Linear Parameter-varying Gain-scheduling Research Articles

Polytopic LPV modeling and gain scheduling [formula omitted] control of ball screw with position- and load-dependent variable dynamics

Ball screw drive (BSD) is a precision transmission mechanism widely used in high-precision positioning or tracking systems. The dynamic behavior of BSD varies with position and load, which causes tracking errors and poor robustness. Therefore, this paper proposes a polytopic linear parameter varying (LPV) model to express the varying dynamic behavior of BSD. The parameters of the LPV model are identified by the closed-loop frequency domain method and Levenberg–Marquardt iterative algorithm. Based on the polytopic LPV model, an LPV gain scheduling (GS) H∞ controller is proposed for the BSD with varying dynamics. Specifically, the controller is designed through polytope-based GS representation and mixed sensitivity synthesis. The most significant part is the proposal of a GS H∞ control algorithm to implement controller parameters that change with changing dynamics. Moreover, the stability of the closed-loop system is achieved by quadratic stabilization with state feedback. Finally, identification experiments and trajectory-tracking comparative experiments are carried out. The experimental results demonstrate that the proposed polytopic LPV modeling and GS H∞ control synthesis are effective in achieving accurate trajectory tracking and excellent robustness.

A robust adaptive linear parameter-varying gain-scheduling controller for aeroengines

This paper presents an on-board model-based adaptive linear parameter-varying (LPV) gain-scheduling controller for aeroengines exhibiting strong nonlinearity, uncertainty, and component performance degradation. A novel hybrid on-board adaptive model is proposed using a dual-loop (fast-slow) structure, which consists of an adaptive LPV model as the fast loop to guarantee the on-board performance, and a component-level model as the slow loop to provide accurate model information at a slow update frequency, without violating the real-time requirement of the fast loop. An innovative mixed adaptive extended Kalman filter is designed to estimate and update the model, by introducing an extended-Kalman-filter-based covariance scaling mechanism and updating the system noise covariance matrix by employing full covariance estimation. The component-level adaptive nonlinear model and mixed adaptive extended Kalman filter increase the accuracy of the on-board model, while the adaptive LPV model enhances its real-time performance. Finally, a robust polytopic adaptive LPV gain-scheduling controller is designed based on the adaptive LPV model by introducing a new scheduling variable, i.e., health parameters estimated by the on-board adaptive model. The proposed adaptive model and controller are implemented to a high fidelity nonlinear aeroengine model. Simulation results demonstrate that the estimation error of health parameters and component degradation level of the proposed method is 0.0763%, which gives an order of magnitude higher health parameter and component degradation level estimation accuracy compared with the other commonly applied models. The proposed model-based adaptive LPV gain scheduling control scheme has a steady-state error of 0.0028%, gives one order of magnitude higher control accuracy than that of three state-of-the-art baseline controllers while demonstrating significantly reduced overshoot and adjustment time. This verifies the robustness and effectiveness of the proposed controller, and verifies that the model can meet the technical requirements of the engine control system and significantly improve the engine control performance.

A method for reducing implementation complexity in linear parameter-varying controllers

Gain-scheduling is a popular control technique to deal with nonlinear and time varying systems. The linear parameter-varying (LPV) system approach offers systematic tools to design gain-scheduled controllers. However, the implementation of these controllers might demand complex mathematical operations to be performed in real-time. This limits the hardware and the applications in which LPV controllers can be used. In this article, we analyze these limitations and propose a design methodology to reduce the implementation complexity of gain-scheduled LPV controllers. The methodology is illustrated with a nonlinear bicycle model used in electric vehicle control.

Gain-scheduling LPV synthesis H∞ robust lateral motion control for path following of autonomous vehicle via coordination of steering and braking

This paper proposes a robust gain-scheduling lateral motion control strategy via coordination of the active front-wheel steering (AFS) and direct yaw moment control (DYC) for path following of autonomous vehicle. Distinguishing from other relevant researches, a seamless application of the DYC is designed to reduce the influence of braking for the vehicle longitudinal dynamics. In order to achieve this objective, the weighting function with a self-scheduling parameter is designed. Based on the above, a novel LPV (Linear Parameter Varying) synthesis H∞ performances lateral motion controller is designed considering the vehicle longitudinal velocity as a time-varying parameter. The path following is realised through achieving a desired yaw rate, which is generated based on the path-following dynamics. The feedback gains can be derived by solving the LMI (Linear Matrix Inequalities). Furthermore, the physical limitations of the actuators (steer-by wire and brake-by-wire) are considered by weighting functions. Finally, experiments in the HIL system are carried out to verify the effectiveness and real-time performance of the proposed control strategy, and the results show that the proposed controller has good tracking capability under different manoeuvres and can reduce the possibility of actuator saturation and the influence of braking for the vehicle longitudinal dynamics.

