Linear Parameter Varying Research Articles

Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine

Wind speed uncertainty and measurement noise affect the control effect in hydraulic wind turbine systems. This paper proposes a model predictive control (MPC) method with a dynamic Kalman filter (KF) based on a linear parameter-varying (LPV) model to address this problem. First of all, the LPV model for a nonlinear system of a hydraulic wind turbine is established using function substitution. Then, a LPV-based KF is introduced into the MPC to provide more precise estimated results and improve the anti-interference ability of the system. According to the current condition of the hydraulic wind turbine, the method updates the Kalman state estimator at each sampling instant and computes the optimal control input by solving a quadratic programming (QP) optimization problem. The performance and the efficiency of the proposed method is validated in simulation and compared with other methods.

Static output feedback H∞ control for switched LPV time-delay systems with nonlinear constraints

This paper addresses the issues of static output feedback [Formula: see text] control for switched linear parameter-varying (LPV) time-delay systems using multiple parameter-dependent Lyapunov functions. First, a parameter and state-dependent switching strategy with dwell time is designed and a sufficient condition ensuring the stability of the unforced switched LPV time-delay systems is established with the aid of the switching law. Then, the piecewise parameter-dependent controller is designed, such that the closed-loop system is asymptotically stable and satisfies an [Formula: see text] performance index. Finally, two examples are provided to show the effectiveness of the results.

Sampled-Data Linear Parameter Variable Approach for Voltage Regulation of DC–DC Buck Converter

This paper addresses the new method for output voltage regulation of DC–DC buck converter nonlinear systems by a sampled-data linear parameter varying (LPV) controller. For this purpose, an output-error state-space affine LPV model is presented for DC–DC buck converter nonlinear systems. The sampled-data structure of the controller is considered as a time delay in the input, and stabilization conditions are obtained for LPV systems with affine dependence on the parameter by using a parameter-dependent Lyapunov–Krasovskii functional. Then, the design condition of the sampled-data LPV controller with an appropriate sampling period is derived to guarantee that the output voltage of the DC–DC buck converter can be adjusted to the desired voltage. Finally, simulation results are provided to show the validity of the presented approach in practical control applications where there are limitations on the value of the sampling period and the cost of the digital implementation.

Model predictive control using LPV approach for trajectory tracking of quadrotor UAV with external disturbances

PurposeThe rotorcraft technology is very interesting area since last few decades due to variety of applications. One of the rotorcrafts is the quadrotor unmanned aerial vehicle (QUAV), which contains four rotors mounted on an airframe with an onboard controller. The QUAV is a highly nonlinear system and underactuated. Its controller design is very challenging task, and the need of controller is to make it autonomous based on mission planning. The purpose of this study is to design a controller for quadrotor UAV for attitude stabilization and trajectory tracking problem in presence of external environmental disturbances such as wind gust.Design/methodology/approachTo address this problem, the model predictive control has been designed for attitude control and feedback linearization control for the position control using the linear parameter varying (LPV) approach. The trajectory tracking problem has been addressed using the circular trajectory and helical trajectory.FindingsThe simulation results show the efficient performance with good trajectory tracking even in presence of external disturbances in both the scenarios considered, one for circular trajectory tracking and other for helical trajectory tracking.Originality/valueThe novelty of the work came from using the LPV approach in controller design, which increases the robustness of the controller in presence of external disturbances.

Prediction of charge-discharge behavior and state of charge estimation for tri-electrode rechargeable zinc-air flow batteries

An effective state of charge (SOC) estimation is essential for the development of a battery management system. At present, the provision of a SOC estimation for zinc-air flow batteries (ZAFBs) is still at its early stage of development. This work sets out to develop the SOC estimator for ZAFBs. The estimator is based-on a linear parameter varying (LPV) model integrated with an extended Kalman filter (EKF). The LPV model is constructed from multiple linear time-invariant (LTI) models with battery current and SOC as scheduling parameters. It is observed that the response data for ZAFBs have an exceptionally flat profile related to SOC change; dynamic differentiation only occurs when SOC is almost depleted. For this reason, the estimation of SOC converges to the true value when SOC is near depletion. In this work, it is shown that by appropriate tuning, the SOC estimation performance of the LPV model combined with EKF performs well as the absolute errors of soc. estimation lie under 2 % after true SOC convergence. The LPV model with the EKF algorithm is also compared with the Luenberger observer (LO). The proposed estimator can surpass the LO estimator. Overall, this SOC estimator provides a systematic way to fulfill the requirements of a battery management system.

