Linear Parameter Varying Techniques Research Articles

A novel state-of-health notion and its use for battery aging monitoring of zinc-air batteries

Accurate monitoring of battery aging is pivotal for optimizing the performance of zinc-air batteries (ZABs). To obtain precise information about battery aging, an appropriate definition of state-of-health (SOH) is essential. However, the definition of SOH for ZABs has not been well-defined. This work introduces a novel SOH concept based on energy efficiency and integrates it with an underlying linear parameter varying (LPV) model. Crucially, the LPV model is chosen for its capability to represent nonlinear behavior, making it apt for capturing the intricacies of battery aging dynamics. With SOH defined as the scheduling parameter, electrochemical impedance spectroscopy (EIS) is employed to assess the influence of SOH. The results validate the model's robustness, as its predictions align closely with the empirical data. This newly proposed SOH definition exhibits a strong association with the model parameters. Furthermore, the efficacy of the LPV technique, especially when paired with the proposed SOH, suggests significant potential for refining battery aging monitoring in ZABs.

Kinematic/Dynamic SLAM for Autonomous Vehicles Using the Linear Parameter Varying Approach.

Most existing algorithms in mobile robotics consider a kinematic robot model for the the Simultaneous Localization and Mapping (SLAM) problem. However, in the case of autonomous vehicles, because of the increase in the mass and velocities, a kinematic model is not enough to characterize some physical effects as, e.g., the slip angle. For this reason, when applying SLAM to autonomous vehicles, the model used should be augmented considering both kinematic and dynamic behaviours. The inclusion of dynamic behaviour implies that nonlinearities of the vehicle model are most important. For this reason, classical observation techniques based on the the linearization of the system model around the operation point, such as the well known Extended Kalman Filter (EKF), should be improved. Consequently, new techniques of advanced control must be introduced to more efficiently treat the nonlinearities of the involved models. The Linear Parameter Varying (LPV) technique allows working with nonlinear models, making a pseudolinear representation, and establishing systematic methodologies to design state estimation schemes applying several specifications. In recent years, it has been proved in many applications that this advanced technique is very useful in real applications, and it has been already implemented in a wide variety of application fields. In this article, we present a SLAM-based localization system for an autonomous vehicle considering the dynamic behaviour using LPV techniques. Comparison results are provided to show how our proposal outperforms classical observation techniques based on model linearization.

Robust Control for Lane Keeping System Using a Linear Parameter Varying Approach with Scheduling Variables Reduction

This paper presents a robust controller using a Linear Parameter Varying (LPV) model of a lane-keeping system with parameter reduction. Both varying vehicle speed and roll motion on a curved road influence the lateral vehicle model’s parameters, such as tire cornering stiffness. Thus, we use the LPV technique to take the parameter variations into account in vehicle dynamics. However, multiple varying parameters lead to a high number of scheduling variables and cause massive computational complexity. In this paper, to reduce the computational complexity, Principal Component Analysis (PCA)-based parameter reduction is performed to obtain a reduced model with a tighter convex set. We designed the LPV robust feedback controller using the reduced model solving a set of Linear Matrix Inequality (LMI). The effectiveness of the proposed system is validated with full vehicle dynamics from CarSim on an interchange road. From the simulation, we confirmed that the proposed method largely reduces the lateral offset error, compared with other controllers based on a Linear Time-Invariant (LTI) system.

Predictive Control using LPV Techniques for Fast Discrete Time Nonlinear Systems with Changing Setpoints

Abstract An approach to model predictive control of nonlinear systems with fast dynamics, disturbances, as well as polytopic state and input constraints is presented. Techniques based on linear parameter varying (LPV) systems are used to obtain multiple polyhedral invariant sets to establish stability constraints and to allow for linear prediction models for fast online computation. The presented approach enables switching between setpoints in different operating regions without the need of re-computing the sets online.

Adaptive Semi-Active Suspension and Cruise Control through LPV Technique

Several studies exist on topics of semi-active suspension and vehicle cruise control systems in the literature, while many of them just consider actual road distortions and terrain characteristics, these systems are not adaptive and their subsystems designed separately. This study introduces a new method where the integration of look-ahead road data in the control of the adaptive semi-active suspension, where it is possible to the trade-off between comfort and stability orientation. This trade-off is designed by the decision layer, where the controller is modified based on prehistorical passive suspension simulations, vehicle velocity and road data, while the behavior of the controller can be modified by the use of a dedicated scheduling variable. The adaptive semi-active suspension control is designed by using Linear Parameter Varying (LPV) framework. In addition to this, it proposes designing the vehicle velocity for the cruise controller by considering energy efficiency and comfort together. TruckSim environment is used to validate the operation of the proposed integrated cruise and semi-active suspension control system.

