Linear Parameter Varying Method Research Articles

LPV Unknown Input Observer-Based Estimation of Driver Intervention Torque and Vehicle Dynamics for Human-Machine Shared Driving

This paper presents an unknown input observer (UIO)-based method to jointly estimate the vehicle dynamics and the driver torque within the framework of human-machine shared driving. To deal with the time-varying vehicle longitudinal speed, the vehicle dynamics is represented as a linear parameter-varying (LPV) model. Based on an unknown input (UI) decoupling technique, an LPV observer is designed, which can guarantee an asymptotic estimation performance of both the vehicle dynamics and the driver torque. Via Lyapunov stability theory, we propose sufficient conditions, expressed in terms of linear matrix inequalities, for LPV unknown input observer design. High-fidelity Simulink-CarSim co-simulations are carried out to show the effectiveness of the proposed LPV UIO-based estimation method for driver-automation shared driving dynamics. Moreover, a comparative study is performed with a recent LPV method to highlight the practical interest of the new estimation solution.

Finite-time bounded control for quadrotors with extended dissipative performance using a switched system approach

In order to deal with the problem of attitude tracking control for quadrotors subject to time-varying inertia and external disturbances, a finite-time bounded switched linear parameter-varying (LPV) control method is presented. The attitude dynamics is described by two subsystems, where the inner angular-velocity system is used to track the desired angular velocities that are generated by the outer attitude-angle system. The angular-velocity system of quadrotors is modeled as a switched LPV model, where a family of linear models is developed to approximate the original nonlinear system and the LPV method is applied to model the time-varying inertia. Specially, a mode-dependent persistent dwell-time (MPDT) switching logic, which is more general than the typically used dwell-time (DT) or average dwell-time (ADT) switching logic, is adopted to govern the switching behaviors among these linear models. A state-feedback controller for the switched LPV error-tracking system is designed, which ensures both finite-time boundedness and extended dissipative performance. Finally, the developed theoretical results are verified by numerical simulation.

Guaranteed performances for a learning-based eco-cruise control using robust LPV method

In this paper the design of an eco-cruise control system with learning-based agent for automated vehicles is proposed. The control design is based on the robust Linear Parameter-Varying (LPV) framework, in which performance levels of the system can be guaranteed. The motivation of the learning-based agent is to reduce the required on-line computation of the eco-cruise control signal, in which several environmental factors are involved, e.g. the forthcoming terrain characteristics, speed limits. In the proposed method the design of the LPV controller and the selection of scheduling variables are performed in an iterative method. As a result, the proposed system is able to handle the degradation of the learning-based agent, while the performance of the system is guaranteed.

Time-Varying Model Predictive Control of a Reversible-SOC Energy-Storage Plant Based on the Linear Parameter-Varying Method

Hydrogen conversion plants based on reversible solid oxide cells (rSOCs) provide a potential solution for large-scale energy storage to facilitate renewable integration. When operating an rSOC plant, the security and performance should be monitored at all times, including the steady-state periods and the transient processes connecting them. Model predictive control (MPC) is an appropriate method for this problem. This paper presents a comprehensive rSOC plant model to describe the multiscale dynamics (such as temperature and mass flows) under both fuel cell and electrolysis modes. Then, a time-varying MPC strategy based on a linear parameter-varying prediction model is proposed to provide fast control to the nonlinear rSOC plant. A numerical case is simulated to validate the effects of the proposed MPC strategy. The results suggest that the automatic coordination of actuators ensures consistent stack security, improves both short-term tracking and long-term production performance, and ultimately benefits the plant economically in practical operation.

Model and robust gain‐scheduled PID control of a bio‐inspired morphing UAV based on LPV method

AbstractIn this paper, a linear parameter‐varying (LPV)‐based model and robust gain‐scheduled structural proportion integral and derivative (PID) control design solution are proposed and applied on a bio‐inspired morphing wing unmanned aerial vehicle (UAV) for the morphing process. In the LPV model method, the authors propose an improved modeling method for LPV systems. The method combines partial linearization and function substitution. Using the proposed method, we can choose the varying parameters simply, thus creating a model that is more flexible and applicable. Then, a robust gain‐scheduled structural PID control design method is given by introducing a structural matrix to design a structural PID controller, which is more consistent with the structure of the PID controller used in practice and has a simpler structure than representative ones in the existing literature. The simulation results show that the developed LPV morphing UAV model is able to catch the response of the original nonlinear model with a smaller error than the existing Jacobian linearization method and the designed controller can maintain stable flights in practice with satisfactory robustness and performance.

