Linear Parameter-varying Methods Research Articles

Rapid empirical battery electromotive-force and overpotential modelling using input–output linear parameter-varying methods

In this paper, battery overpotential model identification approaches based on local and global Linear Parameter-Varying (LPV) input–output models are developed. Key features such as model structure, number of local models, and type and order of basis functions are considered. The LPVcore toolbox (Boef, 2021) has been used to solve the global identification problems. Furthermore, an iterative scheme is proposed which identifies a complete empirical battery model, i.e., both the ElectroMotive Force (EMF), also known as open-circuit voltage, and the overpotential model. This is achieved by iteratively obtaining an EMF realisation by (1) subtracting the modelled overpotential from a measured terminal voltage resulting from Constant-Current (CC) (dis)charging, and (2) using this EMF to calculate the overpotential from dynamic (dis)charging data and identifying an overpotential model using the LPV methods. This approach results in an empirical battery model with a precision similar (around 4 mV root-mean-square error in the range between 100% and 20% SoC) to models identified through a common cascaded approach in which the EMF is obtained separately from, e.g., pulse-(dis)charge data, but requires less measurement data resulting in a reduction factor in the order of 7 to 35 in terms of required experiment time.

Self-Scheduled LPV Control of Asymmetric Variable-Span Morphing UAV

In this study, a novel framework for the flight control of a morphing unmanned aerial vehicle (UAV) based on linear parameter-varying (LPV) methods is proposed. A high-fidelity nonlinear model and LPV model of an asymmetric variable-span morphing UAV were obtained using the NASA generic transport model. The left and right wing span variation ratios were decomposed into symmetric and asymmetric morphing parameters, which were then used as the scheduling parameter and the control input, respectively. LPV-based control augmentation systems were designed to track the normal acceleration, angle of sideslip, and roll rate commands. The span morphing strategy was investigated considering the effects of morphing on various factors to aid the intended maneuver. Autopilots were designed using LPV methods to track commands for airspeed, altitude, angle of sideslip, and roll angle. A nonlinear guidance law was coupled with the autopilots for three-dimensional trajectory tracking. A numerical simulation was performed to demonstrate the effectiveness of the proposed scheme.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Review on LPV Approaches for Suspension Systems

This paper presents a detailed literature review about Linear Parameter Varying (LPV) approaches applied to vehicle suspension systems. Indeed many works have been devoted to vehicle (active and semi-active) suspension in the past 20 years, because this subsystem in the only one affecting passenger comfort and road holding. Moreover several studies have also been concerned with global vehicle dynamic control using the suspension systems in collaboration with other subsystems (steering, braking …). On the other hand, the LPV approaches have proved to be very efficient to control non linear systems as well as to provide some kind of adaptive control. Naturally many LPV methods have been developed for suspension systems in order to take into account the nonlinear characteristics of the dampers, to adapt the suspension performance to the passenger request or to the road profile, to make the suspension systems collaborate with other subsystems, or to provide a fault tolerant control in case of damper loss of efficiency. This survey paper will make a deep analysis about the recent studies dedicated to vehicle suspension systems aiming at providing a better insight on the type of LPV methods that have been considered.

Nonlinear parameter‐varying state‐feedback design for a gyroscope using virtual control contraction metrics

AbstractIn this article, we present a virtual control contraction metric (VCCM) based nonlinear parameter‐varying approach to design a state‐feedback controller for a control moment gyroscope (CMG) to track a user‐defined trajectory set. This VCCM based nonlinear (NL) stabilization and performance synthesis approach, which is similar to linear parameter‐varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and ‐gain performance on NL systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully‐ and under‐actuated operating modes of the CMG show effectiveness of this approach compared with standard LPV control methods.

LPV-based Control Design of an Adaptive Cruise Control System for Road Vehicles

The paper presents a robust cruise control design method for a test vehicle, which is able to guarantee velocity tracking performance. The longitudinal dynamics and the consideration of model uncertainties such as parameters variation and actuator dynamics, are formulated in the vehicle model. The proposed controller has a feedforward term, which reduces the conservativeness of the control system during the compensation of the measured disturbances. The feedback term is designed using robust Linear Parameter-Varying methods, in which the inaccuracy of the feedforward control is considered. The purpose of the feedback control is to guarantee the robust performance and to handle the actuator saturation. The efciency of the method is presented through simulation scenarios.

Linear Parameter-varying Control for Active Vibration Isolation Systems with Stiffness Hysteresis

We consider the use of linear parameter-varying methods for the control of stiffness hysteresis in vibration isolation systems. We assume that the hysteresis model is known, and we describe it using a stiffness parameter that takes values in a compact convex set. The proposed parameter-dependent controller is continuously scheduled based on real-time measurements or estimates of the stiffness, and provides guaranteed stability and performance for the full range of stiffness variability. The method is applied to a simplified model of a microgravity vibration isolation system with an umbilical stiffness hysteresis non-linearity. Simulations show that the parameter-varying design is stable in the presence of hysteresis and that the desired isolation performance is achieved over the full range of displacements considered. The results are compared with those obtained with a fixed robust H∞ controller that considers the stiffness variability as uncertainty. We discuss robustness issues and demonstrate the effect of hysteresis model uncertainty in the implementation of the proposed control scheme.

Kernel methods for subspace identification of multivariable LPV and bilinear systems

Subspace identification methods for multivariable linear parameter-varying (LPV) and bilinear state-space systems perform computations with data matrices of which the number of rows grows exponentially with the order of the system. Even for relatively low-order systems with only a few inputs and outputs, the amount of memory required to store these data matrices exceeds the limits of what is currently available on the average desktop computer. This severely limits the applicability of the methods. In this paper, we present kernel methods for subspace identification performing computations with kernel matrices that have much smaller dimensions than the data matrices used in the original LPV and bilinear subspace identification methods. We also describe the integration of regularization in these kernel methods and show the relation with least-squares support vector machines. Regularization is an important tool to balance the bias and variance errors. We compare different regularization strategies in a simulation study.

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.

Design, Flight Simulation, and Handling Qualities Evaluation of an LPV Gain-Scheduled Helicopter Flight Control System

This paper summarises a recent project involving the design, piloted simulation, and handling qualities evaluation of a linear parameter varying (LPV) gain-scheduled helicopter flight control law. The work was jointly carried out by the Control Systems Research group of Leicester University and the Advanced Engineering group of GKN Westland Helicopters, Yeovil, England. The controller design was based on a Lynx MK7 helicopter model and used the quadratic H ∞ performance methodology with a 2-degrees-of-freedom controller to achieve robustness and good handling qualities across a large region of operation. In an off-line computer analysis, the controller consistently achieved Levell Cooper–Harper handling qualities ratings. A series offlight simulations were performed by two test pilots on GKN Westland's Advanced Engineering Simulation Facility. Both pilots consistently awarded Level 1 handling qualities ratings for the LPV gain-scheduled controller. The paper is tutorial in nature, it presents a novel application, and it demonstrates the potential of LPV methods for designing practical gain-scheduled controllers.