Linear Parameter-varying Model Research Articles

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

This paper presents a practical model predictive control (MPC) framework for gust load alleviation of a flexible flying wing. Both the controller solving and state estimation are based on a reduced-order model, which features a linear parameter-varying (LPV) form, avoiding online linearization and reducing the scale of the corresponding quadratic programming problem. An improved modeling and model reduction process is used to enhance modeling efficiency and ensure that the reduced-order model can accurately capture the rigid-flexible coupled characteristics of the flexible flying wing under arbitrary gusts. By reconstructing the output of the control-oriented model to include both rigid-body motion and flexible vibrations, the rigid-flexible coupled multi-objective control is established as an MPC problem for reference tracking. The online optimization is formulated in a sparse fashion and combined with an iterative algorithm based on predicted trajectories, describing the variation of model dynamics within the prediction horizon more accurately. With a time-varying Kalman estimator for state updating, the closed-loop simulations are performed for gust alleviation performance validation. Additionally, the real-time potential of the proposed MPC framework is demonstrated through Monte Carlo simulations.

Q‐learning‐based H∞ control for LPV systems

AbstractIn this paper, a model‐free H∞ control method is developed for discrete‐time linear parameter‐varying (LPV) systems by leveraging Q‐learning, which employs the data encompassing system states, control inputs, exogenous disturbance, and time‐varying convex hull rather than the dynamical model known a priori. A policy iteration algorithm presented via linear matrix inequality formed by such collected data is developed with convergence guarantee. Our analysis demonstrates that, in the presence of sufficiently rich disturbances, the attenuation level converges to a lower value than the traditional H∞ control solution derived from an exact LPV model. A numerical example is demonstrated to verify the stabilization, disturbance attenuation, adaptivity, and convergence of the H∞ attenuation level. Moreover, a continuous stirred tank reactor (CSTR) approximated by a discrete‐time LPV system is employed to show the practical potential of the developed model‐free approach.

Stochastic LPV MPC-based path following control for bevel-tip flexible needle with probabilistic constraints

This paper addresses the path-tracking problem for flexible needle control systems using a stochastic linear parameter varying (LPV) and model predictive control (MPC) strategy. Flexible needles operating in dynamic environments with non-uniform tissue density often deviate from ideal assumptions, resulting in non-standard models. The bicycle kinematics model for flexible needle motion control is transformed into an LPV model, improving accuracy and enabling more efficient control. The proposed stochastic LPV MPC approach aims to mitigate uncertainties arising from modelling errors and dynamic environmental factors, ensuring accurate trajectory tracking for the flexible needle. The sample and removal method is utilized to reformulate the probabilistic-constrained optimization problem for implementation. The contributions of this work lie in the application of stochastic LPV MPC to address the trajectory tracking problem in the presence of uncertainties. The simulation results illustrate the superior robustness of the stochastic LPV MPC approach, as evidenced by significantly smaller tracking errors across various scenarios.

An optimal load distribution and real-time control strategy for integrated energy system based on nonlinear model predictive control

Efficient operational scheduling and control are vital for the operation process of the Integrated Energy System (IES), especially under varying operational conditions. An optimal load distribution and real-time control strategy for IES based on Nonlinear Model Predictive Control has been developed to synergistically improve equipment output performance and reduce operating costs. In the proposed strategy, the IES model that integrates linear parameter-varying models for devices and dynamic models for pipe networks, has been constructed via system identification methodology under varying operational conditions. Thus, a hierarchical operation and control framework is established using the model predictive control strategy, including real-time prediction objective, optimal load distribution objective, and optimization algorithms. Consequently, a case study is performed to investigate the supply-demand balance and economic benefit of the proposed strategy. From the aspect of supply-demand balance, the average energy supply-demand discrepancy by using the proposed strategy (for cooling and heating) is approximately 25 %∼33 % that under the steady-state strategy. By means of the proposed strategy, an outstanding equipment output performance will be achieved and supply-demand discrepancy can be dramatically reduced. From the perspective of economic performance, the proposed strategy, which fully considers the nonlinearity of devices, exhibits a 16 % decrease in the operational cost compared to that under the linear dynamic strategy. Through the proposed strategy, efficiency losses are expected to degrade with an excellent economic benefit. Therefore, the suggested strategy is promising and suitable for varying operational condition scenarios.