A multi-way LPV modeling method for batch processes

By several simple local linear models a complex nonlinear process can be well approximated, so the linear parameter varying (LPV) method can largely simplify the complexity of model development and is widely used in the continuous process. Directly employing the regular LPV method in batch processes may develop a model for a single batch run; however, a whole batch process usually covers a number of batch runs. To develop a model for the whole batch process, this paper proposes a multi-way LPV (MLPV) approach for batch process modeling. In the proposed MLPV method, a sample is constructed by the measurements of all batch runs at each sampling instant. Comparing with the regular LPV model, the MLPV method extends the input, output and scheduling variables along the time dimension to along both the time dimension and the batch dimension. Then, the regular LPV method is performed on these “extended” samples according to the “extended” scheduling variable, by which both the variation among the batch runs and the dynamics within each batch run are summarized in the model development. The application of the MLPV method in three cases illustrates its advantages.

Integrated control design for driver assistance systems based on LPV methods

ABSTRACTThe paper proposes a control design method for a driver assistance system. In the operation of the system, a predefined trajectory required by the driver with a steering command is followed. During manoeuvres the control system generates differential brake moment and the auxiliary front-wheel steering angle and changes the camber angles of the wheels in order to improve the tracking of the road trajectory. The performance specifications are guaranteed by the local controllers, i.e. the brake, the steering, and the suspension systems, while the coordination of these components is provided by the supervisor. The advantage of this architecture is that local controllers are designed independently, which is ensured by the fact that the monitoring signals are taken into consideration in the formalisation of their performance specifications. The fault-tolerant control can be achieved by incorporating the detected fault signals in their performance specifications. The control system also uses a driver model, with which the reference signal can be generated. In the control design, the parameter-dependent linear parameter-varyingmethod, which meets the performance specifications, is used. The operation of the control system is illustrated through different normal and emergency vehicle manoeuvres with a high-accuracy simulation software.

A multi-model identification method for the fiber stretching process based on the EM algorithm

In the fiber production process, the stretching process plays a key role in the quality of the final fiber product. Due to the fiber stretching process with inborn nonlinearity, the performance of a single controller and an optimizer may be compromised or even unsatisfactory. Thus, we consider a multi-model identification method for the fiber stretching process. The dynamic transitions among different operating points are achieved by the change of the operating conditions in the fiber stretching process. To excite all of the nonlinearity character in the fiber stretching process, the transitions among different operating conditions is achieved. The structure of each sub-models, operating points, operating range are assumed. Based on the input output data of the process, a linear parameter varying (LPV) model is built by applying a probability identification method. To achieve the smoothly connected among the different operating conditions, an exponential function is used. Then a global LPV model is constructed by synthesizing the local models. Simulated results show that the LPV method has the effectiveness in solving the inherent nonlinearity of the fiber stretching process.

Linear Parameter-Varying Controller Design for Four-Wheel Independently Actuated Electric Ground Vehicles With Active Steering Systems

This paper presents a linear parameter-varying (LPV) control strategy to preserve stability and improve handling of a four-wheel independently actuated electric ground vehicle in spite of in-wheel motors and/or steering system faults. Different types of actuator faults including loss-of-effectiveness fault, additive fault, and the fault makes an actuator's control effect stuck-at-fixed-level, are considered simultaneously. To attenuate the effects of disturbance and address the challenging problem, a novel fault-tolerant (FT) robust linear quadratic regulator (LQR)-based $H_{\infty}$ controller using the LPV method is proposed. With the LQR-based $H_{\infty}$ control, the tradeoff between the tracking performance and the control input energy is achieved, and the effect from the external disturbance to the controlled outputs is minimized. The eigenvalue positions of the system matrix of the closed-loop system are also incorporated to tradeoff between the control inputs and the transient responses. The vehicle states, including vehicle yaw rate, lateral and longitudinal velocities, are simultaneously controlled to track their respective references. Simulations for different fault types and various driving scenarios are carried out with a high-fidelity, CarSim®, full-vehicle model. Simulation results show the effectiveness of the proposed FT control approach.