A neural network approach for improving airfoil active flutter suppression under control-input constraints

This study deals with improving airfoil active flutter suppression under control-input constraints from the optimal control perspective by proposing a novel optimal neural-network control. The proposed approach uses a modified value function approximation dynamically tuned by an extended Kalman filter to solve the Hamilton–Jacobi–Bellman equality online for continuously improved optimal control to address optimality in parameter-varying nonlinear systems. Control-input constraints are integrated into the controller synthesis by introducing a generalized nonquadratic cost function for control inputs. The feasibility of using a performance index involving the nonquadratic control-input cost with the modified value function approximation is examined through the Lyapunov stability analysis. Wind tunnel experiments were conducted for controller validation, where an optimal controller synthesized offline via linear parameter-varying technique was used as a benchmark and compared. It is shown, both theoretically and experimentally, that the proposed method can effectively improve airfoil active flutter suppression under control-input constraints.

Adaptive Harmonic and Disturbance Estimators for Rotary Machines with applications to Engines

In this article, we present a new method for estimation of the nonperiodic (mean) value and harmonics of unknown disturbance inputs with parametrically varying harmonic frequencies. The proposed methods shall be studied for mean value and harmonic estimation of internal combustion torque of an engine. The internal torque refers to the oscillatory torque resulting from the combustion process. Its estimation uses an unknown input observer approach with a proportional structure, modeling the combustion torque as disturbance. An adaptive harmonic estimator is developed to filter the nonperiodic mean value and the harmonic components using linear parameter-varying techniques. The developed estimation methods feature phase-free estimation, minimal model assumption, tunable noise attenuation, and efficient time-triggered implementation. Misfire event detection using harmonic filtering of generated torque is demonstrated using simulations. Experimental validation is performed on a dynamical engine test bench with a series-production four-cylinder diesel engine estimating the combustion torque and its mean value during engine start and transient operation. The generic nature of the proposed technique is demonstrated by applying it to estimate nonperiodic speed values of an electric machine operated in tandem with a two-cylinder gasoline engine.

Position‐heading quadrotor control using LPV techniques

This work presents a solution to the position-heading control problem of a small quadrotor. The main idea of this study is to exploit the advantages of the linear parameter varying (LPV) control approach together with a feedback linearisation approach for designing a cascade control structure without the need to perform simplifications with respect to the reference dynamic model used in the literature. The use of a LPV representation of the attitude subsystem allows to consider it as independent of the position one, allowing the use of a cascade control structure. For the inner attitude control loop, the proposed quasi-LPV-linear-quadratic regulator (LQR) controller and proportional-integral observer (PIO) are solved in an optimal manner by solving a set of linear matrix inequalities (LMIs). While for the outer position control loop, a feedback linearisation approach is developed before designing the corresponding controller and PIO also minimising the LQR problem by means of LMIs. Furthermore, another outer loop, interchangeable with the position one, such that controls the velocities in the body frame is proposed. This velocities controller is also solved in an optimal manner using a combination of feedback linearisation and LPV techniques. The proposed solutions are applied to an AscTec Hummingbird unmanned aerial vehicle in simulation.

Output Feedback Tracking Control of Flat Systems via Exact Feedforward Linearization and LPV Techniques

In this article, an output feedback control scheme is proposed for trajectory tracking of differentially flat systems. After applying the exact feedforward linearization, the tracking error dynamics is linearized as a linear time-varying (LTV) system, where only the state matrix is time-varying while the input and output matrices are time-invariant. Using linear parameter-varying (LPV) techniques based on polytopes, for the LTV system the controller matrices, which are set to be affine on time-varying parameters, are calculated by solving a set of linear matrix inequalities (LMIs). An example for trajectory tracking of a two-wheeled mobile robot is given to show the effectiveness of the proposed method.

