Linear Parameter-varying Model Research Articles

Aggressive maneuver oriented integrated fault-tolerant control of a 3-DOF helicopter with experimental validation

In this paper, an integrated fault-tolerant control (FTC) strategy is proposed for unmanned helicopter system under aggressive maneuvers. In order to handle the effect of strong nonlinearities caused by large pitch angle, linear parameter varying (LPV) technique is adopted in the helicopter system modeling. Then, LPV model-based unknown input observer (UIO) design is conducted to simultaneously realize actuator faults and system state estimation, based on which an active fault-tolerant controlleris also constructed. Considering bi-directional robustness interactions between fault as well as state observer and active fault-tolerant controller, an integrated fault-tolerant controller design is further developed. Besides, actuator saturation is also considered in LPV modeling as well as integrated fault-tolerant controller design of the helicopter system. In order to guarantee the robust performance of proposed integrated fault tolerant controller design of helicopter system, energy-to-energy strategy is adopted. And the linear matrix inequality (LMI) toolbox is utilized for gain calculation. Finally, comparative experimental tests are carried out to show the effectiveness and advantages of the proposed FTC strategy.

Robust Controller Designing for an Air-Breathing Hypersonic Vehicle with an HOSVD-Based LPV Model

This paper focuses on the linear parameter varying (LPV) modeling and controller design for a flexible air-breathing hypersonic vehicle (AHV). Firstly, by selecting the measurable altitude and velocity as gain-scheduled variables, the original longitudinal nonlinear model for AHV is transformed into the LPV model via average gridding division, vertex trimming, Jacobian linearization, and multiple linear regression within the entire flight envelope. Secondly, using the tensor product model transformation method, the obtained LPV model is converted into the polytopic LPV model via high-order singular value decomposition (HOSVD). Third, the validity and applicability of the HOSVD-based LPV model are further demonstrated by designing a robust controller for command tracking control during maneuvering flight over a large envelope.

Optimal gain‐scheduling control of proton exchange membrane fuel cell: An LMI approach

Here, an optimal linear parameter varying (LPV) controller is developed for non-linear proton exchange membrane fuel cell (PEMFC) systems. Two performance criteria are involved in the optimal controller, including the membrane pressure and the power of the PEMFC. The former should be minimized; and, the latter should be maximized. Since the goal is to derive sufficient conditions in terms of linear matrix inequality (LMI) constraints, both performances are re-formulated and augmented in a unique convex optimization problem. Further, the non-linear PEMFC with the equilibrium profile dependent on time-varying parameters, that is, current and temperature, is represented by an LPV model. Using the LMI constraints and the obtained LPV model, the gains of the controller are derived. Comparing with the state-of-the-art methods, the proposed approach offers an optimal control approach with a systematic design method, in which both practical issues are treated, simultaneously. To show the advantages of the developed approach, six typical controllers, including the proposed and existing approaches, are considered and several numerical simulation results are conducted.

Interpolation-Based Modeling Methodology for Efficient Aeroelastic Control of a Folding Wing

The aeroelastic model of a folding wing varies with different configurations, so it actually represents a parameter-varying system. Firstly, a new approach based on interpolation of local models is proposed to generate the linear parameter-varying model of a folding wing. This model is capable of predicting the aeroelastic responses during the slow morphing process and is suitable for subsequent control synthesis. The underlying inconsistencies among local linear time-invariant (LTI) models are solved through the modal matching of structural modes and the special treatment of the rational functions in aerodynamic models. Once the local LTI models are represented in a coherent state-space form, the aeroservoelastic (ASE) model at any operating point can be immediately generated by the matrix interpolation technique. Next, based on the present ASE model, the design of a parameterized controller for suppressing the gust-induced vibration is studied. The receptance method is applied to derive fixed point controllers, and the effective independence method is adopted and modified for optimal sensor placement in variable configurations, which can avoid solving ill-conditioned feedback gains. Numerical simulation demonstrates the effectiveness of the proposed interpolation-based modeling approach, and the parameterized controller exhibits a good gust mitigation effect within a wide parameter-varying range. This paper provides an effective and practical solution for modeling and control of the parameterized aeroelastic system.

