Continuous-time Linear Parameter-Varying Research Articles

[formula omitted] gain-scheduled dynamic output feedback control with transient performance applied to electrical microgrid

This paper introduces an approach for designing gain-scheduled dynamic output feedback controllers for continuous-time Linear Parameter-Varying (LPV) systems. The aim is to improve transient response by incorporating both D-stability and H∞ criteria into the synthesis conditions. We achieve this by employing changes of variables and congruence transformations, which lead to new synthesis conditions expressed as linear matrix inequalities. Additional fine-tuned scalar parameters can be used to enhance further the controller performance in terms of less conservative H∞ guaranteed costs. To assess the effectiveness of our proposed synthesis procedure, we conduct computational experiments in the context of a microinverter-based distributed power generation system. These experiments take into account real-world operational characteristics, providing a comprehensive evaluation of our approach. The results demonstrate that the designed controller effectively ensures the desired closed-loop system behavior, even when dealing with state noise and discretization errors originating from digital implementation.

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.

Bounding the Trajectories of Continuous-Time LPV Systems with Parameters known in Real Time

Predicting the exact future of a Linear Parameter-Varying (LPV) system with its parameter exclusively known in real time is by definition an impossible task. In particular, it is difficult to quantify the error induced by a Zero-Order Hold (ZOH) discretization of the parameter which is not verified in practice (e.g. when the parameter depends on the states, inputs or outputs of the continuous-time system). Under a Lipschitz assumption, this paper upper bounds — in terms of uncertain matrices — the greatest possible discrepancy between the real future of the system and its estimate based on the last known values of the input and parameter. This not only upper bounds the error due to the ZOH discretization, but also provides sufficient conditions for controllability and observability of the system in the near future by bounding its Gramians.

An integral architecture for identification of continuous-time state-space LPV models

Abstract This paper presents an integral architecture for direct identification of continuous-time linear parameter-varying (LPV) state-space models. The main building block of the proposed architecture consist of an LPV model followed by an integral block, which is used to approximate the continuous-time state map of an LPV representation. 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 models, the unknown parameters within each coordinate descent step can be computed analytically via ordinary least squares. The effectiveness of the proposed methodology is assessed via a numerical example.

On Gain-Scheduled State-Feedback Controller Synthesis With Quadratic Stability Condition

This letter shows that, as long as continuous-time linear parameter-varying (LPV) systems are concerned, quadratic-stability-based gain-scheduled state-feedback controller synthesis offers no advantage over quadratic-stability-based fixed (parameter-independent) state-feedback controller synthesis in typical control performance specifications. We derive this counterintuitive result by properly extending the previous results on the robust versions of Finsler's lemma and the elimination lemma. We also show that this counterintuitive result is continuous-time LPV system specific, and in the discrete-time LPV system case quadratic-stability-based gain-scheduled state-feedback controller synthesis does bring improvement. These results give a proper warning about the effectiveness of the quadratic-stability-based gain-scheduled state-feedback controller synthesis.

Interval estimation for continuous-time LPV switched systems

This paper deals with interval state estimation for continuous-time linear parameter varying (LPV) switched systems with measured polytopic parameter dependence, assuming a known switching signal. Considering that the measurement noise and the state disturbance are unknown but bounded and that the dynamics of the system are described by a convex combination, lower and upper bounds of the state are therefore determined. An interval observer is designed in order to guarantee both stability and cooperativity of the upper and lower observation errors. For the proposed observer, sufficient input-to-state stability conditions are given in terms of linear matrix inequalities, adopting firstly common quadratic Lyapunov functions, under arbitrary switching signals and secondly multiple quadratic Lyapunov functions, under average dwell time (ADT) switching signals. The efficiency of the proposed interval observer is highlighted through simulation results on academic examples.

State-feedback control for continuous-time LPV systems with polynomial vector fields

This paper is concerned with the design of state-feedback controllers for Linear Parameter Varying (LPV) polynomial continuous-time systems. The vector field presents polynomial dependence on the states. Two synthesis conditions are proposed, the first one considers arbitrary rates of variation in the time-varying parameters, while the second one provides LPV controllers that are constructed based on a smoothed approximation of the time-varying parameter. The sum of squares matrix decomposition is employed to solve the proposed conditions. The L2 gain is also considered to give a robustness measure of the proposed controllers. The results are illustrated with examples from the literature.

Application of ICC LPV control to a blended-wing-body airplane with guaranteed [formula omitted] performance

This paper addresses the Input Covariance Constraint (ICC) control problem with guaranteed H∞ performance for continuous-time Linear Parameter-Varying (LPV) systems. The upper bound of the output covariance is minimized subject to the constraints on input covariance and H∞ output performance. This problem is an extension of the mixed H2/H∞ LPV control problem, in that the resulting gain-scheduling controllers guarantee not only closed-loop system robustness in terms of H∞ norm bound but also output covariance performance over the entire scheduling parameter space. It can be shown that this problem can be efficiently solved by utilizing the convex optimization of Parameterized Linear Matrix Inequalities (PLMIs). The main contributions of this paper are to characterize the mixed ICC/H∞ LPV control problem using PLMIs and to develop the optimal state-feedback gain-scheduling controllers, while satisfying both input covariance and H∞ constraints. The effectiveness of the proposed control scheme is demonstrated through vibration suppression of a blended-wing-body airplane model.