Road-Curvature-Range-Dependent Path Following Controller Design for Autonomous Ground Vehicles Subject to Stochastic Delays

In this paper, we investigate the PID controller design problem of path following for an autonomous ground vehicle (AGV). Firstly, a bicycle model is adopted and a vehicle offset model from the target path is integrated to the bicycle model. The PID controller considers the vehicle longitudinal speed variation for adaption to the road curvature and the stochastic delay induced by the network communication. This is realized by transforming the tuning problem of proportional-integral-derivative (PID) gains for path following into a design problem of a static-output-feedback (SOF) controller for a time-delayed linear parameter varying (LPV) model form. A sufficient condition is adopted to guarantee the stability of the closed-loop system. In order to achieve better tracking performance, we propose a strategy in which the PID gains are piecewise constant and are dependent on the road-curvature ranges. The stability of the switched system is guaranteed via the common Lyapunov function method. Grey wolf optimizer (GWO) is employed to solve the optimization problem with maximum absolute tracking error as the optimization objective and stability condition and actuator dynamics as constraints. Both simulation results based on the CarSim-Simulink joint platform and hardware-in-loop experiment results are used to verify the effectiveness of the proposed control strategy.

A Survey of Output Feedback Robust MPC for Linear Parameter Varying Systems

For constrained linear parameter varying (LPV) systems, this survey comprehensively reviews the literatures on output feedback robust model predictive control (OFRMPC) over the past two decades from the aspects on motivations, main contributions, and the related techniques. According to the types of state observer systems and scheduling parameters of LPV systems, different kinds of OFRMPC approaches are summarized and compared. The extensions of OFRMPC for LPV systems to other related uncertain systems are also investigated. The methods of dealing with system uncertainties and constraints in different kinds of OFRMPC optimizations are given. Key issues on OFRMPC optimizations for LPV systems are discussed. Furthermore, the future research directions on OFRMPC for LPV systems are suggested.

Adaptive Event-Triggered Finite-Frequency Fault Detection With Zonotopic Threshold Analysis for LPV Systems.

This article investigates a class of multiobjective optimization fault detection observer design problems for linear parameter varying (LPV) systems considering the unknown but bounded disturbance with an adaptive event-triggered scheme. In this study, the actuator faults are considered in the low-frequency domain. First, to save the communication bandwidth and improve communication efficiency, an adaptively adjusted event-triggered (AAET) mechanism is proposed. Then, in order to make the designed observer gain satisfy both fault sensitivity and disturbance robust conditions, an H-/L∞ multiobjective optimization problem is proposed and solved by appropriate linear matrix inequalities. Next, the upper and lower bounds of the generated residual are calculated by the zonotope method when considering the estimation uncertainty. Fault detection can be achieved by judging whether the zero value belongs to the generated range of the residual signal. Finally, a simulation case is used to verify the effectiveness of the proposed method.

Gain-Scheduled Control Design Applied to Classical dc–dc Converters in Photovoltaic Systems and Constant Power Loads

This paper investigates the problem of control design for dc–dc converters, where the solution is especially suitable to address variations in the input voltage, a frequent situation in photovoltaic systems, and the problem of constant power load, where a nonlinear load is connected to the output of the converter. The proposed approach models the converters in terms of Linear Parameter-Varying (LPV) models, which are used to compute gain-scheduled robust gains. The synthesis conditions provide stabilizing controllers with an attenuation level of disturbances in terms of the H∞ norm. Moreover, the design conditions can also overcome pole locations to comply with physical application restrictions when ensuring transient performance. The validation of the controllers is made via simulation of the classical converters (buck, boost and buck-boost), showing that the proposed method is a viable and generalized control solution that works for all three converters, with guarantees of closed-loop stability and good performance.

A New Fuzzy Robust Control for Linear Parameter-Varying Systems

The linear parameter-varying (LPV) models have broad applications in advanced mathematics and modern control systems. This paper introduces a new method for controlling the LPV systems. This method includes the gain-scheduled state-feedback technique and a fuzzy system to calculate the state-feedback gain. The main goal of the control system is to stabilize the system and bring its states to equilibrium points. Linear matrix inequalities calculate feedback gains to stabilize the system. On the other hand, a fuzzy control system also produces a combined signal with the primary controller signal to speed up this operation. Lyapunov’s theory is used to guarantee the control system’s stability. Finally, to evaluate the performance of the proposed control system, the inverted pendulum has been investigated as a case study. The results show that the proposed method has good efficiency and 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.

Adaptive Damping Control Scheme for Wind Grid-Connected Power Systems With Virtual Inertia Control

With the large-scale wind power integration into the power system, the inertia and damping characteristics of the system have been weakened, which is not conducive to fulfill the grid-friendly operation of wind power. Aiming at this, an adaptive control scheme combining virtual inertia control (VIC) and supplementary damping controller (SDC) is proposed in this paper. Firstly, the mathematical model of wind grid-connected power system with VIC is established. Secondly, the polytopic linear parameter varying (LPV) system is built to describe the uncertainty of system operating points, and the gap metric-based nonlinear evaluation method is used for polytope vertex configuration. Next, Youla-Kucera parametrization are extended to polytopic LPV system to design an adaptive damping control, in which VIC and SDC are coordinated to provide damping and virtual inertia simultaneously. Finally, the proposed adaptive control scheme is compared with several existing control techniques to validate its effectiveness and advantages in suppressing system oscillation in the modified IEEE 39-bus system integrated with 2 wind turbines.

