Linear Parameter Varying Research Articles

Linear Parameter-Varying Polytopic Modeling and Control Design for Guided Projectiles

In this paper, a linear parameter varying (LPV) modeling and control design approach is applied to a new class of guided projectiles, aiming to exploit the advantages of the LPV framework in terms of guaranteed stability and performance. The investigated concept consists of a planar symmetric 155 mm fin-stabilized projectile equipped with a reduced amount of control actuators and characterized by a predominantly unstable behavior across the analyzed flight envelope. A dedicated modeling procedure allows reformulating the nonlinear projectile dynamics as a LPV polytopic system, employed for the controller design. The procedure intends to reduce the computational complexity and the conservativeness affecting the overall controller synthesis. A trajectory-tracking simulation scenario is performed in a realistic simulator environment to assess the performance of the resulting LPV polytopic autopilot across the entire flight envelope.

Multiobjetive H2/H control of a pitch regulated wind turbine for mechanical load reduction.

The paper deals with the design of acontrol system for a variable-speed pitch-regulatedwind turbine in the operating region correspond-ing to wind speeds above rated wind speed. Thecontrol objectives are mostly to regulate the plantoutput power and to reduce the mechanical fatigueof the plant components. The controller is designedfrom a non linear model of the system which takesinto account the blades, shaft and tower flexibil-ities. A Linear Matrix Inequalities (LMI) formu-lation of the control problem permits to obtaina Linear Parameter Varying (LPV) controller op-timizing, throughH2/H∞norm minimization, acriteria close to mechanical fatigue affecting theplant. The proposed controller performances arethen compared in simulation with those of a gainscheduling Linear Quadratic Gaussian (LQG) con-troller and with a gain scheduling PI controller, andis seen to be more efficient.

Polytopic LPV modeling and gain scheduling [formula omitted] control of ball screw with position- and load-dependent variable dynamics

Ball screw drive (BSD) is a precision transmission mechanism widely used in high-precision positioning or tracking systems. The dynamic behavior of BSD varies with position and load, which causes tracking errors and poor robustness. Therefore, this paper proposes a polytopic linear parameter varying (LPV) model to express the varying dynamic behavior of BSD. The parameters of the LPV model are identified by the closed-loop frequency domain method and Levenberg–Marquardt iterative algorithm. Based on the polytopic LPV model, an LPV gain scheduling (GS) H∞ controller is proposed for the BSD with varying dynamics. Specifically, the controller is designed through polytope-based GS representation and mixed sensitivity synthesis. The most significant part is the proposal of a GS H∞ control algorithm to implement controller parameters that change with changing dynamics. Moreover, the stability of the closed-loop system is achieved by quadratic stabilization with state feedback. Finally, identification experiments and trajectory-tracking comparative experiments are carried out. The experimental results demonstrate that the proposed polytopic LPV modeling and GS H∞ control synthesis are effective in achieving accurate trajectory tracking and excellent robustness.

An event‐triggered subspace predictive control method for partially unknown linear parameter‐varying systems

AbstractThis article develops a novel event‐triggered subspace predictive control (ET‐SPC) method for discrete‐time linear parameter‐varying (LPV) systems with partially unknown system parameters. An event‐triggered law is developed to alleviate the heavy load of data transmission and computation in the conventional subspace predictive control methods for the LPV systems. The design of the event‐triggered law relies on the input‐to‐state stability (ISS) theory and applies the robust stability condition based on linear matrix inequalities (LMIs), which guarantees the stability of the proposed method. Consequently, the input component can be directly transmitted to the system without receding horizon optimization when the event‐triggered law evaluates that the system satisfies the stability condition. The simulation results illustrate its satisfactory performance, which indicates its potential application involving a considerable amount of data transmission and computation such as the network control systems (NCSs).

A Comparison of Two Methods of Adaptive Nonlinear Model Predictive Control

Conventional nonlinear model predictive control (NMPC) relies on an accurate process model. However, real-world systems’ models are often imperfect due to parametric variations, modelling errors and additive noise, leading to degraded control performance. This study investigates the effectiveness of two adaptive NMPC methods in solving this problem, namely, linear parameter varying (LPV) model predictive control (LPV-MPC) and model predictive control based on successive linearization (SL-MPC). In addition, an innovative approach for identifying LPV models is proposed and applied to three simulation examples. The identified LPV models gave a very strong fit. Also, simulation results demonstrate that both adaptive predictive NMPC (LPV-MPC and SL-MPC) exhibit performance similar to conventional NMPC and superior to Linear MPC. Notably, the two adaptive predictive controllers offer significantly reduced computational time compared to conventional NMPC.