Compensating Thermal Derated Torque of IPMSM Centric Electric Vehicles

A novel control approach based on Linear Parameter Varying (LPV) is designed for Electric Vehicles (EVs) to address the crucial challenge of torque derating. A high fidelity Interior Permanent Magnet Synchronous Motor (IPMSM) based EV is modelled by taking into account the influence of temperature. A closed loop torque compensation control architecture with LPV based Field Oriented Control (FOC) has been designed to mitigate the thermal effects. In order to curtail deteriorating of FOC due to parameter variation, a robust LPV observer has been proposed to estimate the degraded Permanent Magnet (PM) flux linkage and instantaneous torque production caused by uncertainties in stator resistance arises due to thermal effects. A LPV gain scheduling robust current controller for inner control loop of FOC has also been designed which ensures internal stability. The LPV observer-controller gains are computed by solving Linear Matrix Inequalities (LMIs) using convex optimization and singular value decomposition. The experiments simulations have been performed for EV operation against the Worldwide Harmonized Light Vehicles Test Procedure (WLTP) class 3, New European Driving Cycle (NEDC) and Federal Test Procedure (FTP) driving cycles considering thermal effects in Matlab/Simulink. The efficacy of proposed control architecture for managing the derating torque of IPMSM based EV is demonstrated through the validity of results and detailed data analysis. The LPV based FOC is compared with conventional FOC control counterpart. The comparative experiments simulation results show that the overall Mean Square Error (MSE) value is exponentially reduced which establish superiority of the proposed control scheme.

An Improved Integral Inequality for Delay-Dependent Gain-Scheduled LPV Control

The present work examines the delay-dependent gain-scheduling feedback control with guaranteed closed-loop stability and induced L2 norm performance for continuous-time linear parameter-varying (LPV) systems with arbitrary time-varying delay. An extension of Lyapunov stability utilizing Krasovskii functionals is considered to derive stability analysis and synthesis conditions for delay-dependent dynamic output feedback LPV control design. The main challenges associated with this approach are selecting appropriate Lyapunov-Krasovskii functionals (LKFs) and finding efficient integral inequalities to bound the derivative of the LKF. Accordingly, a novel modified parameter-dependent LKF candidate along with an affine version of Jensen’s inequality bounding technique are employed leading to the derivation of less conservative sufficient conditions expressed in terms of convex linear matrix inequalities (LMIs). The proposed methodology is compared with past work in the literature in terms of conservatism reduction and performance improvement through a numerical example. Finally, the application of the proposed output-feedback LPV control design is evaluated on the automated mean arterial blood pressure (MAP) regulation in critical patient resuscitation via vasoactive drug infusion. Closed-loop simulation results are presented to illustrate the potential of the introduced LPV gain-scheduling design to provide MAP set-point tracking in the presence of disturbances and varying input delays.

Robust linear parameter-varying output-feedback control of permanent magnet synchronous motors

This paper investigates the design of a robust linear parameter-varying (LPV) controller for speed regulation of surface permanent magnet synchronous motors (SPMSMs). Motor dynamics is defined in the α–β stationary frame and a parameter-varying model formulation is provided to describe its nonlinear dynamics. A robust gain-scheduled LPV dynamic output-feedback controller is designed to guarantee the asymptotic stability and performance requirements, as well as, guarantee robustness against parameter perturbations and torque load disturbances. As a novel aspect in the SPMSM control, the real-time impact of temperature variation on the winding resistance and magnet flux during motor operation is explicitly considered in the LPV modeling as a scheduling parameter and the subsequent LPV control design compensating for demagnetization effects in the motor response. The controller synthesis conditions guaranteeing stability and robust performance to norm-bounded uncertainty in the system matrices are formulated in a convex linear matrix inequality (LMI) optimization framework. Finally, the validity of the proposed method is assessed in simulation studies. The closed-loop simulation studies demonstrate that the proposed LPV controller provides improved transient response with respect to settling time, overshoot, and disturbance rejection in tracking the velocity profile under the influence of parameter perturbation, temperature variations, and load disturbances.

Engine EGR Valve Modeling and Switched LPV Control Considering Nonlinear Dry Friction

Exhaust gas recirculation valves used in internal combustion engines are highly nonlinear due to its nonlinear mechanism and dry friction dominated at low valve speed that could lead to large steady-state displacement errors. A multiple friction factor model is adopted in this article using a switched linear parameter-varying (LPV) modeling approach, where the scheduling parameter is the friction coefficient as a function of valve speed. Switched gain-scheduling LPV controllers are designed based on the hysteresis switching logic with guaranteed ${\mathscr{H}}_{\infty }$ performance, where parameterized linear matrix inequality (LMI) conditions are relaxed to a set of LMI conditions for synthesizing the switched LPV controllers by convex optimization. The LPV control performance is compared with that of proportional–integral–derivative controllers through both simulation and experimental studies, showing a notable improvement in the system response performance and robustness.