LPV interpolation modeling and modal-based pole placement control for ball screw drive with dynamic variations

This paper presents a linear parameter varying (LPV) interpolation modeling method and modal-based pole placement (PP) control strategy for the ball screw drive (BSD) with varying dynamics. The BSD is modeled as a global LPV model with position-load dependence by selecting position and load as scheduling variables. The global LPV model is obtained from local subspace closed-loop identification and LPV interpolation modeling. A modal-based global LPV model is obtained through the similarity transformation. Based on this model, a modal-based LPV PP control strategy is proposed to achieve various modal control. Specifically, a state feedback control structure with an LPV state observer is designed to realize online state estimation and real-time state feedback control of modal state variables which cannot be measured directly. The steady-state error is minimized by introducing an error state space (SS) model with the integral effects. Moreover, the stability of the closed-loop system is analyzed according to the controllable decomposition and principle of separation. It is experimentally demonstrated that the proposed modal-based LPV PP control strategy can effectively achieve precise tracking and outstanding robustness meantime.

Uncertainty-aware output feedback model predictive combustion control of RCCI engines

Accurate model development is essential for effective model-based control of Reactivity Controlled Compression Ignition (RCCI) engines. However, due to the intricate nature of engine combustion process, achieving a precise model that can capture the complex dynamic behavior and ensure high control performance poses a significant challenge. In this paper, we propose an uncertainty-aware output feedback model predictive control approach for efficient combustion management in RCCI engines. In contrast to the previously developed approaches, this method adopts a data-driven approach within the linear parameter-varying (LPV) framework for model development. To address the model mismatch between the LPV model and the real system/data, Bayesian Neural Networks (BNNs) are employed which provide the probability distribution of the uncertainties. The BNNs enable the formation of a scenario tree, effectively characterizing the range of potential uncertainties in the system. Through the implementation of scenario-based model predictive control, our approach ensures high tracking performance for the RCCI engine in the presence of modeling uncertainties and measurement noise. Extensive simulations and experimental validations demonstrate the superiority of our uncertainty-aware model predictive control over traditional control strategies.

A comprehensive approach to sparse identification of linear parameter-varying models for lithium-ion batteries using improved experimental design

This paper proposes a comprehensive approach to the identification of battery models in the linear parameter-varying (LPV) framework inspired by the equivalent-circuit model structures. The proposed LPV model structure is formulated using the input–output representation, wherein the model parameters are considered to depend on the state-of-charge, the current magnitude, and the current direction. The aforementioned dependence is explained using a suitable set of basis functions motivated with appropriate physical insight. Furthermore, the optimal experimental design problem is discussed to propose an improved input design for the model identification procedure. Subsequently, the Least Absolute Shrinkage and Selection Operator (LASSO) along with the ridge regression are employed for the selection of significant model terms and parameter estimation to yield a sparse model with adequate simulation capabilities. Finally, several battery models with varying model order and basis-function complexity are identified, which are subsequently validated and compared using a real drive-cycle dataset. The corresponding voltage simulation results yield the root-mean-squared error (RMSE) value for the best-performing model to be around 24.5 mV when a 1 A h NMC battery gets discharged with the lower voltage cutoff as low as 2.5 V.

A robust [formula omitted] fault-tolerant control approach for time-delay LPV systems with uncertain parameters and unknown disturbances

The article proposes a H∞ fault-tolerant control approach for a series of uncertain linear parameter-varying (LPV) time-delay models to obtain disturbance suppressions. Specifically, by applying the Lyapunov functions, a series of feedback controllers are provided to ensure the robust performance of LPV models with actuator faults. Meanwhile, a convex optimization strategy is developed for resolving optimization problems in the presence of bilinear matrix inequalities (BMIs), where the robustness conditions are improved to guarantee the stability of LPV model under uncertain factors. By resolving a class of linear matrix inequalities (LMIs), the gain matrices for LPV systems can be obtained. Furthermore, the less conservative conditions are developed and supported by strict theoretical derivation. Ultimately, the validity of proposed approach is confirmed by simulation analyses of truck–trailer systems.

A control-oriented LPV model of large-scale offshore wind turbines for deloading operation

ABSTRACT This article develops a new control-oriented linear parameter varying (LPV) model, which is a linear state-space model with varying parameters aimed at efficiently representing large-scale offshore wind turbines (LOWTs). Firstly, the LPV model is constructed by the mechanism analysis of a 15-MW direct-drive permanent magnet wind turbine. Subseuently, based on the operational data from FAST, the parameters with unknown values in the LPV model are determined by gain scheduling and parameter estimation. Furthermore, a deloading operation for the active output power regulation of LOWTs is proposed based on coordinating the rotor over-speed control (ROC) and the pitch angle control (PAC).