Gain-scheduled robust control for lateral stability of four-wheel-independent-drive electric vehicles via linear parameter-varying technique

This paper proposes a robust gain-scheduled H∞ controller for lateral stability control of four-wheel-independent-drive electric vehicles via linear parameter-varying technique. The controller aims at tracking the desired yaw rate and vehicle sideslip angle by controlling the external yaw moment. In the design of controller, uncertain factors such as vehicle mass and tire cornering stiffness in vehicle lateral dynamics are represented via the norm-bounded uncertainty. To address the importance of time-varying longitudinal velocity for vehicle lateral stability control, a linear parameter-varying polytopic vehicle model is built, and the built vehicle model depends affinely on the time-varying longitudinal speed that is described by a polytope with finite vertices. In order to reduce conservative, the hyper-rectangular polytope is replaced by a hyper-trapezoidal polytope. Simultaneously, the quadratic D-stability is also applied to improve the transient response of the closed-loop system. The resulting gain-scheduling state-feedback controller is finally designed, and solved utilizing a set of linear matrix inequalities derived from quadratic H∞ performance and D-stability. Simulations using Matlab/Simulink-Carsim® are carried out to verify the effectiveness of the proposed controller with a high-fidelity, CarSim®, full-vehicle model. It is found from the results that the robust gain-scheduled H∞ controller suggested in this paper provides improved vehicle lateral stability, safety and handling performance.

Model reference FTC for LPV systems using virtual actuators and set‐membership fault estimation

SummaryIn this paper, a model reference fault tolerant control (FTC) strategy based on a reconfiguration of the reference model, with the addition of a virtual actuator block, is presented for linear parameter varying (LPV) systems. The advantage of the proposed FTC method is that the control system is reconfigured in such a way that the nominal controller is used without the need of retuning it. Moreover, the presence of saturations is taken into account through their incorporation in the reference model, and the introduction of additional varying parameters, such that the system exhibits some graceful performance degradation when the system could not achieve the desired state because of the actuator limits. The design of the control scheme is based on linear matrix inequalities (LMIs) and polytopic LPV techniques. In order to implement the proposed active FTC strategy, a fault estimation is required. In this paper, the fault estimation is formulated as a parameter estimation problem, which is solved using a set‐membership approach. An aeronautical application is used to assess the performance of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.

A virtual actuator and sensor approach for fault tolerant control of LPV systems

In this paper, a fault tolerant control (FTC) strategy using virtual actuators and sensors for linear parameter varying (LPV) systems is proposed. The main idea of this FTC method, initially developed for LTI systems, is to reconfigure the control loop such that the nominal controller could still be used without need of retuning it. The plant with the faulty actuator/sensor is modified adding the virtual actuator/sensor block that masks the actuator/sensor fault. The suggested technique is an active FTC strategy that reconfigures the virtual actuator/sensor on-line taking into account faults and operating point changes. The stability of the reconfigured control loop is guaranteed if the faulty plant is stabilizable/detectable. The LPV virtual actuator/sensor is designed using polytopic LPV techniques and linear matrix inequalities (LMIs). A two-tank system simulator is used to assess the performance of the proposed method. In particular, it is shown that the application of the proposed technique results in an improvement, in terms of performance, with respect to the LTI counterpart.

Fault-tolerant control of systems with convex polytopic linear parameter varying model uncertainty using virtual-sensor-based controller reconfiguration

In this paper, a novel robust sensor fault tolerant control strategy for systems with linear parameter varying (LPV) uncertainty model description is proposed. The strategy combines a robust fault detection and identification (FDI) unit based on an invariant-set approach with controller reconfiguration based on the use of a virtual sensor. The robust FDI unit employs a bank of observers that can detect faulty and healthy situations based on the separation of relevant sets, whose computation takes into account system disturbances and model uncertainty. The closed-loop system is reconfigured by means of a virtual sensor which is adapted to the fault situation detected by the FDI unit. The FDI and virtual sensor modules are designed using polytopic LPV techniques and bilinear matrix inequalities. The resulting robust fault tolerant control scheme is guaranteed to preserve boundedness of the closed-loop system trajectories under a wide range of sensor fault scenarios. The performance of the proposed scheme is illustrated by a simulation example.

Obstacle-Sensitive Trajectory Regulation via Gain Scheduling and Semidefinite Programming

The regulation of vehicle trajectories in the vicinity of obstacles must focus on “critical outputs,” which vary as a function of the vehicle's position relative to obstacles as exemplified by the task of parking a car. We present an application of linear parameter-varying techniques to address this problem. We design closed-loop stable, parameter-dependent controllers, whose strategy changes depending on the position of the vehicle in the obstacle environment. We also provide a fast and easy-to-implement algorithm for online controller construction. Last, the proposed approach is demonstrated on a three degrees-of-freedom helicopter.

Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter

Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used.

A LPV approach for early fault detection in aircraft control surfaces servo-loops

The work presented in this paper is undertaken within the European FP7 funded ADDSAFE* project. The goal is to propose new fault diagnosis techniques that could significantly help developing environmentally-friendlier aircraft, by optimizing structural load design objectives. In this paper, a Linear Parameter Varying (LPV) model-based fault detection scheme is proposed for robust and early detection of faults in aircraft control surfaces servo-loop. The proposed methodology is based on the H∞/H_ LPV technique proposed in (Henry, 2012), for LPV systems modeled in a linear fractional representation (LFR) fashion. Simulation results using a “high-fidelity” simulator provided by AIRBUS, are presented to demonstrate the potential of the proposed technique.

Fault Estimation and Virtual Actuator FTC Approach for LPV Systems

In this paper, a Fault Tolerant Control (FTC) strategy using a virtual actuator for Linear Parameter Varying (LPV) systems is proposed. The main idea of this FTC method is to reconfigure the control loop such that the nominal controller could still be used without need of retuning it. The plant with the faulty actuator is modified adding the virtual actuator block that masks the fault. The suggested strategy is an active FTC strategy that reconfigures the virtual actuator on-line taking into account faults and operating point changes. In order to implement the virtual actuator approach, a fault estimation is required. In this work, the fault estimation is formulated as a parameter estimation problem. The LPV virtual actuator is designed using polytopic LPV techniques and Linear Matrix Inequalities (LMIs). To assess the performance of the proposed approach an aeronautical application is used.

Fault-Tolerant Control of Convex Polytopic Linear Parameter Varying Systems Using Virtual-Sensor-Based Reconfiguration

In this paper, a novel robust sensor fault tolerant control strategy for systems with linear parameter varying (LPV) uncertainty model description is proposed. The strategy combines a robust fault detection and identification (FDI) unit based on an invariant-set approach with controller reconfiguration based on the use of a virtual sensor. The robust FDI unit employs a bank of observers that can detect faulty and healthy situations based on the separation of relevant sets, whose computation takes into account system disturbances and model uncertainty. The closed-loop system is reconfigured by means of a virtual sensor which is adapted to the fault situation detected by the FDI unit. The FDI and virtual sensor modules are designed using polytopic LPV techniques and bilinear matrix inequalities. The resulting robust fault tolerant control scheme is guaranteed to preserve boundedness of the closed-loop system trajectories under a wide range of sensor fault scenarios. The performance of the proposed scheme is illustrated by a simulation example.

Modelling and H∞ control of diesel engine boost pressure using a linear parameter varying technique

In this paper, a model-based boost pressure control of a turbocharged common-rail directed injected diesel engine is proposed. An advanced linear parameter varying (LPV) technique is adopted for model development and an H∞ control scheme is synthesized for control purposes. The LPV technique has an advantage in deriving a linear model from a complex non-linear system and guarantees higher linear model precision. The boost pressure model of the diesel engine is obtained as a simple second-order linear system and the parameters of the model are estimated by the LPV identification method. With the help of the LPV modelling method, the behaviour of boost pressure of the diesel engine is precisely characterized using a second-order linear model. Based on the simplified LPV boost pressure model, a robust H∞ controller is synthesized. The state-space representation is derived to follow the control design framework of an H∞ scheme, and weighting functions for improving control performance are added into the closed-loop control system. The experimental results show that the LPV model-based diesel engine boost pressure control allows better tracking performance than the production engine management system (EMS), which requires difficult calibration work.

Fault-Tolerant Control using a Virtual Actuator using LPV Techniques: Application to a Two-Degree of Freedom Helicopter

AbstractIn this paper, a Fault Tolerant Control (FTC) strategy using a virtual actuator for non-***linear systems represented as Linear Parameter Varying (LPV) models is proposed. The main idea of this FTC method is to adapt the faulty plant to the nominal controller instead of adapting the controller to the faulty plant. That is, the faulty plant together with the virtual actuator block allows the controller to see the same plant as before the fault. This virtual actuator is designed using polytopic LPV techniques and LMIs. To assess the performance of the proposed approach a two degree of freedom helicopter is used.