Linear Parameter-varying Model Research Articles

Embedded predictive controller based on fuzzy linear parameter-varying model: A hardware-in-the-loop application to an ESP-lifted oil well system

This work addresses the development of a fuzzy infinite horizon model predictive control (FIHMPC) strategy and its application to an ESP-lifted oil well system in an embedded hardware. The proposed scheme is based on a fuzzy model to approximate the nonlinear system to a linear parameter-varying model and incorporate it into the proposed MPC law. Slacked terminal constraints and zone control scheme are incorporated to the FIHMPC controller assuring optimization feasibility to handle ESP time-varying operation envelope. The implementable zone FIHMPC controller is applied through an ESP32 micro-controller to ESP-lifted oil well system equations, executed in MATLAB, composing a hardware-in-the-loop (HIL) simulation scheme. Nonlinear mismatch scenarios with unmeasured disturbances show the effectiveness of the proposed controller over multiple operating conditions. Computational memory and processing analysis over simulations also validates the controller application.

Linear parameter-varying gain-scheduled preview-based robust attitude control design for a staring-mode satellite

It is challenging to precisely control the attitude of a satellite when performing a fast and large-angle maneuver, for instance, in the staring mode. To solve this issue, this paper investigates a gain-scheduled preview-based robust attitude control method in the framework of linear parameter-varying control theory. Firstly, the linear parameter-varying model of an observation satellite with large-angle rotations is developed by choosing the attitude angles as scheduling parameters to take the dynamics variation into consideration. In order to ease the implementation in practical engineering applications, the structure of the linear parameter-varying controller is in the form of modified proportional-integral-derivative control. To simultaneously satisfy the requirements of fast rotational speed and high dynamic tracking performance, a gain-scheduled proportional-integral-derivative controller is designed with the future information of desired attitude signals included in the feedforward path. The proposed controller is synthesized within the framework of H∞ robust control to enhance the robustness against inaccurate previewed information and external disturbances. The corresponding control synthesis condition is derived as an optimization problem with linear matrix inequality constraints. Monte Carlo simulation results demonstrate that the dynamic tracking accuracy of the proposed control algorithm can be guaranteed to be less than 0.01 deg in the face of fast large-angle commands, inaccurate previewed information and external disturbances.

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.

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.

Dynamic load change operation education in air separation processes using a multivariable and nonlinear model

An operator training system (OTS) for dynamic load change operation education in air separation processes is developed. A linear parameter varying (LPV) dynamic model based on an iterative optimization strategy is identified to represent the nonlinear characteristics of the air separation process. First, the local models at typical working points are identified. Second, the weighting functions between the local models are designed and estimated. Finally, an iterative optimization strategy optimizes the local models and weighting functions. The identified LPV model is used as the core training model of the OTS. Model validation with actual data shows that the identified OTS model has reasonable simulation accuracy. By designing a model predictive control (MPC) algorithm, a multidimensional skill evaluation algorithm based on MPC operation data is proposed. The developed OTS and skill evaluation algorithm are applied in a vocational skill competition. Results show that the operation skills of different operators can be reflected and distinguished.

Development of an autonomous fog computing platform using control-theoretic approach for robot-vision applications

