows the DYM to focus more on other stabilization tasks and maintain tire/road friction within its workable linear range. The implementation relies on a reference steering angle and a reference vehicle state, derived from a linear vehicle model considering tire/road friction limitations. When the driver’s steering angle and the system state deviate from these reference values, the control system intervenes by applying both the steering saturation scheme and DYM method. This ensures the front-wheel steering angle and system state remain close to the reference values. The control strategy is developed using the polytopic Linear Parameter Varying (LPV) technique and Linear Matrix Inequality (LMI) to account for the changes in vehicle speed. It is further enhanced with an input saturation technique based on a high-gain approach, which improves control utilization and system response during emergency situations. The advantages of the proposed control strategy are demonstrated through simulation results.