Controlling neural activity: LPV modelling of optogenetically actuated Wilson–Cowan model * *This work was supported by ANPCyT, Ministry of Science & Technology, Argentina Grant PICT2017-2417. Demián García-Violini is supported by the Agencia I+D+i, Ministry of Science & Technology, Argentina, under PICT-2021-I-INVI-00190.

Objective. This paper aims to bridge the gap between neurophysiology and automatic control methodologies by redefining the Wilson–Cowan (WC) model as a control-oriented linear parameter-varying (LPV) system. A novel approach is presented that allows for the application of a control strategy to modulate and track neural activity. Approach. The WC model is redefined as a control-oriented LPV system in this study. The LPV modelling framework is leveraged to design an LPV controller, which is used to regulate and manipulate neural dynamics. Main results. Promising outcomes, in understanding and controlling neural processes through the synergistic combination of control-oriented modelling and estimation, are obtained in this study. An LPV controller demonstrates to be effective in regulating neural activity. Significance. The presented methodology effectively induces neural patterns, taking into account optogenetic actuation. The combination of control strategies with neurophysiology provides valuable insights into neural dynamics. The proposed approach opens up new possibilities for using control techniques to study and influence brain functions, which can have key implications in neuroscience and medicine. By means of a model-based controller which accounts for non-linearities, noise and uncertainty, neural signals can be induced on brain structures.

An online state-of-health estimation method for lithium-ion battery based on linear parameter-varying modeling framework

The accurate estimation of state-of-health (SOH) is crucial for ensuring the safe and reliable operation of lithium-ion battery systems. However, the intimate coupling between SOH and state-of-charge (SOC) is often overlooked in existing estimation methods, leading to inaccurate estimates. To address this, we propose a linear parameter-varying (LPV) battery model that captures both gradual capacity degradation and rapid dynamic changes. This model integrates traditional linear models with emerging nonlinear models, providing a comprehensive online SOH estimation framework that effectively separates the effects of SOC in the LPV model structure. The model parameters are identified using a subspace algorithm with accelerated aging data. The proposed method is validated by accelerated aging experiments on two sets of battery samples, one for model development and another for model validation. The experimental data show that the LPV battery model can achieve high SOH estimation accuracy, with an average error of 2.85 % and 5.51 % for SOH, and 0.63 % and 1.20 % for capacity, respectively. The method also shows the advantages of being easy to implement and highly generalizable, making it suitable for different battery types and application scenarios.

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

Joint extension speed dictates bio-inspired morphing trajectories for optimal longitudinal flight dynamics.

Avian wing morphing allows dynamic, active control of complex flight manoeuvres. Previous linear time-invariant (LTI) models have quantified the effect of varying fixed wing configurations but the time-dependent effects of morphing between different configurations is not well understood. To fill this gap, I implemented a linear parameter-varying (LPV) model for morphing wing gull flight. This approach models the wing joint angles as scheduled parameters and accounts for nonlinear kinematic and gravitational effects while interpolating between LTI models at discrete trim points. With the resulting model, I investigated the longitudinal response associated with various joint extension trajectories. By optimizing the extension trajectory for four independent objectives (speed and pitch angle overshoot, speed rise time and pitch angle settling time), I found that the extension trajectory inherent to the gull wing does not guarantee an optimal response but may provide a sufficient response with a simpler mechanical implementation. Furthermore, the results indicated that gulls likely require extension speed feedback. This morphing LPV model provides insights into underlying control mechanisms, which may allow for avian-like flight in future highly manoeuvrable uncrewed aerial vehicles.

Linear parameter-varying output-feedback for active vibration control of an elastic kinetic roof structure with experimental validation

Elastic kinetics are an approach to design transformable lightweight structures with a stable transformation process. The transformation is realized through elastic bending of structural members by exploiting the compliant material behavior. This lightweight and flexible design comes at the cost of increased sensitivity to static and dynamic disturbances. However, most of the current research focuses on the principles of elastic kinetic transformation instead of effective disturbance mitigation. This work focuses on dynamic disturbance mitigation for such transformable lightweight structures using active control. Modeling and controller synthesis are performed in the linear parameter-varying (LPV) framework, since the dynamics of elastic kinetic structures are transformation-state dependent due to geometric nonlinearities. Based on an LPV model in a grid-based representation, an LPV output-feedback control can be designed and synthesized via a gridding approach. This methodology is experimentally tested and validated for the example of an active hybrid roof structure prototype.