This paper presents the dynamic modelling and linear matrix inequality (LMI) based controller design of a distributed fog computing framework for real-time robot vision applications. A mobile robot vision system acquires the images from an application environment such as a warehouse, where articles are stacked in numerous racks. We characterise the mobile robot vision data (MRVD) using frames per second (FPS) and the image resolution. From the MRVD, object detection is performed by an open-source deep learning (DL) platform for detecting and localising various objects. However, with higher FPS together with high-resolution images, the processing time by the DL algorithm increases significantly. This necessitates the deployment of a distributed computing platform with several computing nodes. In this work, we deploy a distributed fog computing environment (DFCE) for the real-time object detection in an application environment.The processing time required to handle the MRVD is called the service time. However, for efficient auto-scaling performance, the mathematical model of the DFCE, taking into consideration the characteristics of the MRVD is necessary. In this context, we envisage the application of control theory to build the dynamic model of the DFCE. A Linear Parameter Varying (LPV) model is proposed for the DFCE with the service time as the output, the number of fog nodes as the input, and the characteristics of MRVD as the time-varying parameters. At first, an LPV model for the DFCE is derived using system identification, and the model is validated using the real-time test data. The LPV model is converted to a Polytopic LPV (PLPV) model for LMI based controller design. Finally, we develop and validate a Linear Matrix Inequality (LMI) based LPV controller to meet the service time constraints for a given application environment.For localisation and trajectory tracking with obstacle avoidance in the application environment, the mobile robot implements an Extended Kalman Filter (EKF) based simultaneous localisation and mapping (SLAM) and a bug-based path planning algorithm respectively. Finally, we present, detailed controller validation results illustrating the mobile robot navigation together with the auto-scaling control for the fog computing platform to modulate the service time.

Aggressive Maneuver Oriented Robust Actuator Fault Estimation of a 3-DOF Helicopter Prototype Considering Measurement Noises

This article presents a robust actuator fault estimation strategy design for a three-degree of freedom (3-DOF) helicopter prototype which can be adapted to aggressive maneuvers. First, considering large pitch angle condition during flight, nonlinear coupling characteristic of the helicopter system is exploited. As the pitch angle can be measured in real time, a polytopic linear parameter varying (LPV) model is developed for the helicopter system. Furthermore, considering measurement noises in the actual helicopter system, the dynamical model of helicopter system is modified accordingly. Then, based on the modified polytopic LPV model, a robust unknown input observer is developed for the helicopter system to realize actuator fault estimation, in which both measurement noises and large pitch angle are considered. Robust performance of proposed fault estimation approach is guaranteed by using energy-to-energy strategy. And the observer gains are calculated by using linear matrix inequalities. Finally, based on a 3-DOF helicopter prototype, both simulations and experiments are conducted. The effects of measurement noises and large pitch angle on the fault estimation performance are sufficiently demonstrated. And effectiveness as well as advantages of the proposed observer is verified by using comparative analysis.

Imbalance compensation of active magnetic bearing systems using model predictive control based on linear parameter-varying models

Active magnetic bearing (AMB) is a suspension system to levitate a rotating shaft freely without any physical contact which allows extremely fast rotation speeds. One big control challenge of the AMB systems, which appears during high rotation speeds, is the non-uniform distribution of the rotor weight about its rotating axis. This is usually referred to as the rotor imbalance problem which produces sinusoidal disturbance forces. These disturbances lead to undesirable vibrations and large deviations of the rotor shaft from its desired trajectories. We adopt in this work model predictive control (MPC) to reduce the effect of these sinusoidal disturbances and to achieve a stable levitation of the rotor shaft while tracking a reference trajectory. Owing to the MPC capability of handling constraints in an optimal manner, physical input constraints can be committed. Moreover, state constraints can be imposed to ensure safety of operation. For tractable implementation, we embed the nonlinear dynamics of the system in a linear parameter-varying (LPV) representation. To guarantee stability of the closed-loop system, a terminal cost and a terminal constraint set are included in the MPC optimization problem. For tractable computations of these terminal ingredients, a reduced LPV model is considered. The performance of the proposed LPV-MPC scheme is validated via simulation on the nonlinear model of an experimental setup of an AMB system and it is compared with two other classical controllers commonly used for these AMB systems in practice.

Direct identification of continuous-time LPV state-space models via an integral architecture

In this paper, we present a block-structured architecture for direct identification of continuous-time Linear Parameter-Varying (LPV) state-space models. The proposed architecture consists of an LPV model followed by an integral block. This structure is used to approximate the continuous-time LPV system dynamics. The unknown LPV model matrices are estimated along with the state sequence by minimizing a properly constructed dual-objective criterion. A coordinate-descent algorithm is employed to optimize the desired objective, which alternates between computing the unknown LPV matrices and estimating the state sequence. Thanks to the linear parametric structure induced by the LPV model, the optimization variables within each coordinate-descent step can be updated analytically via ordinary least squares. Furthermore, in order to handle large-size datasets, we discuss how to perform optimization based on short-size subsequences. The effectiveness of the proposed methodology is demonstrated via an academic example and two case studies. The first case study consists of identifying an LPV model describing the behaviour of an electronic bandpass filter from benchmark experimental data. The second case study involves identification of the plasma safety factor from a tokamak plasma simulator.