State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers

ABSTRACTThis paper proposes a linear parameter varying (LPV) interval observer for state estimation and unknown inputs decoupling in uncertain continuous-time LPV systems. Two different problems are considered and solved: (1) the evaluation of the set of admissible values for the state at each instant of time; and (2) the unknown input observation, i.e. the design of the observer in such a way that some information about the nature of the unknown inputs affecting the system can be obtained. In both cases, analysis and design conditions, which rely on solving linear matrix inequalities (LMIs), are provided. The effectiveness and appeal of the proposed method is demonstrated using an illustrative application to a two-joint planar robotic manipulator.

Data-driven predictive control for continuous-time linear parameter varying systems with application to wind turbine

A new data-driven predictive control method based on subspace identification for continuous-time linear parameter varying (LPV) systems is presented in this paper. It is developed by reformulating the continuous-time LPV system which utilizes Laguerre filters to obtain the subspace prediction of output. The subspace predictors are derived by QR decomposition of input-output and Laguerre matrices obtained by input-output data. The predictors are then applied to design the model predictive controller. It is shown that the integrated action is incorporated in the control effect to eliminate the steady-state offset. We control the continuous-time LPV systems to obtain the attractive performance with the proposed data-driven predictive control method. The proposed controller is applied to a wind turbine to verify its effectiveness and feasibility.

Discretization and event triggered digital output feedback control of LPV systems

This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.

Sampled‐data MPC for LPV systems with input saturation

In this work, a sampled-data model predictive control (MPC) design method is proposed for continuous-time linear parameter varying (LPV) systems. The input saturation and parameter uncertainties are both considered. Using a method to deal with actuator saturation, the MPC controller is permitted to saturate. Using the measurable parameter vector, a scheduled state-feedback MPC controller is computed at each time instant which fully exploits the real-time information on the variations of the plant characteristics. By modelling the closed-loop systems of the continuous-time LPV systems with a piecewise constant sampled-data control input as linear impulsive systems, the stability properties of the proposed MPC are studied. The sampling interval in this work is not required to be periodic. The proposed MPC design method is expected to further reduce the conservativeness. The improvements of the proposed sampled-data MPC method w.r.t. other existing MPC techniques are demonstrated by an example.

Sampled-data filtering for linear parameter varying systems

In this paper, we address the sampled-data filter design problem for continuous-time linear parameter-varying (LPV) systems. The filtering error system obtained from augmenting a continuous-time LPV system and the sampled-data filter is a hybrid system. The sampled-data filter design objective is to ensure the error system stability and a prescribed level of the induced energy-to-energy gain (or norm) from the disturbance input to the estimation error. To this purpose, we employ a lifting method to derive an equivalent discrete-time LPV representation for the continuous-time LPV system. In the present study, the sampled-data filter synthesis conditions are formulated in terms of linear matrix inequality optimisation problems. The viability of the proposed design method to cope with variable sampling rates is illustrated through numerical examples, where reliable estimation of the LPV system outputs is achieved.

Gain-scheduled output-feedback controllers using inexact scheduling parameters for continuous-time LPV systems

This paper addresses the design problem of Gain-Scheduled Output-Feedback (GSOF) controllers for continuous-time Linear Parameter-Varying (LPV) systems. In contrast to the conventional problem setting, scheduling parameters are supposed to be provided with bounded absolute/proportional uncertainties. H∞-type problem is tackled and a sufficient condition for our problem is given in terms of Parameter-Dependent Linear Matrix Inequalities (PDLMIs) with a single line search parameter. It is also proved that, our method is no more conservative than an existing method in proportional uncertainty case.

On Interval Observer Design for a Class of Continuous-Time LPV Systems

This work is devoted to interval observer design for Linear Parameter-Varying (LPV) systems under assumption that the vector of scheduling parameters is not available for measurements. Stability conditions are expressed in terms of matrix inequalities, which can be solved using standard numerical solvers. Robustness and estimation accuracy with respect to model uncertainty is analyzed using L ∞ /L 1 framework. Two solutions are proposed for nonnegative systems and for a generic case. The efficiency of the proposed approach is demonstrated through computer simulations.

Gain-scheduled output-feedback controllers depending solely on scheduling parameters via parameter-dependent Lyapunov functions

In this paper, we propose a new design method for Gain-Scheduled Output Feedback (GSOF) controllers for continuous-time Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). The GSOF controllers depend solely on scheduling parameters. Although our method requires a line search to obtain suboptimal controllers, it produces practical GSOF controllers, being independent of the derivatives of scheduling parameters. Our method is proved to be no more conservative than conventional design methods via constant Lyapunov functions as well as particularly structured PDLFs.

Gain-Scheduled H∞ Controllers being Derivative-Free of Scheduling Parameters via Parameter-Dependent Lyapunov Functions

AbstractWhen Gain-Scheduled (GS) H∞ output-feedback controllers are designed for continuous-time Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs) using existing design methods, the designed controllers depend not only on the scheduling parameters but also on their derivatives. However, estimating parameters in real-time is a difficult task, obtaining their derivatives is even harder, if not impossible in the real world. In this paper, we propose a new design method for GS H∞ output-feedback controllers, which depend solely on the scheduling parameters, via PDLFs. It is also shown that our method is no more conservative than the conventional design methods via constant Lyapunov functions or via some particularly structured PDLFs. A numerical example which demonstrates the effectiveness of our method is included.