A Semilinear Parameter-Varying Observer Method for Fabric-Reinforced Soft Robots.

This paper presents an observer architecture that can estimate a set of configuration space variables, their rates of change and contact forces of a fabric-reinforced inflatable soft robot. We discretized the continuum robot into a sequence of discs connected by inextensible threads; this allows great flexibility when describing the robot’s behavior. At first, the system dynamics is described by a linear parameter-varying (LPV) model that includes a set of subsystems, each of which corresponds to a particular range of chamber pressure. A real-world challenge we confront is that the physical robot prototype exhibits a hysteresis loop whose directions depend on whether the chamber is inflating or deflating. In this paper we transform the hysteresis model to a semilinear model to avoid backward-in-time definitions, making it suitable for observer and controller design. The final model describing the soft robot, including the discretized continuum and hysteresis behavior, is called the semilinear parameter-varying (SPV) model. The semilinear parameter-varying observer architecture includes a set of sub-observers corresponding to the subsystems for each chamber pressure range in the SPV model. The proposed observer is evaluated through simulations and experiments. Simulation results show that the observer can estimate the configuration space variables and their rate of change with no steady-state error. In addition, experimental results display fast convergence of generalized contact force estimates and good tracking of the robot’s configuration relative to ground-truth motion capture data.

Predicting Wide-Dynamic Range Neuron Activity from Peripheral Nerve Stimulation using Linear Parameter Varying Models.

Neuromodulation treatments for chronic pain are programmed with limited knowledge of how electrical stimulation of nerve fibers affects the dynamic response of pain-processing neurons in the spinal cord and the brain. By modeling these effects with tractable representations, we may be able to improve efficacy of stimulation therapy. However, pain transmitting neurons in the dorsal horn of the spinal cord, the first pain relay station in the nervous system, have complex responses to peripheral nerve stimulation (PNS) with nonlinearities and history effects. Wide-dynamic range (WDR) neurons are well studied in pain models and respond to peripheral noxious and non-noxious stimuli. We propose to use linear parameter varying (LPV) models to capture PNS responses of WDR neurons of the deep lamina in the dorsal horn in the spinal cord. Here we show that LPV models perform better than a single linear time-invariant (LTI) model in representing the responses of the WDR neurons to widely varying amplitudes of PNS current. In the future, we can use these models alongside LPV control techniques to design closed-loop PNS stimulation that may accomplish optimal pain treatment goals.Clinical Relevance- Electrical nerve stimulation as a therapy for chronic pain is in need of a more informed approach to programming. By describing the effects of stimulation on the pain system with tractable mathematical models, we may be able to titrate the stimulation to more effectively treat chronic pain.

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.

LPV modeling of nonlinear systems: A multi-path feedback linearization approach.

This article introduces a systematic approach to synthesize linear parameter‐varying (LPV) representations of nonlinear (NL) systems which are described by input affine state‐space (SS) representations. The conversion approach results in LPV‐SS representations in the observable canonical form. Based on the relative degree concept, first the SS description of a given NL representation is transformed to a normal form. In the SISO case, all nonlinearities of the original system are embedded into one NL function, which is factorized, based on a proposed algorithm, to construct an LPV representation of the original NL system. The overall procedure yields an LPV model in which the scheduling variable depends on the inputs and outputs of the system and their derivatives, achieving a practically applicable transformation of the model in case of low order derivatives. In addition, if the states of the NL model can be measured or estimated, then a modified procedure is proposed to provide LPV models scheduled by these states. Examples are included to demonstrate both approaches.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Prediction of flow by linear parameter varying model under disturbance