Tensor product model HOSVD based polytopic LPV controller for suspension anti-vibration system

This paper presents a polytopic linear parameter varying (LPV) controller design methodology for nonlinear anti-vibration suspension based on stochastic road identification. As the main nonlinear component in semi-active suspension, the continuous damping control (CDC) damper value is mapped by damping velocity and control current through a bench experiment. linear parameter varying gain-scheduled method is applied for dealing with the nonlinear deterministic model. As the uncertainties caused by road stochastic excitation to suspension cannot be ignored, it is essential to identify the excitation signal as a measurable variable parameter. Empirical-mode-decomposition (EMD) and support vector machine (SVM) are utilized to identify and classify the road stochastic signal input into standard level, so polytopic LPV controller can be designed with CDC damper velocity, control current, and road level as variable parameters. Meanwhile the exponential increase of high-order plant elements in multi-parameter LPV model makes it too complicated for real-time computing. Hence the tensor product model transformation is utilized to identify the orthogonal basis of system plant so that low-rank approximation of it can be implemented by truncated high-order singular value decomposition (T−HOSVD) method. Real-time simulation shows the performance and feasibility of controller, which can efficaciously identify the road stochastic excitation as measurable variable parameters for nonlinear suspension polytopic LPV control.

Soft sensor for an orifice flowmeter in presence of disturbances

Measurements using an orifice flowmeter are widely used in industry. In certain instances, the output of the flowmeter may be corrupted due to plate contamination, changes in fluid density, or incorrect insertion of the plate. This paper describes a method for estimating the correct output in the presence of such disturbances. First, a linear parameter-varying model of the orifice flowmeter is developed using data extracted from computational fluid dynamics simulations. The simulation and experimental output are found to have an average deviation of 6.5% and 3.49% in terms of the differential pressure and discharge coefficient, respectively. Observer-based estimators for the linear parameter-varying models are developed for different combinations of the settling time and maximum overshoot. These estimators enable the disturbance-induced output to be corrected close to the true value. The error in the disturbed output due to plate contamination is reduced from 45% to 0.82%. Similarly, the error due to an accidental change of plate decreases from 76% to 2.03%. Thus, the proposed estimator can be used to nullify the disturbances induced in the measurements from orifice flowmeters.

Linear parameter-varying-based transition flight control design for a tilt-rotor aircraft

This paper presents the development of novel transition flight controllers for a class of urban air mobility aircrafts configured with a fixed-wing and six distributed electric rotor assemblies. Only the two tilt-rotors are utilized for thrust vectoring during transition flight from hovering to steady-level flight, while the four lift-rotors are modulated with aerodynamic lift induced by fixed-wing to maintain stable altitude-hold. Three tractable tilt-rotor articulation profiles are proposed by taking into account of various aircraft and hardware constraints. Given a predefined nominal tilting profile, a family of linear models is obtained by linearizing the nonlinear aircraft model at multiple tilt-rotor angular positions along the tilting profile. Using tilt-rotor angular position as a scheduling parameter, a discrete-time linear parameter-varying model can be constructed, which is then used to develop a novel transition flight control architecture that integrates the adaptive model predictive control law with feedforward effect of the dynamic reference compensation. The simulation results demonstrate the effectiveness of proposed transition flight controllers and its robustness subject to external disturbance.