An information theory approach for recursive LPV-ARX model identification via LS-SVM

When modeling a dynamical system, linear models are always the first choice due to their simplicity. However, many times the system is too complex so that employing linear models results in poor performances. In this context, Linear Parameter Varying (LPV) models allow to represent non-linear input/output relationships while preserving the simple structure of linear models. The method of Least Squares Support Vector Machines (LS-SVM) is one of the most common approaches to identify a LPV model in an ARX formulation (LPV-ARX). However, due to its computational cost, it is difficult to identify a LPV-ARX model using LS-SVM in online applications, where the model must be updated every time new data are collected. An efficient update algorithm has been presented for online identification of such models, where the idea is to update the model only upon certain data that are considered informative. However, this approach requires the tuning of some hyperparameters and in certain conditions can stop updating the model even when data are informative. This paper proposes an information-based algorithm to overcome these drawbacks. Evaluation on simulated and experimental data show the effectiveness of the proposed approach on both identification and computational sides.

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.

Supervised reinforcement learning based trajectory tracking control for autonomous vehicles

Recent developments in autonomous vehicle technologies and applications gain a lot of interest by the public, as the popularity of both driver assistance and automated driving systems increase. One of the most promising aspect of the autonomous vehicle compared to conventional human driven vehicle is the increased level of safety. Machine learning techniques enables to achieve fast and efficient control actions compared to model based techniques. However, the advantages of a more conservative model based controller are their better robustness properties. In this paper a synergy of the two control philosophy is presented through a trajectory tracking control design for autonomous vehicles. A supervised reinforcement learning (RL) control method is introduced, where a robust Linear Parameter Varying (LPV) controller supervises the operation of the trained RL agent. Thus, in case sensor noise is detected, the guaranteed stability LPV controller takes over the steering control action. In order to demonstrate the operation of the proposed method, three different simulations have been evaluated and compared in CarSim simulation environment.

Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems

<p>In this paper, a novel observer-based robust preview tracking controller design method is proposed for a class of continuous-time Lipschitz nonlinear systems with external disturbances and unknown states. First, a state observer is designed to reconstruct unknown system states. Second, using differentiation, the state lifting technique, the differential mean value theorem, and several ingenious mathematical manipulations, an augmented error system (AES) containing the previewable information of a reference signal is constructed, thereby transforming the tracking control problem into a robust $ H_{\infty} $ control problem. Based on linear parameter-varying (LPV) system theory, a sufficient condition for asymptotic stability of a closed-loop system with a robust $ H_{\infty} $ performance level is established in terms of the linear matrix inequality (LMI). Furthermore, a tracking controller, which includes observer-based feedback control, integral control, and preview feedforward compensation, is established for the original system. In particular, the tracking controller design is simplified by computing the observer and tracking controller gains simultaneously via only a one-step LMI algorithm. Finally, numerical simulation results demonstrate that the proposed controller leads to superior improvement in the output tracking performance compared with the existing methods.</p>

A global approach to estimate continuous-time LPV models for wastewater nitrification

In wastewater treatment, understanding and modeling the nitrification process is crucial to implement control. However, the complexity of this process makes it challenging to create simplified models. This study introduces an innovative method for estimating linear parameter-varying (LPV) models in the context of biological nitrification processes. The research focuses on the development of a continuous-time LPV model for a submerged aerated biofiltration system, considering the conversion of ammonium to nitrate in wastewater treatment. The methodology adopts the reinitialized partial moment approach within a global identification framework. The resultant LPV model is structured to capture the dynamics of the biological nitrification process, considering various factors like flow rates, feed concentrations and environmental regulations. Application of this approach to measured data from a wastewater treatment plant, demonstrates its effectiveness in accurately estimating the LPV model parameters. The results not only offer valuable insights into the dynamics and the nonlinear behaviour of the nitrification process but also contribute to the design and optimization of wastewater treatment plants, particularly those employing submerged aerated nitrifying biofilters.