Scheduling Parameter Reduction of Diesel Engine Air Path LPV Model by PCA and Autoencoder-Based Method

This study presents a method to reduce the number of scheduling variables in a linear parameter-varying (LPV) model of a diesel engine air path system. The reduction of these scheduling variables is very important because it exponentially decreases the computational complexity for the gain-scheduled LPV controller synthesis. Principal component analysis (PCA) and autoencoder (AE) based neural networks are applied to the LPV diesel engine’s air path model, and the relationship between the accuracy of the reproduced scheduling variables and the number of the reduced scheduling parameters is evaluated via conduction of numerical simulations.

Hard Constrained LPV Virtual Control with Application to Flutter Suppression of a Smart Airfoil

Hard constrained control problems are popular in practical applications due to physical and power limitations. For instance, the displacement of a linear actuator is finite. A lot of studies have been conducted in this area to deal with certain hard constrained control problems and some are computationally expensive. This paper introduces a novel LPV (linear parameter-varying) virtual control scheme to deal with a class of hard constrained control problems with an application to flutter suppression of a smart airfoil, leading to a state-feedback LPV gain scheduling controller with the guaranteed $${{\cal H}_\infty}$$ performance. The basic idea of LPV virtual control is to add virtual components (such as variable stiffness springs and dampers) near to the hard constraints to prevent actuators from reaching their limits. The LPV virtual controller will be designed based on the model with virtual components and in the implementation stage, these virtual dynamics becomes part of the gain-scheduling controller. The concept is validated by a smart airfoil example. In the smart airfoil example, the virtual varying springs and dampers are placed at both ends of groove to constrain the mass movement. Comparisons studies with conventional LPV hard constrained control, nonlinear control, and regular LPV control without considering hard constraints are conducted to assess the performance of the proposed method and showed advantage over the existing methods. For instance, the control mass $${{\cal L}_2}$$ norm is reduced by 77.5% over the nonlinear control and 35% over the conventional LPV control.

A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control

Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.

Gain‐scheduling LPV control for autonomous vehicles including friction force estimation and compensation mechanism

This study presents a solution for the integrated longitudinal and lateral control problem of urban autonomous vehicles. It is based on a gain-scheduling linear parameter-varying (LPV) control approach combined with the use of an Unknown Input Observer (UIO) for estimating the vehicle states and friction force. Two gain-scheduling LPV controllers are used in cascade configuration that use the kinematic and dynamic vehicle models and the friction and observed states provided by the Unknown Input Observer (UIO). The LPV-UIO is designed in an optimal manner by solving a set of linear matrix inequalities (LMIs). On the other hand, the design of the kinematic and dynamic controllers lead to solve separately two LPV-Linear Quadratic Regulator problems formulated also in LMI form. The UIO allows to improve the control response in disturbance affected scenarios by estimating and compensating the friction force. The proposed scheme has been integrated with a trajectory generation module and tested in a simulated scenario. A comparative study is also presented considering the cases that the friction force estimation is used or not to show its usefulness.

Contouring Control of CNC Machine Tools Based on Linear Parameter-Varying Controllers

This paper proposes a method to design a multi-input multi-output (MIMO) linear parameter-varying (LPV) feedback controller for contour error minimization in two- and three-axis computer-numerical-control (CNC) machines. The design method generates a controller of a special and novel structure, that is, a series connection of a coordinate transformation matrix that varies with the machine tool trajectory angles, and an LPV controller that depends on the trajectory angles and angular velocities. To design the LPV controller part, a well-established gain-scheduled LPV controller design technique based on linear matrix inequalities is applied to the linear time-invariant CNC machine model combined with the parameter-varying coordinated transformation matrix. Simulations in both frequency domain and time domain, as well as experimental results for a two-axis machine, demonstrate a potential of the proposed MIMO LPV control approach for reducing the contouring error further than conventional contouring control methods.

Gain-scheduling multivariable LPV control of an irrigation canal system

The purpose of this paper is to present a multivariable linear parameter varying (LPV) controller with a gain scheduling Smith Predictor (SP) scheme applicable to open-flow canal systems. This LPV controller based on SP is designed taking into account the uncertainty in the estimation of delay and the variation of plant parameters according to the operating point. This new methodology can be applied to a class of delay systems that can be represented by a set of models that can be factorized into a rational multivariable model in series with left/right diagonal (multiple) delays, such as, the case of irrigation canals. A multiple pool canal system is used to test and validate the proposed control approach.