Conversion From Unstructured LTI Controllers to Observer-Structured Ones for LPV Systems

This paper considers the conversion problem from unstructured linear time-invariant (LTI) controllers to observer-structured LTI controllers, whose structure is similar to but not exactly the same as the so-called “Luenberger observer–based controllers,” for linear parameter-varying (LPV) plant systems. In contrast to Luenberger observer–based controllers, observer-structured LTI controllers can be defined and constructed even if the plant systems are given as LPV systems. In the conversion problem, the state-space matrices of the observer-structured LTI controller are parameterized with those of the given unstructured LTI controller, one free matrix, and a state transformation matrix. We also show a method to obtain the optimal state transformation matrix with respect to the convergence of the discrepancy between the plant state and the observer-structured controller state for a stochastically defined non-zero initial plant state. Several toy examples are included to illustrate the effectiveness and the usefulness of observer-structured LTI controllers, and the utility of the proposed conversion parametrization.

Analysis and Control for the Mode Transition of Tandem-Wing Aircraft with Variable Sweep

Morphing aircraft can alter their aerodynamic configuration to obtain multitask adaptability and improve flight performance. In this paper, we apply the variable sweep concept on a tandem-wing micro aerial vehicle (MAV) for multitask adaptability, the two canards of which can undergo backward sweep and the two wings can undergo forward sweep. The variable sweep morphing mode can not only weaken the additional inertia forces and moments caused by morphing, but can also maintain the longitudinal dynamic balance without elevator changes, which generates trim drag. What is more, it was demonstrated that sweep morphing can exert a great effect on the aerodynamic characteristics during the transition process, which are functionalized with the sweep inputs. The effect of addition forces and moments during the transition process was analyzed by dynamic response, and the longitudinal stability of the MAV were evaluated based on a linear parameter varying (LPV) model. Due to the dramatic effects of sweep morphing on the longitudinal stability, a gain scheduled transition controller based on a convex hull algorithm is proposed to guarantee the transition stability and improve the robustness, and a linear quadratic regulator (LQR) is used to guarantee the stability of the boundary point with the consideration of input saturation. Finally, the superior performance of the proposed controller was demonstrated by a theoretical simulation based on a nonlinear model.

Economic Linear Parameter Varying Model Predictive Control of the Aeration System of a Wastewater Treatment Plant.

This work proposes an economic model predictive control (EMPC) strategy in the linear parameter varying (LPV) framework for the control of dissolved oxygen concentrations in the aerated reactors of a wastewater treatment plant (WWTP). A reduced model of the complex nonlinear plant is represented in a quasi-linear parameter varying (qLPV) form to reduce computational burden, enabling the real-time operation. To facilitate the formulation of the time-varying parameters which are functions of system states, as well as for feedback control purposes, a moving horizon estimator (MHE) that uses the qLPV WWTP model is proposed. The control strategy is investigated and evaluated based on the ASM1 simulation benchmark for performance assessment. The obtained results applying the EMPC strategy for the control of the aeration system in the WWTP of Girona (Spain) show its effectiveness.

Gain-Scheduled Steering and Braking Coordinated Control in Path Tracking of Intelligent Heavy Vehicles

Abstract In the context of intelligent transportation system and advanced vehicle control system, higher requirements for intelligent control and coordinated control of heavy vehicles (HVs) have been proposed. Automatic path tracking control is essential for automatic driving of heavy vehicles. However, uncertain lateral disturbances and time-varying characteristics of system parameters make it difficult to guarantee roll stability and path tracking accuracy during automatic path tracking. This paper investigates the coordination of active front steering (AFS) and direct yaw moment control (DYC) in the automatic path tracking system for intelligent heavy vehicles. The main idea is to adjust the braking action according to the rollover risk evaluated by a specific rollover index (RI). The coordination of steering and braking systems and the robustness of the system against time-varying parameters are achieved by a gain-scheduled linear parameter varying (LPV) controller. Based on the linear matrix inequality (LMI) framework, the LPV controller is synthesized to ensure the robust H∞ performance against external disturbances. Simulation results show that the proposed gain-scheduled LPV/H∞ control strategy can enhance roll stability and path tracking accuracy in the path tracking process of intelligent heavy vehicles.