Automated Tuning of Gain-Scheduled PI Controllers Based on SANARX Models

This paper presents a data-driven method to automatically tune gain-scheduled PI controllers for linear parameter-varying (LPV) systems. First, input-output data from a system is used to train a neural network (NN) based simplified additive nonlinear autoregressive exogenous (SANARX) model. After reformulating this into a state space representation, an H∞ method is used to obtain the PI parameters for any sampled working point. Throughout the entire pipeline, this work uses data from a real-world hydraulic test rig, which also serves as the system where the resulting gain-scheduled controller is evaluated on. Overall, no prior system knowledge is necessary to utilize this method.

Genetic-Algorithm-Assisted Self-Scheduled Multidelay PIR Control: Experiments in a Car-Like Vehicle System.

The path-tracking control of an intelligent vehicle always suffers from the high-frequency measurement noises. To confront this issue, this work puts forward a novel delayed output-feedback implementation of proportional-integral-derivation (PID) control, which is called multidelay proportional-integral-retarded (PIR) control. The mathematical model of the vehicle system is represented in the form of a linear parameter-varying (LPV) system, which uses the car position as the scheduling variable for regulation. On this basis, the multidelay PIR controller is designed such that the tracking errors gradually converge to zero with the aid of the proportional and integral actions, and the harmful high-frequency measurement noises are attenuated by the retarded term consisting of a few delayed proportional actions. To tune the PIR controller parameters, linear matrix inequalities (LMIs), derived by applying Taylor's expansion to the retarded term, are used to compute the convex subcontroller gains. Then, the self-scheduled tracking controller is formulated as the weighted sum of convex subcontrollers, and the weight functions scheduled by the current position are adaptive to the different operational conditions. Experiments in real time using a laboratory car-like vehicle are employed to assess the performance of the proposed controller.

Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower dimensional state-space. In step two, an LPV model is learned on the reduced-order state-space using a novel, efficient parameterization in terms of neural networks. The improved modeling accuracy of the method compared to an existing method is demonstrated by simulation examples.

Novel criteria of sampled-data synchronization controller design for gated recurrent unit neural networks under mismatched parameters

Synchronization between neural networks (NNs) has been intensively investigated to analyze stability, convergence properties, neuronal behaviors and response to various inputs. However, synchronization techniques of NNs with gated recurrent units (GRUs) have not been provided until now due to their complicated nonlinearity. In this paper, we address the sampled-data synchronization problems of GRUs for the first time, and propose controller design methods using discretely sampled control inputs to synchronize master and slave GRUs. The master and slave GRUs are mathematically modeled as a linear parameter varying (LPV) system in which the parameter of the slave GRUs is constructed independently of the master GRUs. This distinctive modeling feature provides flexibility to extend the existing master and slave NNs into a more general structure. Indeed, the sampled-data synchronization can be achieved by formulating the design condition in terms of linear matrix inequalities (LMIs). The novel sampled-data synchronization criteria are devised by combining the H∞ controller design with the looped-functional approach. The synthesized synchronization controllers guarantee not only asymptotic stability of the synchronization error system with aperiodic sampling, but also provides a satisfactory H∞ control performance. Moreover, the communication efficiency is improved by using the proposed method in which the sampled-data synchronization controller is combined with the event-triggered mechanism. Finally, the numerical example validates the proposed theoretical contributions via simulation results.

Software sensors design for a class of non linear coupled PDE systems: The Vlasov–Poisson dynamical system

This paper presents the synthesis of a state observer for the 1D×1D Vlasov–Poisson (VP) equations. To derive the LPV (linear parameter-varying) formulation of the system, the Vlasov equation is approximated using the discontinuous Galerkin method and the Poisson problem is approximated using the Raviart–Thomas mixed finite element approach. The paper demonstrates the asymptotic and exponential stability of the discretized VP system. Furthermore, the synthesis is extended to include H∞ state estimation. A simulation code has been developed to validate the obtained results.