Flight control system design for hypersonic reentry vehicle based on LFT–LPV method

An angle-of-attack tracking control system is designed for the hypersonic reentry vehicle, whose aerodynamic parameters vary dramatically during reentry phase. The linear parameter-varying (LPV) theory based on linear fractional transformation (LFT) model (named as LPV–LFT method) is applied to design the controller for hypersonic reentry vehicle. Longitudinal moment trim of the hypersonic reentry vehicle is made along the desired flight trajectory, and a damping feedback loop is firstly designed to improve the system’s damping and static stability. Then, the linear dynamics model with damping feedback loop is established in LFT structure and treated as the controlled plant, and a parameter-varying reference model is utilized to guarantee the transient performance. The effectiveness of the proposed angle-of-attack tracking control system is validated through the frequency domain analysis and step response simulations. Finally, the actual angle-of-attack command tracking simulations using the nonlinear time-varying mathematical dynamics model are carried out to verify the accuracy and robustness of the hypersonic reentry vehicle control system.

Robust tracking control for an air-breathing hypersonic vehicle with input constraints

The focus of this paper is on the design and simulation of robust tracking control for an air-breathing hypersonic vehicle (AHV), which is affected by high nonlinearity, uncertain parameters and input constraints. The linearisation method is employed for the longitudinal AHV model about a specific trim condition, and then considering the additive uncertainties of three parameters, the linearised model is just in the form of affine parameter dependence. From this point, the linear parameter-varying method is applied to design the desired controller. The poles for the closed-loop system of the linearised model are placed into a desired vertical strip, and the quadratic stability of the closed-loop system is guaranteed. Input constraints of the AHV are addressed by additional linear matrix inequalities. Finally, the designed controller is evaluated on the nonlinear AHV model and simulation results demonstrate excellent tracking performance with good robustness.

On modeling and control of a flexible air-breathing hypersonic vehicle based on LPV method

This article develops a polytopic linear parameter varying (LPV) model and presents a non-fragile H2 gain-scheduled control for a flexible air-breathing hypersonic vehicle (FAHV). First, the polytopic LPV model of the FAHV can be obtained by using Jacobian linearization and tensor-product (TP) model transformation approach, simulation verification illustrates that the polytopic LPV model captures the local nonlinearities of the original nonlinear system. Second, based on the developed polytopic LPV model, a non-fragile gainscheduled control method is proposed in order to reduce the fragility encountered in controller implementation, a convex optimisation problem with linear matrix inequalities (LMIs) constraints is formulated for designing a velocity and altitude tracking controller, which guarantees H2 control performance index. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.

Linear Parameter-Varying Modeling of Electric Vehicle Air Conditioning System

This article presents the approach of quasi LPV (Linear Parameter-Varying) modeling techniques for an air conditioning system of an electric vehicle. Vehicle air conditioning systems are strongly non-linear systems and it is a challenging task to get a precise real time model for control purposes. Therefore, an LPV method is first introduced to estimate the air conditioning system. Experimental results show that the LPV model delivers a very high accuracy for the COP (Coefficient Of Performance) estimation, that can’t be reached by traditional identification methods. Some discussion about the model structure and its application are presented and a non-linear LPV model structure similar to the Hammerstein structure is proposed.

Actuator fault detection for suspension system

This paper focuses on the derivation of a Fault Detection and Identification (FDI) filter for the detection of the faults that might occur during the operation of the actuator built in the suspension system. The design of the proposed FDI filter is based on dynamic inversion and on a Linear Parameter Varying (LPV) observer design. To improve the performance properties of heavy vehicles, i.e. to reduce the risk of rollovers, improve passenger comfort and road holding, a reconfigurable fault-tolerant control design of the active suspensions and the active brake is performed. However when a fault (loss in effectiveness) occurs at one of the suspension actuators a further reconfiguration is needed in order to maintain the same performance level. The proposed reconfiguration scheme is based on an LPV method that uses the fault information as one of the scheduling variables. The LPV based control design and the operation of the control mechanism are demonstrated through a vehicle maneuver.