Flowrate being one of the most measured process parameters, thus it is essential to produce higher accuracy. The objective of the paper is to design an estimator using the Linear Parameter Varying (LPV) model which would estimate the flow rate using the data from the orifice meter for varying parameters like, the beta ratio of an orifice, and liquid density. For the development of an estimator, a process model is used, which is designed with the help of a system identification technique using a data-driven method. Data for system identification is obtained by the process model designed using Computational Fluid Dynamics (CFD). The output of the CFD model is compared with experimental results, there is a good agreement in results obtained with an average of 5.97% and 3.19% error in terms of differential pressure and discharge coefficient respectively. The estimated output from the LPV model is compared with that of results obtained from the neural network model and experimental setup, which are also in good agreement with an average error of 2.14%. Thus can be used to estimate flow, when orifice design or density of fluid change intentionally or unintentionally.

Linear parameter-varying modeling and identification of lithium-ion battery for control-oriented applications

Model-based approaches are popularly used for real-time management of lithium-ion batteries. However, building accurate models to characterize the inherent nonlinear dynamic properties of electrochemical processes is still a challenge for control-oriented applications. Instead of building a model independently from physical laws or experimental data, a linear parameter-varying (LPV) modeling method for lithium-ion batteries is proposed in this research. In the LPV modeling structure, the nonlinear relationships are considered to be dependent on the so-called scheduling variables. In combination with the subspace identification algorithm, a global method is proposed to identify the LPV battery model based on a single data set with constantly changing scheduling variables. The validity of this modeling approach is verified by an experimental study of lithium iron phosphate (LiFePO4) cells. Experimental results reveal that state-of-charge (SOC) and SOC change rate are key scheduling variables that determine the model nonlinearities, and the identified model provides good results in terms of prediction accuracy and robustness. Meanwhile, comparison results show that the global LPV modeling approach can describe the nonlinear battery dynamics adequately with first-order model, which makes it a promising method for control-oriented applications.

A novel integrated framework for fault diagnosis with application to process safety

A novel integrated framework for Fault Detection and Isolation(FDI) is proposed, with applications to process safety, by sequentially integrating model-free(MFA) and model-based(MBA) approaches. The MFA includes Limit Checking/Visual and Plausibility analysis, Artificial Neural Network and Fuzzy Logic, Adaptive Neuro-Fuzzy Inference System. The MBA uses a Linear Parameter-Varying model to handle a wide class of generally-nonlinear physical systems. The adaptive Kalman filter(KF) residuals are used for FDI in the MBA. Novel emulators, cascaded with the system during off-line data acquisition, system identification and Bayes’measure of belief computation for each FDI scheme, have their parameters perturbed at each operating point, to mimic unforeseen operational scenarios, thus covering all operating regions. Critical information about the presence/absence of a fault is quickly gained via the faster FDI scheme. A more accurate subsystem’s status is unfolded sequentially by the slower FDI scheme. The final decision on the fault status is obtained using a weighted Bayes classifier fusion scheme meeting the critical requirements of high(low) probability of correct decision (false alarm). Implications of FDI in process safety/environment protection are discussed. This framework is successfully evaluated on simulated and physical systems, including benchmarked laboratory-scale two-tank system, by detecting and isolating sensor, actuator and leakage faults.

Flight evaluation of simultaneous actuator/sensor fault reconstruction on a quadrotor minidrone

In view of the increase in the number of Unmanned Aerial Vehicles (UAVs) in the commercial and private sectors, it is imperative to make sure that such systems are safe, and thus resilient to faults and failures. This paper considers the numerical design and practical implementation of a linear parameter-varying (LPV) sliding mode observer for Fault Detection and Diagnosis (FDD) of a quadrotor minidrone. Starting from a nonlinear model of the minidrone, an LPV model is extracted for design, and the observer synthesis procedure, using Linear Matrix Inequalities (LMI), is detailed. Simulations of the observer FDD show good performance. The observer is then implemented on a Parrot® Rolling Spider minidrone and a series of flight tests is performed to assess the FDD capabilities in real time using its on-board processing power. The flight tests confirm the performance obtained in simulation, and show that the sliding mode observer is able to provide reliable fault reconstruction for quadrotor minidrone systems.