Modeling and control of a class of urban air mobility tiltrotor aircraft

This paper aims at developing a control-centric analytical formulation for aeromechanics and flight dynamics of urban air mobility (UAM) vehicles. Such vehicles feature a hybrid configuration with tiltrotors and fixed wings, enabling vertical takeoff/landing capability while attaining level flight range and endurance. A comprehensive nonlinear rigid-body dynamic model is developed by incorporating multiple tiltrotor dynamics and their gyroscopic and inertial coupling effects. A quasi-steady aerodynamic formulation is used to derive the aerodynamic loads on all lifting surfaces. In addition to the conventional control surfaces of the fixed-wing aircraft, the tiltrotor angular positions and rotational speeds are also considered additional control inputs in the derivation of nonlinear flight dynamic equations. These nonlinear equations are then linearized with respect to a set of trimmed conditions to generate the corresponding linear time-invariant state-space models, which are best suited for flight control design. In particular, to capture the critical dynamical behaviors during the transition from vertical to forward flight, the linear models are attained at various angular positions of the tiltrotors. These linear models are then utilized to develop a linear parameter-varying (LPV) model in which the tiltrotor angular position is considered the scheduling parameter. Subsequently, the adaptive model predictive control (MPC) methodology is used to design the flight controllers to achieve a stable and smooth transition flight. The numerical simulations demonstrate the efficacy of the proposed modeling and control approach.

Finite-time bounded control for quadrotors with extended dissipative performance using a switched system approach

In order to deal with the problem of attitude tracking control for quadrotors subject to time-varying inertia and external disturbances, a finite-time bounded switched linear parameter-varying (LPV) control method is presented. The attitude dynamics is described by two subsystems, where the inner angular-velocity system is used to track the desired angular velocities that are generated by the outer attitude-angle system. The angular-velocity system of quadrotors is modeled as a switched LPV model, where a family of linear models is developed to approximate the original nonlinear system and the LPV method is applied to model the time-varying inertia. Specially, a mode-dependent persistent dwell-time (MPDT) switching logic, which is more general than the typically used dwell-time (DT) or average dwell-time (ADT) switching logic, is adopted to govern the switching behaviors among these linear models. A state-feedback controller for the switched LPV error-tracking system is designed, which ensures both finite-time boundedness and extended dissipative performance. Finally, the developed theoretical results are verified by numerical simulation.

Parameter-dependent Lyapunov function based fault estimation and fault-tolerant control for LPV systems

In this paper, an integrated fault estimation (FE) and fault-tolerant control (FTC) method is proposed for linear parameter varying (LPV) systems using the parameter-dependent Lyapunov function. The observer-based estimation and fault-tolerant control structure causes an uncertainty between systems which is called the bi-directional uncertainty. Additionally, with simultaneous actuator and sensor faults, disturbances, the overall performance of the FTC system decreases. To maintain robust stability of closed-loop systems, an unknown input observer fault estimator approach with both state feedback control and sliding mode control is implemented as a solution by solving optimisation using a linear matrix inequality (LMI) formulation. The efficiency of the integrated FE/FTC design is demonstrated using the pitch-axis missile LPV model and simulated to evaluate the merits of the suggested approach.

State-of-charge dependent equivalent circuit model identification for batteries using sparse Gaussian process regression

Due to their ease of implementation, equivalent circuit models (ECMs) of batteries are widely used in battery management systems. Generally, ECM parameters vary with operating conditions, thus how such parameter dependencies are addressed substantially influences the accuracy of an ECM over a wide operating range. In this paper, we identify an ECM whose parameters have nonlinear dependence on state-of-charge (SOC). By transforming the SOC-dependent ECM into a linear parameter varying (LPV) input–output model, we propose a non-parametric sparse Gaussian process regression (GPR) approach, which alleviates the difficulty of specifying parametric functional SOC-dependencies of model parameters. The proposed approach derives the posterior distributions of ECM parameters, thus is capable to provide both parameter estimates and their associated uncertainties. The computational cost over large datasets is significantly reduced by adopting the sparse GPR. The proposed approach is applied to the above LPV model with two noise model structures, i.e., white and colored noises. Identification results using experimental data illustrate the efficacy of the proposed approach. The use of colored noise enhances robustness under different noise levels, and achieves higher output prediction accuracy over experimental datasets.