Gain-scheduling control of a floating offshore wind turbine above rated wind speed

This paper presents an application of gain-scheduling (GS) control techniques to a floating offshore wind turbine on a barge platform for above rated wind speed cases. Special emphasis is placed on the dynamics variation of the wind turbine system caused by plant nonlinearity with respect to wind speed. The turbine system with the dynamics variation is represented by a linear parameter-varying (LPV) model, which is derived by interpolating linearized models at various operating wind speeds. To achieve control objectives of regulating power capture and minimizing platform motions, both linear quadratic regulator (LQR) GS and LPV GS controller design techniques are explored. The designed controllers are evaluated in simulations with the NREL 5MWwind turbine model, and compared with the baseline proportional-integral (PI) GS controller and non-GS controllers. The simulation results demonstrate the performance superiority of LQR GS and LPV GS controllers, as well as the performance trade-off between power regulation and platform movement reduction.

A Gain-Scheduled LPV Control for Oxygen Stoichiometry Regulation in PEM Fuel Cell Systems

This paper addresses the linear parameter varying (LPV) control of a polymer electrolyte membrane fuel cell (PEMFC). To optimize efficiency, PEMFCs require reliable control systems ensuring stability and performance, as well as robustness to model uncertainties and external perturbations. On the other hand, PEMFCs present a highly nonlinear behavior that demands nonlinear and/or adaptive control strategies to achieve high performance in the entire operating range. Here, an LPV gain scheduled control is proposed. The control is based on a piecewise affine LPV representation of the PEMFC, a model that can be available in practice. To deal with the saturation of the control action, an LPV antiwindup compensation is also proposed. The complete control strategy is applied to several experimental practical situations in a laboratory fuel cell system to evaluate its performance and the reliability of the proposed algorithms.

Smooth switching LPV controller design for LPV systems

This paper presents a method to design a smooth switching gain-scheduled linear parameter varying (LPV) controller for LPV systems. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching, and one gain-scheduled LPV controller is assigned to each of the local subregions. For each switching subregion, a function interpolating two local LPV controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices. The smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities. To find a solution to the feasibility problem, an iterative descent algorithm which solves a series of convex optimization problems is proposed. The usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball-screw drive system.

Discrete-time Switching MIMO LPV Gain-scheduling Control for the Reduction of Engine-induced Vibrations in Vehicles

The work of this paper is an extension of the previous work realized by the authors. The main objective of this work is the reduction of the engine-induced vibrations in vehicles using a switching strategy to augment the controller range of actuation. Two inertia mass actuators and two accelerometers are attached to the engine mounts. Multiple input multiple output (MIMO) linear parameter-varying (LPV) controllers are designed for the reduction of the engine-induced vibrations and validated experimentally with test drives in a Golf VI Variant. The stability of the controllers is guaranteed since LPV gain-scheduling techniques are used. The MIMO LPV controllers achieved excellent results for the reduction of nine frequency components of the engine-induced vibration using only two gain-scheduling parameters for a range of 750 rpm.

Integrated vehicle dynamics control via coordination of active front steering and rear braking

This paper investigates the coordination of active front steering and rear braking in a driver-assist system for vehicle yaw control. The proposed control system aims at stabilizing the vehicle while achieving a desired yaw rate. During normal driving situations, active steering control is involved for steerability enhancement. However, when the vehicle reaches the handling limits, both steering and braking collaborate together to ensure vehicle stability. The coordination of these actuators is achieved through a suitable gain scheduled LPV (Linear Parameter Varying) controller. The controller is synthesized within the LMI (Linear Matrix Inequalities) framework, while warranting robust H∞ performances. Time and frequency simulation results show the effectiveness of the proposed control scheme when the vehicle is subject to various critical driving situations.

Linear Parameter-Varying Modeling for Gain-Scheduling Robust Control Synthesis of Flexible Joint Industrial Robot

Industrial robot features a multivariable, nonlinear and coupled dynamics property, which is always the inevitable topic for control engineer to face during the design of motion controller to achieve desired performance. In the past half century, motion control of industrial robot has gone through a sustainable development from no model involved to model based, from rigid body model to flexible joint model, and even more delicate models of higher order with flexibility in non-drive-train components are also introduced lately. Involvement of gradually refined dynamic model into control design, as well as manipulator design, has become a dominating approach for robot manufacturer to pursue competitive performance and keep technological leadership. Focusing on dynamic modeling, this paper introduces the formulation and approximation of a novel linear parameter-varying (LPV) model for the three main axes of typical six degrees-of-freedom (DOF) elbow type robot, which converts the strong nonlinear system into a quasi linear one globally dependent on certain scheduling parameters. This modeling method, as the prerequisite step for gain-scheduling robust control synthesis, paves the way for further step towards the implementation of LPV gain-scheduling modeling and control techniques for full robot in the next step.