Linear Parameter-varying Systems Research Articles

Design and Validation of a State-Dependent Riccati Equation Filter for State of Charge Estimation in a Latent Thermal Storage Device

Abstract Latent thermal energy storage (TES) devices could enable advances in many thermal management applications, including peak load shifting for reducing energy demand and cost of HVAC or providing supplemental heat rejection in transient thermal management systems. However, real-time feedback control of such devices is currently limited by the absence of suitable state of charge estimation techniques, given the nonlinearities associated with phase change dynamics. In this paper, we design and experimentally validate a state-dependent Riccati equation (SDRE) filter for state of charge estimation in a phase change material (PCM)-based TES device integrated into a single-phase thermal-fluid loop. The advantage of the SDRE filter is that it does not require linearization of the nonlinear finite volume model; instead, it uses a linear parameter-varying system model which can be quickly derived using graph-based methods. We leverage graph-based methods to prove that the system model is uniformly detectable, guaranteeing that the state estimates are bounded. Using measurements from five thermocouples embedded in the PCM of the TES and two thermocouples measuring the fluid temperature at the inlet and outlet of the device, the state estimator uses a reduced-order finite volume model to determine the temperature distribution inside the PCM and in turn, the state of charge of the device. We demonstrate the state estimator in simulation and on experimental data collected from a thermal management system testbed to show that the state estimation error converges near zero and remains bounded.

A Linear Variable Parameter Observer-Based Road Profile Height Estimation for Suspension Nonlinear Dynamics Improvements

The accuracy of road profile height estimation has a significant impact on suspension control quality, which in turn influences handling, stability of vehicle motion and occupants' comfort. Based on our previous published work, this article designs and proposes a novel method for road profile estimation that is based on suspension nonlinear dynamics. The proposed approach first establishes the road profile height estimation model considering a real suspension design, including nonlinear characteristics of the shock absorber, bushing stiffness and damping, actual geometry of the control arms, and positioning of absorber. Unlike the conventional sprung-unsprung mass model, the real nonlinear suspension model provides much higher output prediction accuracy as computational and experimental results demonstrated. Moreover, the established estimation method and model require only two easily measurable parameters, which are the acceleration of the sprung mass and the travel of the shock absorber. While considering nonlinearity and hysteretic characteristics of the damping force, the proposed approach is based on the estimation framework of linear parameter-varying systems and establishes a sliding mode observer for estimating the road profile height. The stability of estimation error dynamics of the observer is guaranteed by the Lyapunov stability analysis. As bench-test experiments of a hardware implementation of the suspension-wheel unit validated the computational results. The tests demonstrated that the proposed method allows for real-time estimating of the road profile height in different road conditions and electric currents of the suspension damper and is robust to uncertainty of the payload.

Observer-based event-triggered control for continuous-time switched linear parameter-varying systems

This paper researches the interval observer–based event-triggered control of switched linear parameter-varying (LPV) systems, which involve unknown external disturbance and measurement noise. First, we offer an event-triggering condition and a controller which are correlated with state estimations. Then, by analyzing the relationship between switching sequences and sampling sequences, we model the resulting systems as switched time-delay systems. It deserves to note that the mismatches of the switching signal for the controllers and the systems may occur due to the sampling of switching signal. Using the merging switching signal technique and the multiple Lyapunov–Krasovskii functional method, and thinking over both synchronous and asynchronous switching of the systems and the controllers, we acquire relevant conditions which are used to realize the stability of the whole switched LPV closed-loop systems under the mode-dependent average dwell time (MDADT) switching. Next, we give a specific algorithm to design the controller gains. Finally, a numerical example is provided to verify the superiority of the outcomes.

