Linear Parameter-varying Model Research Articles

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 under varying operational conditions, which 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 extremely 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.

Linear Parameter-Varying Model Predictive Control for Intelligent Energy Management in Battery/Supercapacitor Electric Vehicles

Linear Parameter-Varying Model Predictive Control for Intelligent Energy Management in Battery/Supercapacitor Electric Vehicles

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.

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.

Open-Loop Control Co-Design of Semisubmersible Floating Offshore Wind Turbines Using Linear Parameter-Varying Models

Abstract This paper discusses a framework to design elements of the plant and control systems for floating offshore wind turbines in an integrated manner using linear parameter-varying models. Multiple linearized models derived from aero-elastic simulation software in different operating regions characterized by the incoming wind speed are combined to construct an approximate low-fidelity model of the system. The combined model is then used to generate open-loop, optimal control trajectories as part of a nested control co-design strategy that explores the system’s power production and stability using the platform pitch tilt as a proxy in the context of crucial plant and control design decisions. The radial distance between the central and outer columns and the diameter of the outer columns of the semisubmersible platform are the plant design variables. The platform stability and power production are studied for different plant design decisions. The effect of plant decisions on subsequent power production and stability response of the floating wind turbine is quantified in terms of the levelized cost of energy. The results show that the inner-loop constraints and the plant design decisions affect the turbine’s power and, subsequently, the cost of the system.