Robust Linear Parameter Varying Research Articles

Trajectory Tracking for Autonomous Vehicles Using Robust Model Predictive Control

This paper proposes a novel trajectory tracking control method using a robust model predictive control (RMPC) design technique based on matrix inequality and the theoretical approach of the hybrid & switched system. Firstly, considering bounded model uncertainties and norm-bounded external disturbances, the system states and control matrices are modified. In addition, vehicle time-varying longitudinal speed is considered, and a vehicle lateral dynamic model based on Linear Parameter Varying (LPV) is established by utilizing a polytope with finite vertices. Then the Min-Max robust MPC state feedback control law is obtained at every timestamp by solving a set of matrix inequalities which are derived from Lyapunov stability and the minimization of the worst-case in infinite-horizon quadratic objective function. The numerical simulation results demonstrated that the proposed robust LPV MPC can effectively track vehicle lateral dynamics on both straight and curved roads with varying longitudinal speeds.

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.

Robust linear parameter varying frequency control for islanded hybrid AC/DC microgrids

• The LPV representation of a nonlinear isolated hybrid microgrid model is investigated. • The intermittent nature of the wind speed, solar irradiation, and loads, and several parameter uncertainties are considered in the frequency control design procedure. • A dynamic robust LPV controller synthesis based on the three-step algorithm is proposed for the nonlinear model. • The proposed secondary frequency control approach suggests a practical dynamic output feedback controller with lower order than the IHMG model. • The algorithm superiority is verified in various disturbance-based and uncertain parameter-based scenarios. The applicability of a robust linear parameter varying (LPV) control for frequency fluctuation damping in an islanded hybrid microgrid (IHMG) system (DEG/WTG /PV/FC/ESSs) is investigated in this paper. Due to the erratic behavior of the majority of the renewable energy sources (RESs) and the varying time nature of loads, frequency deviation from the nominal value is inevitable, especially in the islanded mode. Load variation, solar irradiation, and wind power disturbance, as well as system parametric uncertainties, can significantly disturb the system frequency operation. In this paper, the wind speed and rotated speed of the nonlinear wind turbine are highlighted as scheduling parameters, and the nonlinearity of the wind turbine is hidden by the LPV approach. In the proposed method, a dynamic output feedback controller is obtained based on the power balance equation, by solving three LMIs to minimize the upper bound of the L 2 -Norm of the uncertain IHMG in an algorithmic approach. For better evaluation, the ultimate LPV control approach is compared with two other methods on the understudy IHMG model. The result represents a noticeable advantage of the proposed robust method compared to other methods in terms of frequency stability based on time-domain and norms characteristics in presence of the simultaneous disturbances and parametric uncertainties.

Linear Fractional Transformation Modeling of Multibody Dynamics Around Parameter-Dependent Equilibrium

This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. Traditional multibody approaches, which consist in building the nonlinear model of the whole structure and linearizing it around equilibrium after a numerical trimming, do not allow to isolate parametric variations with the LFT form. Although additional techniques, such as polynomial fitting or symbolic linearization, can provide an LFT model, they may be time-consuming or miss worst-case configurations. The proposed approach relies on the trimming and linearization of the equations at the substructure level, before assembly of the multibody structure, which allows to only perform operations that preserve the LFT form throughout the linearization process. Since the physical origin of the parameters is retained, the linearized LFT-LPV model of the structure exactly covers all plants, in a single parametric model, without introducing conservatism or fitting errors. An application to the LFT-LPV modeling of a robotic arm is proposed; in its nominal configuration, the model obtained with the proposed approach matches the model provided by the software Simscape Multibody, but it is enhanced with parametric variations with the LFT form; a robust LPV synthesis is performed using Matlab robust control toolbox to illustrate the capacity of the proposed approach for control design.

Robust LPV-H∞ control for active steering of tram with independently rotating wheels

A new methodology is proposed in this study for active steering of a tram with independently rotating wheels (IRWs). This methodology has been developed specifically to improve the tram’s steering capability and to reduce wheel-rail wear. The tram is represented by a complex dynamic model with a diverse range of operating conditions, and traditional active steering methods cannot ensure that the tram can remain well-controlled throughout the entire range of operating conditions. The linear parameter-varying (LPV)- H∞ control method proposed in this paper uses variable parameter theory to represent the nonlinearity, the parameter uncertainty, and the external force changes in the IRW. The LPV- H∞ steering controller can not only ensure the robustness of the uncertain system, but also can balance the complexity and the performance of the controller. This allows the tram to offer good steering performance under various running conditions. The simulation results presented in this research show that application of the proposed control method improves the running performance of the tram and reduces the wheel-rail wear significantly on both straight and curved tracks when compared with the passive case.