Leak diagnosis in pipelines based on a Kalman filter for Linear Parameter Varying systems

This paper proposes a new approach for the leak diagnosis problem in pipelines based on the use of a Kalman filter for Linear Parameter Varying (LPV) systems. Such a filter considers the availability of flow and pressure measurements at each end of the pipeline. The proposed methodology relies on an LPV model derived from the nonlinear description of the pipeline. For the Kalman filter design purposes, the LPV model is transformed into a polytopic representation. Then, using such a representation, the LPV Kalman filter is designed by solving a set of Linear Matrix Inequalities (LMIs) offline. In the online implementation, the observer gain is calculated as an interpolation of those gains previously computed at the vertices of the polytopic model. The main advantages of this approach are: a) the embedding of the nonlinearities in the varying parameters allows the quasi-LPV system to be obtained which is equivalent to the original nonlinear one, and; b) the use of the well-known LMIs to compute the Kalman gain allows the extension to the LPV case. Those aspects are the main advantages with respect to the classic design of the Extended Kalman Filter (EKF) that requires a linearization procedure and the solution of the Ricatti equation at each iteration. To illustrate the potential of this method, a test bed plant built at Cinvestav-Guadalajara is used. Additionally, the results presented are compared with those results obtained through the classical EKF showing that LPV Kalman observer outperforms the classical EKF.

Adaptive model predictive control of a six-rotor electric vertical take-off and landing urban air mobility aircraft subject to motor failure during hovering

In this article, motor failure control of a six-rotor electric vertical take-off and landing (eVTOL) urban air mobility aircraft is investigated using adaptive model predictive control (MPC) based on the linear parameter-varying (LPV) model developed using the nonlinear rigid-body aircraft model. For capturing the aircraft dynamics under motor failure conditions, a family of linearized models are obtained by trimming the nonlinear aircraft model at multiple equilibrium conditions and the LPV model is obtained by linking the linear models using the failed rotor speed, where the system transition from healthy to failure is modeled by a scheduling parameter calculated based on failed rotor speed caused by available motor peak power after failure. The proposed adaptive MPC is developed to optimize the system output performance, including the rigid-body aircraft velocity and altitude, by using quadratic programming optimization with reference compensation subject to a set of time-varying constraints representing the current available propeller acceleration calculated based on the motor power. Simulation study is conducted based on the developed LPV control design and original nonlinear rigid-body model, and the simulation results demonstrate that the designed adaptive MPC controller is able to recover and maintain the aircraft at desired stable condition after motor failure.

Compensating nonlinear temperature dependence of ultrasonic motor

This article aims at realizing the linear parameter-varying (LPV) controller synthesis to compensate temperature dependence for the ultrasonic motor (USM). Initially, based on the improved optimal frequency tracking scheme, the compact LPV model is investigated to approximate the nonlinear temperature dependence. With the aid of the simulation tool, the accuracy of the proposed LPV model is proven. The LPV controller can be an appropriate choice to ensure the stability of passive nonlinear system. In view of the very strictly passivity (VSP) theorem, the VSP LPV controller is constructed as negative feedback. A set of well-designed experimental setup employed the Shinsei USR60 type USM is built afterwards, and the controller implemented by the host is applied to verify the control effect. Compared with the non-model-based controller, the USM with the proposed controller displays better performance, such as more stable output rotational speed. The feasible model in this paper is of great significance to USM. Particularly, the proposed modeling and control methodology are beneficial to the existing optimum frequency tracking technology for the USM.