Optimal Control of Hybrid Photovoltaic/Thermal Water System in Solar Panels Using the Linear Parameter Varying Approach

During photovoltaic (PV) conversion in solar panels, a part of the solar radiation is not converted to electricity by the cells, producing heat that could increase their temperature. This increase in temperature deteriorates the performance of the PV panel. In this paper, a hybrid PV/thermal (PV/T) water system is proposed to mitigate this problem. This system combines a PV panel and a thermal collector. In this paper, we focused on the modeling and control of this hybrid system in the linear parameter varying (LPV) framework. An optimal linear quadratic regulator (LQR) is proposed to control the PV cell temperature around an optimal value that maximises electricity generation. Since the system model is nonlinear, an optimal LQR gain-scheduling state-feedback control approach based on an LPV representation of the nonlinear model is designed using the Linear Matrix Inequality (LMI) method. The goal is to obtain the maximum electrical power for each solar panel. Since a reduced number of sensors is available, an LPV Kalman filter is also proposed to estimate the system states required by the state-feedback controller. The obtained results in a laboratory setup in simulation are used to assess the proposed approach, showing promise in terms of control performance of the PV/T system.

Design of shifting state‐feedback controllers for constrained feedback linearized systems: Application to quadrotor attitude control

AbstractThis paper proposes a shifting feedback linearization controller for nonlinear systems under input saturation. The suggested approach for determining a linear parameter‐varying (LPV) state‐feedback controller is based on employing a linear matrix inequality (LMI)‐based methodology, the input‐output feedback linearization approach, and the shifting paradigm concept. The resultant controller deals with a full linearized version of the nonlinear system under state‐dependent input constraints, and it modifies the closed‐loop convergence speed of the system in accordance with changes in the system's region of linearity. The proposed approach is validated by means of an experimental example.

Application of gap metric for model selection in linear parameter varying model-based predictive control

Selecting the minimum number of linear models required to characterize a nonlinear dynamic system in the local approach to linear parameter varying (LPV) model identification remains a challenge. This study proposes the use of the gap metric for such selection. Subsequently, the identified LPV model is proposed for use in the design of LPV-based model predictive control (MPC). The results of the validation experiment reveal that the identified gap-based local and global LPV models provide a good fit, which is superior to that of any individual linear model, as measured by the computed mean squared error values. Furthermore, the closed-loop results show that the performance of the LPV-MPC closely matches that of the full-blown nonlinear MPC and multi-MPC, while LPV-MPC clearly outperforms Linear MPC. Additionally, the proposed LPV-MPC is found to be robust to process model mismatches and measurement noise, and is much less computationally intensive than nonlinear MPC.

Output Feedback MPC for Nonlinear System in Large Operation Range

This paper studies the output feedback model predictive control (MPC) being suitable to a large operation range of the constrained system represented by a nonlinear model with a bounded disturbance. The model is further parameterized as a multiple linear parameter varying (LPV) state-space equation, each LPV representation being valid around an exclusive equilibrium. Off-line, for each equilibrium, a set of local control laws (in the dynamic output feedback), each having its region of attraction, are calculated. All the control laws for all the equilibriums constitute a lookup table, and all the corresponding regions of attraction take a union. On-line, the real-time control law is searched as one, as per its region of attraction, in the lookup table when the estimated system state moves inside of the union. Once the initial estimation error lies in a pre-specified set, the augmented state is guaranteed to converge to the neighborhood of the target equilibrium, and the constraints on input and output are consistently satisfied. An example is given to illustrate the effectiveness of the proposed algorithm.

An improved linear parameter-varying modeling, model order reduction, and control design process for flexible aircraft

This paper presents an improved process for the modeling, model order reduction (MOR), and control design of a flexible flying wing unmanned aerial vehicle based on the linear parameter-varying (LPV) technology. By applying the Lagrangian formulation and doublet lattice method, the aeroservoelastic (ASE) model of the flexible aircraft is first derived and then rewritten as an airspeed-dependent LPV system, which consists of rigid-body states, structural modes, aerodynamic states, etc. This leads to a high-order LPV model, and the stability of the system varies from stable to unstable when the speed of the aircraft exceeds the critical flutter speed. To facilitate the control design, an oblique projection-based MOR method is then adopted to reduce the order of the plant. Different from previous studies, the MOR method is improved to systematically generate a reduced-order LPV model with consistent states for both the stable and unstable dynamics parts. Finally, an output-feedback LPV controller is designed to simultaneously achieve the body freedom flutter suppression and longitudinal attitude control. Numerical simulation results show the effectiveness of the improved LPV-based ASE modeling, order reduction, and control design process for the flexible aircraft.