Parameter varying control of wind turbine smart rotor for structural load mitigation

This study investigates the Linear Parameter Varying (LPV) control of a Horizontal Axis Wind Turbine (HAWT) smart rotor in order to alleviate the structural loads. The smart rotor blades are equipped with actuators called Deformable Trailing Edge Flap (DTEF). These flaps benefit from a continuous airfoil deformation on the trailing edge in order to change the aerodynamic properties of blades. The objective of using a flap is to reduce the amplitude of load fluctuations in high wind speeds to decrease the fatigue loads on the wind turbine components and increase their working life. Here, the aerodynamic behavior of NACA 64-418 airfoil in the presence of DTEF deflection is studied numerically. The airfoil with 10% chord deformation is mounted on 5 MW NREL reference wind turbine blades in 67% to 95% of its length relative to the blade root. The nonlinear aeroelastic FAST code is used to determine the effects of DTEFs on structural load mitigation. Consequently, the modeling of nonlinear wind turbine system using LPV approach is discussed including the angle of DTEFs as a control input. A robust LPV controller has been designed using Linear Matrix Inequality (LMI) solution along the operating trajectory to guarantee the internal stability and H∞ robust performance of the closed-loop system in the presence of modeling uncertainties as well as wind turbulence. In sum, the idea of this study is the aerodynamic modeling of the wind turbine equipped with a smart rotor, designing an LPV controller and comparing the results with the conventional PI gain-scheduled controller. The principal objective is to reduce the amplitude of blade root flapwise bending moment oscillations about its mean values along the operating trajectory. As a summary of the results, a reduction in blade root flapwise bending moment fatigue load has been observed by 33% based on Damage Equivalent Load (DEL) calculation.

Robust LPV control synthesis for learning-aided driver assistance systems

This paper proposes a control design framework with guarantees for systems, which contains learning-based control elements. The framework is based on a supervisory control structure, which contains a supervisor, a robust Linear Parameter Varying (LPV) controller and the learning-based control elements. This paper presents the design of a lateral path following control for driver assistance systems, which is aided with a learning-based agent. In the paper the formulation of the supervisor, the design method of the robust LPV controller are provided, while the learning-based agent via an imitation learning process is considered to be given. The effectiveness of the method on driver-in-the-loop simulation scenario is demonstrated. It is shown that the proposed control system is able to provide guarantee on the limitation of the path following error, and to guarantee transition between the driver steering actuation and the automated control intervention.

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.

LPV control design based on ultra-local model for trajectory tracking problem

Model Free Control (MFC) is a novel technique to overcome some modeling and control challenges of highly nonlinear systems. The MFC control strategy consists of two parts, i.e., ultra-local model-based control and state feedback control. This paper proposes the robust Linear Parameter-Varying (LPV) method for design the state feedback control part of the strategy. In the design of robust LPV control the effect of the ultra-local model, formed as a disturbance, is involved. The contribution of this extension to the original concept of MFC design is that a desired performance of the closed-loop system can be achieved. The effectiveness of the presented control strategy is demonstrated through a trajectory tracking problem of autonomous vehicles using the high-fidelity simulation software, IPG CarMaker.

Direct thrust control for multivariable turbofan engine based on affine linear parameter-varying approach

A novel turbofan Direct Thrust Control (DTC) architecture based on Linear Parameter-Varying (LPV) approach for a two-spool turbofan engine thrust control is proposed in this paper. Instead of transforming thrust command to shaft speed command and pressure ratio command, the thrust will be directly controlled by an optimal controller with two control variables. LPV model of the engine is established for the designing of thrust estimator and controller. A robust LPV Hρ filter is introduced to estimate the unmeasurable thrust according to measurable engine states. The thrust estimation error system is proved to be Affinely Quadratically Stable (AQS) in the whole parameter box with a prescribed Hρ performance index ?. Due to the existence of overdetermined equations, the solving of controller parameters is a multi-solution problem. Therefore, Particle Swarm Optimization (PSO) algorithm is used to optimize the controller parameters to obtain satisfactory control performance based on the engine s LPV model. Numerical simulations show that the thrust estimator can acquire smooth and accurate estimating results when sensor noise exists. The optimal controller can receive desired control performance both in steady and transition control tasks within the engine working states above the idle, verifying the effectiveness of the proposed DTC architecture s application in thrust direct control problem.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Nested Robust Controller Design for Interconnected Linear Parameter Varying Aerial Vehicles

A framework for a systematic design of robust controllers to guarantee desired output performance for an interconnected group of multi-input–multi-output dynamic systems is presented. The framework enables design of a robust linear parameter varying (LPV) controller for all individual vehicles as well as the interconnected group to account for uncertainties associated with the individual vehicles as well as the interconnections. In this paper, the robust controller design methodology for the individual systems and the cooperative system is implemented in a nested manner to enhance the performance. The application of the nested robust controller is distributed wherein well-known robust performance analysis is adopted and modified, and the controller synthesis methodology is developed on top of the same performance condition. Nested robust LPV controllers are synthesized for the short-period dynamics of F-16 VISTA over a flight envelope defined by Mach number and altitude of the aircraft. Then a group of homogeneous F-16 VISTA with individually designed LPV controllers is interconnected using a connection topology that suffers time delays, and a cooperative controller is designed using two methods described in this work. Numerical simulation results presented in the paper show that the group performance is enhanced with the robust LPV controller design methodology.