Sparse identification for ball-screw drives considering position-dependent dynamics and nonlinear friction

Establishing accurate dynamic models in a form that is suitable for integration with model-based control methods, is of great significance for further improving the dynamic motion control precision of ball-screw drives. However, due to the nonlinear time-varying factors such as position-dependent dynamics and nonlinear friction disturbance, it is difficult to model the dynamic characteristics of ball-screw drives accurately, concisely and efficiently. To overcome this challenge, a sparse identification method for ball-screw drives is proposed. Ball-screw drives are modeled as discrete-time linear parameter-varying systems under nonlinear friction disturbance, and two types of dictionary function libraries are designed to represent the position-dependent dynamics and nonlinear friction respectively. After constructing the regression form of the system model, a stepwise sparse regression policy is proposed to solve all the coefficients of dictionary functions. The proposed method is verified in both simulation and real environments. The results both show that by the proposed method, an accurate and linearizable dynamic model of ball-screw drives can be identified only using the data from only one global random excitation experiment covering the working stroke.

QLPV modeling and mixed-sensitivity control for a magnetic levitation system

ABSTRACT This paper proposes a comprehensive mixed-sensitivity control design for an experimental magnetic levitation (Maglev) system. The control strategy can be seen as an extension of the loop-shaping procedure for discrete-time linear parameter-varying (LPV) systems using linear-fractional representation (LFR). By making use of an efficient quadratic approach given in the form of linear matrix inequalities (LMIs), a functional and computationally attractive gain-scheduling technique is achieved. Despite the rigorous mathematical considerations to obtain the controller, the guidelines to its practical implementation are presented as a straightforward method using LMIs. A detailed modeling of the Maglev plant manufactured by Quanser is carried out to illustrate the procedure, including a description of the nonlinear equations embedding process to obtain a discretized quasi-LPV (qLPV) model. Experimental results demonstrate the effectiveness of the proposed control design.

Fault detection and isolation for linear parameter-varying systems with time-delays: a geometric approach

Fault detection and isolation for linear parameter-varying systems with time-delays: a geometric approach

Oblique Projection-Based Modal Matching Algorithm for LPV Model Order Reduction of Aeroservoelastic Systems

An aeroservoelastic system can be described as a gridding-based linear parameter-varying (LPV) model, whose dynamic characteristics usually vary with the airspeed. Due to the high order of the system, it is necessary to perform order reduction on LPV models to overcome the control design challenges. However, when directly extending linear time-invariant (LTI) model order reduction technologies to the LPV system, states of the reduced-order LTI models generated separately at different grid points could be inconsistent. In this paper, a novel modal matching algorithm is proposed to solve the problem of state inconsistency by identifying the internal connection between the models at adjacent grid points. An oblique projection-based distance metric is defined to improve the reliability of the modal matching algorithm. The reduced-order LPV model constructed based on this method would have a high fidelity relative to the original model and a smooth interpolation performance between grid points. The proposed algorithm is applied to the X-56A aircraft, and numerical results show its effectiveness.

Geometric approach to robust stability analysis of Linear Parameter-Varying systems: Computational trade-offs between the exact and the simplex convex hulls

Robust stability is investigated for continuous-time, affine, Linear Parameter-Varying (LPV) models, with bounded variation rates of uncertainty. Towards this end, affine Parameter Dependent Lyapunov Functions (PDLF) are considered to certificate stability in the Lyapunov sense. In the literature, the search for PDLFs amounts to a non conservative Linear Matrix Inequality (LMI) problem, at expense of a factorial growth in its complexity. Remedies to overcome this complexity have been proposed recently, exploiting geometrical aspects of the problem, however, they can be conservative. This paper presents new stability tests that are a trade-off between the exact and the fastest solutions. We offer an analytical procedure to indicate when the proposed tests are prone to reduce conservativeness. Also, a simple procedure is introduced to possibly improve existing and new tests, without impacts on the computation effort. Numerical simulations illustrate the improvements of the proposed strategies.

선형 파라미터 변형 시스템에 대한 이벤트-트리거 외란 관측기 기반 강인 제어

In this paper, an event-triggered disturbance observer-based robust control strategy is proposed for linear parameter-varying systems. In the proposed control strategy, the disturbance observer estimates the plant’s states and external disturbances, and the robust tracking controller uses the estimated values to compensate for the external disturbance. The scenario of the transmission of the estimated values from the disturbance observer through shared networks was considered. An event-triggered observer scheme was proposed to reduce communication resources while ensuring the stability of the closed-loop system. A stability analysis was performed by considering external disturbances. The simulation results demonstrated that the output follows the desired value, compensating for external disturbances.