Tube-Based Output Feedback Robust MPC for LPV Systems With Scaled Terminal Constraint Sets.

This article provides a solution to tube-based output feedback robust model predictive control (RMPC) for discrete-time linear parameter varying (LPV) systems with bounded disturbances and noises. The proposed approach synthesizes an offline optimization problem to design a look-up table and an online tube-based output feedback RMPC with tightened constraints and scaled terminal constraint sets. In the offline optimization problem, a sequence of nested robust positively invariant (RPI) sets and robust control invariant (RCI) sets, respectively, for estimation errors and control errors is optimized and stored in the look-up table. In the online optimization problem, real-time control parameters are searched based on the bounds of time-varying estimation error sets. Considering the characteristics of the uncertain scheduling parameter in LPV systems, the online tube-based output feedback RMPC scheme adopts one-step nominal system prediction with scaled terminal constraint sets. The formulated simple and efficient online optimization problem with fewer decision variables and constraints has a lower online computational burden. Recursive feasibility of the optimization problem and robust stability of the controlled LPV system are guaranteed by ensuring that the nominal system converges to the terminal constraint set, and uncertain state trajectories are constrained within robust tubes with the center of the nominal system. A numerical example is given to verify the approach.

Tube-MPC Control via Notch Filter for Flexible Air-Breathing Hypersonic Vehicle with Actuator Fault

In this paper, the tube model predictive control (Tube-MPC) via notch filter is proposed for flexible air-breathing hypersonic vehicle with actuator fault. Firstly, considering the low-order flexible modes, the polytopic linear parameter varying (LPV) model of flexible air-breathing hypersonic vehicle is established using Jacobian linearization and tensor product. Actuator fault and parameter uncertainty are transformed into a lumped disturbance term. The baseline Tube-MPC trajectory tracking controller is developed by designing robust auxiliary feedback control law and nominal control law. In order to weaken the effect of flexibility, a notch filter is introduced to eliminate the frequency response peak of flexible modes. And the effect of notch filter on control performance and stability is analysed. Secondly, an alternative controller design strategy is proposed to ensure stability of the closed-loop system. The filter and the original nonlinear model are combined together such that the new polytopic LPV model is codesigned. On the basis, the adjustable Tube-MPC controller is developed to improve the control performance and ensure the stability of the system. Finally, the effectiveness of the two controllers is verified by simulations.

Predictive management of the hybrid generation dispatch and the dispatchable demand response in microgrids with heating, ventilation, and air-conditioning (HVAC) systems

Heating, ventilation, and air-conditioning (HVAC) systems are considered essential technologies for modern human life for many different purposes, such as providing human comfort or increasing agricultural production. However, the energy consumption of HVAC systems is very high, and usually leads to peak power demand issues that require adequate mitigation measures to ensure grid stability and not to exceed the maximum power demand allowed. In this work, a model predictive control (MPC) scheme is proposed for the joint management of hybrid generation dispatch and dispatchable demand response of HVAC systems in microgrids. The energy generation, the storage devices, and the controllable loads are managed simultaneously to improve the performance of the microgrids without losing thermal comfort. Demand response strategies are applied explicitly (constraining controllable loads) and implicitly (optimizing system operation by means of its thermal inertia). This simple MPC scheme is based on linear parameter-varying (LPV) modeling for HVAC system and battery bank, and rough predictions for external temperature, renewable generation and non-dispatchable demand. As MPC tolerates large plant-model mismatches, simple forecasting models are suitable for the required rough predictions. The LPV model scheduling signals are forecast to predict the time variable parameters and thus improve feedback and feedforward control. Viable MPC formulations for embedded processors are derived for off-grid and grid-connected operation. The developed scheme is applied to two case studies of interest in Argentina, an automated poultry farm (isolated from the grid), and a health facility (connected to the grid) with an expensive bill due to penalties. The simulation results demonstrate the effectiveness and the economic benefit of the management strategies proposed. Indeed, the isolated case provided 55% fuel saving and better use of the resources compared to the conventional rule-based controller. Furthermore, the connected case provided 26% monthly bill saving and 750% investment saving.

Fault-Tolerant Control of Wind Turbine System Using Linear Parameter-Varying Model

This paper proposes a fault-tolerant control scheme for WTS with actuator faults and disturbance, based on a linear parameter-varying (LPV) model. First, a LPV model of WTS subject to disturbances and actuator fault is obtained. Using this model, unknown input observer (UIO) is developed to estimate the WTS fault and state variables. Then, an integral tracking controller for LPV systems is developed. Based on the Lyapunov and H ∞ theory, the convergence of UIO and the stability of the closed-loop system are analyzed and ensured. The proposed fault-tolerant controller is applied to a wind turbine system with pitch and torque actuator faults, and its performances are compared with those of controller without integral action.