Design of LPV control for autonomous vehicles using the contributions of big data analysis

The paper deals with a robust autonomous path-following functionality, in which the safe velocity and the motion profile of the vehicle with varying tyre-road contact must be guaranteed. The integration of Linear Parameter-Varying (LPV) control and the results of the machine learning-based analysis on the big data of autonomous vehicles is proposed. The integration is achieved in two steps. First, an estimation method on the adhesion coefficient through decision trees is presented. The result of the estimation is incorporated in the robust LPV control through a scheduling variable. During the control design, the error of the machine-learning algorithm is incorporated. Second, an optimisation method of the longitudinal velocity on a predicted horizon is proposed, which is aided with the machine learning-based reachability set approximation of the steering intervention. The effectiveness of the control strategy is illustrated through CarSim simulations.

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.

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.

Robust Linear Parameter Varying Scalar Control Applied in High Performance Induction Motor Drives

This article presents a robust stabilizer designed to damp low-frequency electromechanical oscillations which occurs in induction machines controlled by scalar control when operating at low speed and light load. The robust stabilizer design is based on the linear parameter varying (LPV) approach. A discrete LPV model is identified to allow the design of the robust LPV controller. Experimental tests are performed on a 7.5-kW induction motor dynamometer using an industrial inverter driver. The results show satisfactory improvement of the motor performance with the damping controller activated.

DO-LPV-based robust 3D path following control of underactuated autonomous underwater vehicle with multiple uncertainties

This study investigates a path following problem of underactuated autonomous underwater vehicle under multiple uncertainties in three-dimensional space. The uncertainties are partly induced by hydrodynamic coefficient uncertainty, ocean currents and unmodeled hydrodynamics, namely dynamic uncertainties. In addition, velocities are assumed to be measured with bounded noise, which is called velocity measurement uncertainties. To address this issue, a compound robust path following control strategy is developed. At the kinematic level, an improved kinematic controller is developed by utilizing disturbance observer to recover the unknown time-varying attack and side-slip angular velocity. At the dynamic level, a novel dynamic tracking model is firstly established via linear parameter varying (LPV) technique, by which multiple uncertainties are expressed in a comprehensive way. Subsequently, a robust LPV controller is employed to track desired velocities generated by kinematic controller, which has less dependence on accurate model and exact velocity measurement. Finally, rigorous stability analysis proves the uniform and ultimate boundedness of path following errors. The comparative numerical results also substantiate the efficacy and superiority of designed method.

On robust LPV-based observation of fuel slosh dynamics for attitude control design

Most attitude control scenarios are highly affected by fuel slosh dynamics that must be carefully taken into account to preserve pointing accuracy. Since such dynamics are not easily predictable, standard strategies consist of bounding the performances of the control system to avoid interactions between the rigid dynamics of the spacecraft and the oscillating liquid motion inside the fuel tank. Thanks to a recently developed control-oriented CFD-based fuel slosh model, an alternative approach is evaluated in this paper. It is based on a reformulation of the slosh effects in the Linear-Parameter-Varying (LPV) framework from which a robust LPV observer is easily derived. The latter is then classically used in a disturbance compensation scheme. The proposed strategy is illustrated on a simple but realistic single axis attitude control scenario for a small satellite using reaction wheels.

LPV model identification with an unknown scheduling variable in the presence of missing observations – a robust global approach

This study focuses on identifying the linear parameter varying (LPV) system with an unknown scheduling variable in the presence of missing measurements and the system output data contaminated with outliers. The parameter interpolated LPV autoregressive exogenous (ARX) model with an unknown scheduling variable is considered and the scheduling variable dynamic is described by a non-linear state-space model. The outliers treatment and unknown scheduling variable estimation with missing observations are both taken into consideration. The robust LPV model is established based on the Student's t -distribution in order to handle the outliers and the particle smoother is adopted to estimate the true scheduling variable from incomplete data set. The formulations of the proposed algorithm are finally derived in the expectation-maximisation algorithm scheme and the formulas to estimate the unknown parameters of LPV ARX model and scheduling variable dynamic model are derived simultaneously. A numerical example and a chemical process are used to present the efficacy of the proposed approach.

Missile autopilot design based on robust LPV control

This paper proposes an effective algorithm to work out the linear parameter-varying (LPV) framework autopilot for the air defense missile so as to simultaneously guarantee the closed-loop system properties globally and locally, which evidently reduces the number of unknown variables and hence increases the computational efficiency. The notion of quadratic is inducted to meet the global properties, including the robust stability and robust performance, while the regional pole placement scheme together with the adoption of a model matching structure is involved to satisfy the dynamic performance, including limiting the fast poles. In order to reduce the conservatism, the full block multiplier is employed to depict the properties, with all specifications generalized in integral quadratic constraint frame and finally transformed into linear matrix inequalities for tractable solutions through convex optimization. Simulation results validate the performance of the designed robust LPV autopilot and the proposed framework control method integrating with the full block multiplier approach and the regional pole placement scheme, and demonstrate the efficiency of the algorithm. An efficient algorithm for the air defense missile is proposed to satisfy the required global stability and local dynamical properties by a varying controller according to the flight conditions, and shows sufficient promise in the computational efficiency and the real-time performance of the missile-borne computer system.