Automated nonlinear feedforward controller identification applied to engine air path output tracking

This paper introduces a feedforward control method for physical systems that can be described with linear parameter-varying (LPV) models. The proposed feedforward controller structure is consequently derived from a generic LPV representation and is shown to be identifiable directly from noisy measurement data. The identified structure is advantageous for feedforward control, as using a simple least squares algorithm allows to parameterise basis functions representing the required input trajectory to follow a given output trajectory. Also, with the proposed regularisation, the input trajectory remains bounded even when the physical system exhibits non-minimum phase behaviour. Additionally, the proposed controller structure does not possess states but only considers the inputs and outputs signals and their derivatives, leading to a unique physical interpretation of each controller's parameter. Multiple feedforward controllers identified at various operating points can therefore be directly merged to create a parameter-varying controller. A nonlinear and locally non-minimum phase system is considered in this study, i.e. an engine air path, to evaluate the performances of the proposed feedforward strategy. The controller parameters are first identified from noisy measurement data, and then the proposed feedforward controller is implemented with a feedback controller to track the exhaust pressure and NO x concentration. Using a detailed physical simulation of the engine air path, the proposed feedforward strategy showed encouraging output tracking performances compared to state-of-the-art control methods. The presented feedforward method is shown to be straightforward to identify and calibrate while guaranteeing a contained computational complexity and being applicable to many physical systems thanks to its modularity.

LPV-Based Offline Model Predictive Control for Free-Floating Space Robots

In this article, an offline model predictive control (MPC) based on the linear parameter-varying (LPV) model is developed for free-floating space robots. Parameter set mapping is employed to obtain an LPV model with fewer scheduling parameters, which can enable easier control design and achieve more objectives by using linear control methods. In terms of the LPV system with external disturbance, an MPC method is proposed. Since large disturbance to the base attitude is not admissible in certain missions such as communication with the earth, a term related to the base angular velocity is considered as a part of the cost function of MPC. To deal with actuator saturation, input limitations are included in the constraints of MPC. Moreover, an offline algorithm is introduced to reduce the online computation. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

Gain-Scheduled Model Predictive Control for a Commercial Vehicle Air Brake System

This paper presents a control-oriented Linear Parameter-Varying (LPV) model for commercial vehicle air brake systems with the electro-pneumatic proportional valve based on the nonlinear mathematical model, a set of discrete-time linearized models at different target pressures with the q-Markov Cover system identification method. The scheduled parameters for the LPV model were the brake chamber pressure, which was controlled by the electro-pneumatic proportional valve. On the basis of the LPV model, a family of Model Predictive Control (MPC) controllers with a Kalman filter was designed at each operation point. Then, the gain-scheduled MPC was designed over the entire operating range with the switched strategy, which was validated by experimental data. Furthermore, compared with the PID controller, the performance of the system was improved with a gain-scheduled MPC controller.

Linear Parameter-Varying Model Predictive Control of AUV for Docking Scenarios

A control system for driving an Autonomous Underwater Vehicle (AUV) performing docking operations in presence of tidal current disturbances is proposed. The nonlinear model of the vehicle has been modelled in a Linear Parameter-Varying (LPV) form. This is suitable for the design of the control system using a model-based approach. The LPV model was used for a Model Predictive Control (MPC) design for computing the set of forces and moments driving the nonlinear vehicle model. The LPV-MPC control action is mapped into the reference signals for the actuators by using a Thrust Allocation (TA) algorithm. This was based on the nonlinear models for the actuators and their position and orientation on the vehicle’s hull. The structural decomposition of MPC and TA reduces the computational burden involved in computing the control law on-line on an embedded control board. Both MPC and TA algorithms use the vehicle’s linear and angular positions, and velocities that are estimated by an LPV based Kalman Filter (KF). The proposed control system has been tested in different docking scenarios using various tidal current disturbances acting on the vehicle as an unmeasured disturbance. The simulation results show the controller is effective in controlling the AUV over the range of control scenarios meeting the constraints and specifications.