An Online Data-Driven LPV Modeling Method for Turbo-Shaft Engines

The linear parameter-varying (LPV) model is widely used in aero engine control system design. The conventional local modeling method is inaccurate and inefficient in the full flying envelope. Hence, a novel online data-driven LPV modeling method based on the online sequential extreme learning machine (OS-ELM) with an additional multiplying layer (MLOS-ELM) was proposed. An extra multiplying layer was inserted between the hidden layer and the output layer, where the hidden layer outputs were multiplied by the input variables and state variables of the LPV model. Additionally, the input layer was set to the LPV model’s scheduling parameter. With the multiplying layer added, the state space equation matrices of the LPV model could be easily calculated using online gathered data. Simulation results showed that the outputs of the MLOS-ELM matched that of the component level model of a turbo-shaft engine precisely. The maximum approximation error was less than 0.18%. The predictive outputs of the proposed online data-driven LPV model after five samples also matched that of the component level model well, and the maximum predictive error within a large flight envelope was less than 1.1% with measurement noise considered. Thus, the efficiency and accuracy of the proposed method were validated.

Safe control of nonlinear systems in LPV framework using model-based reinforcement learning

This paper presents a safe model-based reinforcement learning (MBRL) approach to control nonlinear systems described by linear parameter-varying (LPV) models. A variational Bayesian inference Neural Network (BNN) approach is first employed to learn a state-space model with uncertainty quantification from input-output data collected from the system; the model is then utilised for training MBRL to learn control actions for the system with safety guarantees. Specifically, MBRL employs the BNN model to generate simulation environments for training, which avoids safety violations in the exploration stage. To adapt to dynamically varying environments, knowledge on the evolution of LPV model scheduling variables is incorporated in simulation to reduce the discrepancy between the transition distributions of simulation and real environments. Experiments on a parameter-varying double integrator system and a control moment gyroscope (CMG) simulation model demonstrate that the proposed approach can safely achieve desired control performance.

A linear parameter-varying modelling approach for dielectric elastomer loudspeakers

In this paper, we present a linear parameter-varying (LPV) model of an electrostatic loudspeaker driven by dielectric elastomer (DE) actuators. Because of its numerical simplicity, this LPV model represents a convenient tool to develop real-time control strategies for the speaker. Starting from a non-linear reduced model of the device, we assume that the control input can be broken into two components: a small-amplitude high-frequency component, responsible for the sound generation, and a slowly-varying bias component, which can be used as a free control parameter to tune and adjust the speaker response. We thus build an LPV model, treating the dynamic response to the high-frequency input component as linear, and parametrising the coefficients of such linear system with respect to the low-frequency input component. We present a validation of the model against experiments, and show that the proposed LPV formulation captures the most relevant non-linearities involved in the DE speaker operation.

Linear Parameter-varying Model for Prediction of Charge / Discharge Behavior of Tri-Electrode Zinc-air Flow Battery

Recently, energy storage systems have been a hot topic of research due to their potential to enable the use and integration of renewable energy into a power grid. Zinc-air flow batteries (ZAFBs) are viewed as having significant promise for usage as renewable energy storage devices due to their high energy density and low cost. The battery management system (BMS) for ZAFBs, on the other hand, is still in its infancy, as a precise prediction of their nonlinear behavior is necessary. To address this shortcoming, a linear parameter varying (LPV) model is constructed via a multiple linear time-invariant (LTI) model using charge/discharge current and state of charge (SOC) as scheduling parameters. The model created is validated using a variety of battery data from several experimental batches. According to the discharge current and state of charge, the results reveal that the established LPV model can accurately predict the nonlinear behavior of the ZAFBs. Thus, it is determined that in terms of local accuracy, the LPV model is comparable to the linear model. With respect to the global accuracy, the analysis demonstrates that the LPV model outperforms the linear model. This result provide arguments for the LPV model's capacity to anticipate the dynamics of ZAFBs and their suitability for usage in the BMS.