Model Development for Off-Road Traction Control: A Linear Parameter-Varying Approach

The number of highly automated machines in the agricultural sector has increased rapidly in recent years. To reduce their fuel consumption, and thus their emission and operational cost, the performance of such machines must be optimized. The running gear–terrain interaction heavily affects the behavior of the vehicle; therefore, off-road traction control algorithms must effectively handle this nonlinear phenomenon. This paper proposes a linear parameter-varying model that retains the generality of semiempirical models while supporting the development of real-time state observers and control algorithms. First, the model is derived from the Bekker–Wong model for the theoretical case of a single wheel; then, it is generalized to describe the behavior of vehicles with an arbitrary number of wheels. The proposed model is validated using an open-source multiphysics simulation engine and experimental measurements. According to the validated results, it performs satisfactorily overall in terms of model complexity, calculation cost, and accuracy, confirming its applicability.

Data-driven integrated study on operational performance degradation detection and recovery control of VFDR

The Variable Flow Ducted Rocket (VFDR) serves as the preferred propulsion system for hypersonic aircraft. However, it is prone to health degradation issues due to component failures, aging, and changes in operational conditions, which significantly challenge flight safety. This study introduces a data-driven integrated control approach for modeling, diagnosing, and remedying performance deterioration. Initially, a method for open-set modeling of performance degradation is developed using the Linear Parameter-Varying (LPV) modeling technique and gap metric theory, tackling the hurdles of data collection, overlapping fault classes, and modeling of unidentified faults in the VFDR system; thus, providing vital data support for detecting performance degradation. Moreover, employing the LPV model for performance degradation, a hybrid deep neural network combining multi-scale CNN and LSTM is trained to diagnose system performance issues online using multi-dimensional time-domain sequential data. Subsequently, a smooth transition control method utilizing sliding mode compensation is applied to regain control of system performance based on diagnostic outcomes and a pre-established VFDR performance recuperation controller. Simulations of three types of performance deterioration scenarios caused by changes in actuators, sensors, and the system's operational environment are conducted to demonstrate the efficiency of the proposed approach. The simulation outcomes affirm that the proposed approach is capable of effectively modeling system performance deterioration, diagnosing faults, and controlling recovery, offering promising technical support for the secure operation of intricate closed-loop control systems with stringent precision and reliability requirements.

Low Temperature Combustion Modeling and Predictive Control of Marine Engines

The increase of popularity of reactivity-controlled compression ignition (RCCI) is attributed to its capability of achieving ultra-low nitrogen oxides (NOx) and soot emissions with high brake thermal efficiency (BTE). The complex and nonlinear nature of the RCCI combustion makes it challenging for model-based control design. In this work, a model-based control system is developed to control the combustion phasing and the indicated mean effective pressure (IMEP) of RCCI combustion through the adjustments of total fuel energy and blend ratio (BR) in fuel injection. A physics-based nonlinear control-oriented model (COM) is developed to predict the main combustion performance indicators of an RCCI marine engine. The model is validated against a detailed thermo-kinetic multizone model. A novel linear parameter-varying (LPV) model coupled with a model predictive controller (MPC) is utilized to control the aforementioned parameters of the developed COM. The developed system is able to control combustion phasing and IMEP with a tracking error that is within a 5% error margin for nominal and transient engine operating conditions. The developed control system promotes the adoption of RCCI combustion in commercial marine engines.

Enhanced robust adaptive flight control for a convertible VTOL UAV

In this paper, we propose less conservative formulations for candidate controllers of robust adaptive mixing control (RAMC) strategies. The RAMCs are employed to solve the trajectory tracking problem throughout the full flight envelope, with guaranteed stability, of a convertible plane (CP) vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV). Initially, the multi-body nonlinear dynamic model of the CP VTOL UAV is obtained using the Euler–Lagrange formalism, from which a linear parameter-varying (LPV) model is derived to be used in the design of the RAMC candidate controllers. The new formulations of the candidate controllers are proposed considering two approaches: a (i) Parallel Distributed Compensation (PDC); and (ii) a parameter-dependent Lyapunov function. Hardware-In-the-Loop (HIL) experiments are performed in a high-fidelity flight simulator to verify the fulfillment of real-time constraints, ensuring a computationally lightweight control strategy ready for implementation in a low-cost embedded computational system.

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.

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.