Functional interval observer design for multivariable linear parameter-varying systems

This paper presents a new functional interval observer design methodology for discrete-time multivariable Linear Parameter-Varying (LPV) systems subject to bounded uncertainties. A functional interval observer is designed to estimate the bounds of the functional state using H∞/L∞ formalism to attenuate the effects of the uncertainties and to improve the accuracy of the estimation. The sufficient conditions of the observer design are developed in terms of Linear Matrix Inequalities (LMIs) constraints using the Lyapunov stability theory. Eventually, the effectiveness of the proposed methodology is illustrated by a numerical example.

Computation of parameter dependent robust invariant sets for LPV models with guaranteed performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As real-time measurements of the scheduling parameters are typically available, we allow the RCI set description and the invariance-inducing controller to be scheduling parameter dependent. Thus, the considered formulation leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequalities (LMIs) via Polya’s relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. Besides ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. Using numerical examples, we show that the presented iterative algorithm can generate RCI sets for large parameter variations where commonly used robust approaches fail.

Active input design for simultaneous fault estimation and fault-tolerant control of LPV systems

This paper considers the problem of integrating fault estimation (FE) and fault-tolerant control (FTC) for linear parameter varying (LPV) systems with inexact scheduling variables from a new perspective. Unlike the conventional passive FE approaches that maintain the performance of FE by only adjusting parametric matrices, the proposed method guarantees the precision and optimality of FE by actively designing optimal inputs at each time instant under the set-theoretic framework, which is named as active fault estimation (AFE). Meanwhile, by constructing a quadratic Lyapunov function, the stability of augmented estimation-error dynamics can be guaranteed based on H∞ setting by solving a group of matrix inequalities. In addition, the optimal inputs are also designed to implement the objective of integrated AFE and FTC for LPV systems, which leads to a balance between the goal of AFE and the reference output tracking performance. Although the original optimization problem computing the optimal inputs is not convex, it is proved that this problem can be equivalently transformed to a family of convex quadratic programming problems with linear constraints. At the end, a physical vehicle model is used to verify the effectiveness of our proposed integrated AFE and FTC method.

Optimal Control of TBCC Engines in Mode Transition

This paper mainly studies the optimal control problem of turbine-based combined cycle (TBCC) engines in the mode-transition stage. Based on the TBCC scheme proposed by Xiamen University, an aerothermodynamic model is established as a verification model for the validity of control laws. To reduce the complexity of control design, a control-oriented linear parameter-varying (LPV) model with Mach number as a scheduling variable is established under a given flight path. The design of mode-transition points and distribution of air-flow-rate among paths during the mode-transition process are transformed into linear quadratic (LQ) optimal control problems for an LPV system under the initial and terminal as well as process constraints. By optimizing the opening of the splitters of the inlet and the fuel flow in each channel, the optimal mode-transition points are found to achieve coordinated control and complete the high-precision thrust tracking during the mode-transition process.

An Integrated Design Approach for Fault-Tolerant Control of Switched LPV Systems With Actuator Faults

In this article, the active fault-tolerant control (FTC) issue is addressed for switched linear parameter varying (LPV) systems in the discrete-time domain. A general dwell-time property is considered in the system setup to govern the switching dynamics between subsystems, and the parameter variations within each subsystem are subjected to the polytopic uncertainties. The main innovation of the developed active FTC approach is to effectively cope with switched LPV models where both input and output matrices can be of parameter-dependent form. By virtue of a novel Lyapunov function approach depending on both dwell time and parameter variations, the joint task for fault detection, estimation, and compensation is fulfilled via an integrated design scheme. The input-to-state stability (ISS) conditions are obtained for the augmented faulty system satisfying a given ISS-gain performance requirement. The desired effect of active FTC is achieved in three critical steps: 1) construct a fault detection filter in terms of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> norm; 2) design an observer-based estimator to estimate the system states and faults simultaneously; and 3) synthesize a fault-tolerant controller with the LPV structure using the estimated states and faults for fault compensation. Finally, an application example is utilized to illustrate the efficiency and availability of the proposed control approach.