Design of nonlinear controllers for active vehicle suspension with state constraints

Design of active vehicle suspension has tradeoffs between three main performance metrics (passenger comfort, suspension deflection and road holding ability). It has been known that each performance can be achieved by H∞ controller and they can be gathered by LPV (Linear Parameter Varying) method. However, because the suspension deflection limit was not explicitly considered, this limit may be exceeded. In this paper, the authors propose a “reference shaping“ based method in order to improve the control performance. In this approach, a “virtual reference” signal is imposed to the system such that the suspension deflection is kept small. The effectiveness of the approach is examined by numerical simulations.

Rollover stability control in steer-by-wire vehicles based on an LPV method

In this paper a combined control structure, which includes an active steering and an active brake system, is proposed for tracking the path of the vehicle. Besides tracking, this control also guarantees the prevention of rollovers. First, a linear parameter varying (LPV) model is constructed, in which both the performance specifications and the model uncertainties are taken into consideration. Then a parameter-dependent LPV controller based on the H∞ method is designed. The control mechanism is demonstrated in various manoeuvre situations.

A fault-tolerant rollover prevention system based on an LPV method

In this paper, a reconfigurable control structure called a Fault-Tolerant Rollover Prevention System is proposed. This structure includes active suspensions, active anti-roll bars and an active brake. The purpose of this structure is to improve the performance properties of heavy vehicles, i.e. to reduce the risk of rollovers and to improve passenger comfort and road holding. In the control design, the changes in forward velocity, the performance specifications both for rollover and suspension problems and the model uncertainties are taken into consideration. The design of the control system is based on the H∞ linear parameter varying (LPV) method. The LPV based control design and the operation of the control mechanism are demonstrated in various vehicle manoeuvres.

Rollover Stability Control for Heavy Vehicles by Using LPV Model

The paper is concerned with the use of active roll control systems employing active anti roll bars in order to improve the roll stability of heavy vehicles. Since the forward velocity of the vehicle changes in time, the combined yaw-roll dynamic model has a nonlinear structure. Selecting the velocity as a scheduling parameter, a Linear Parameter Varying (LPV) model is constructed. In the control design based on an LPV method, the changes in the forward velocity and both the performance requirements and the model uncertainties are taken into consideration. The control design is demonstrated in different situations.

The Application of Linear Parameter Narying Control to Active Suspension Design

In this paper the Linear Parameter-Varying (LPV) approach is applied in the modelling and control of vehicle suspension systems. In the LPV modelling the dynamics of the hydraulic actuator is considered. In the LPV model for control design, both the performance requirements and the model uncertainties are taken into consideration. The trade-off between the performance demands is guaranteed by using parameter dependent gains. Simulation examples illustrate the modelling of a quarter-car model and the control design by using the LPV method.

Missile autopilot design via a multi‐channel LFT/LPV control method

AbstractIn this paper, the missile pitch‐axis autopilot design is revisited using a new and recently available linear parameter‐varying (LPV) control technique. The missile plant model is characterized by a linear fractional transformation (LFT) representation. The synthesis task is conducted by exploiting new capabilities of the LPV method: firstly, a set of H2/H∞ criteria defined channel‐wise is considered; secondly, different Lyapunov and scaling variables are used for each channel/specification which is known to reduce conserva tism; and finally, the controller gain‐scheduling function is constructed as affine matrix‐valued function in the polytopic co‐ordinates of the scheduled parameter. All these features are examined and evaluated in turn for the missile control problem. The method is shown to provide additional flexibility to tradeoff conflicting and demanding performance and robustness specifications for the missile while preserving the practical advantage of previous single‐objective LPV methods. Finally, the method is shown to perform very satisfactorily for the missile autopilot design over a wide range of operating conditions. Copyright © 2001 John Wiley & Sons, Ltd.