A novel geometry optimization strategy to online active fault diagnosis of LPV systems

This paper proposes a novel geometry optimization strategy for the online robust active fault diagnosis (AFD) of discrete-time linear parameter varying (LPV) systems under set-theoretic framework. By establishing a bank of zonotopic set-value observers to match healthy/faulty system modes, the key of the optimization strategy comes down to the design of the optimal system inputs and gain matrices simultaneously. The criterion on the design of optimal inputs is characterized by fully utilizing the geometry property of zonotopes, which formulates a non-convex fractional programming problem able to be solved under 0–1 mixed integer quadratic programming framework based on a series of transformations. While the optimal gain matrices can be obtained analytically based on a so-called zonotopic kalman filtering process. The proposed method can improve the sensitivity of AFD as much as possible while ensuring the stability of the designed observer. At the end, two physical models are used to verify the effectiveness of our proposed method.

Design of a mixed ℋ2/ℋ∞ gain scheduling state derivative feedback controller for linear parameter-varying systems

In this paper, the mixed guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed guaranteed cost minimisation.

Active Fault Diagnosis for LPV Systems: An Index-Based Approach

This article investigates the active fault diagnosis (AFD) problem for linear parameter-varying (LPV) systems. The system uncertainties, including system disturbances, noises, and initial conditions, are characterized by uncertain Gaussian zonotopes (UGZs). An index-based AFD scheme is proposed, which can avoid the requirement of complete separation of output sets of different system modes and reduce conservatism to a certain extent. A new index is proposed to characterize the similarity between two zonotopes. According to this index, the auxiliary input is designed by solving a quadratic programming problem. A novel fault diagnosis strategy is proposed to determine which mode the system is actually operating in. A numerical example is presented to demonstrate the effectiveness of the proposed approach.

On Robust Stabilization of Discrete-Time LPV/LFR Systems

This technical article presents novel robust stabilization conditions for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). The proposed conditions rely on the use of slack variables and decision matrices associated with the LFR approach to provide new controller designs. In addition, we address parameter-dependent Lyapunov functions and full-block multipliers to obtain less conservative synthesis conditions for discrete-time LPV/LFR systems. Design conditions are cast in the form of linear matrix inequalities to generate robust state-feedback and output-feedback controllers. Numerical examples demonstrate the effectiveness of the proposed method.

Design of switching state-feedback controllers for linear systems subject to asymmetric saturations*

This paper considers the problem of controlling a linear system affected by asymmetrical input saturation. The proposed solution is based on using a linear matrix inequality (LMI)-based methodology to find the gains of a switching state-feedback controller. The main difference and contribution when compared to existing approaches is that the switching rule is chosen based on the closed-loop performance that each of the non-saturating controller gains can achieve when used with the current value of the state vector. Although the main focus of the paper is on time-invariant systems, the possible extension to linear parameter-varying (LPV) systems is discussed. An illustrative example is used to show the main features of the proposed approach.

Dynamic-Memory Event-Based Asynchronous Attack Detection Filtering for a Class Of Nonlinear Cyber-Physical Systems.

In this article, we endeavor to address the problem of asynchronous attack detection for a class of nonlinear cyber-physical system (CPS) under the dynamic-memory event-triggered transmission protocol (DMETP). Malicious attacks under consideration are composed of the parameter-dependent false data-injection (FDI) attacks and the multichannel deception attacks with the time delay. Meanwhile, we attempt to employ the T-S fuzzy singular Semi-Markov jump linear parameter-varying (SS-MJLPV) systems to describe the stochastic jump characteristics and nonlinear time-varying characteristics of CPSs. Then, the DMETP is proposed for the first time, which can not only relieve the bandwidth pressure but also obtain the key released packets at the crest or trough of the curve. By augmenting the states of the original system and the asynchronous attacks detection filter, the issue of attacks detection is converted into an auxiliary dissipative filtering for the CPS. Moreover, sufficient conditions for the existence of the attacks detection filter are obtained. Finally, the effectiveness of the proposed scheme is verified via the networked truck-trailer reversing system.