Estimation of Linear Parameter-Varying affine state space models using synchronized periodic input and scheduling signals

This paper presents a nonparametric identification method for state-space linear parameter-varying (LPV) models using a modified support vector machine (SVM) approach. While most LPV identification schemes in the state-space form fall under the general category of parametric methods, regularization-based SVMs provide a viable alternative to model scheduling dependencies, without the need of specifying the dependency structure and with an attractive bias-variance trade-off. In this paper, a solution is proposed for nonparametric identification of LPV state-space models in terms of least-squares SVMs (LS-SVM) and is then extended in a way that the proposed estimation is robust to errors in the noise model estimation. The so-called instrumental variables (IV) method has been used in linear system identification for quite some time, and has recently seen its application in the identification of both nonlinear and LPV systems in the input-output (IO) form. The IV method reduces the bias in estimated LPV state-space models in case the noise model is not estimated properly or is unknown. In the proposed method of this paper, the attractive bias-variance trade-off properties of LS-SVMs are combined with statistical properties of IV-based methods to give robust estimates of the functional dependencies. Numerical examples are provided to compare the performances of the proposed IV-based technique with the LS-SVM-based LPV model identification methods.

International audience

It is challenging to design a controller for a wind turbine system because of its nonlinear time-varying dynamics. To solve this issue, linear parameter-varying (LPV) control theory has been applied in the recent ten years to deal with nonlinear and wind-speed-dependent dynamics. Before applying the LPV control method, it is required to transform the nonlinear model of the system to an LPV model. The main objectives of this research are to model a 5-MW Reference Wind Turbine for Offshore System as an LPV system, develop a nonlinear wind turbine simulator using MATLAB/Simulink to validate the LPV model, and conduct a preliminary study on LPV control design to test the simulator, which will be used in the future research for applying different LPV control techniques, such as switching LPV control, LPV antiwindup control, etc.

Input Estimation from Sparse Measurements in LPV Systems and Isotopic Ratios in Polar Firns

In this paper, a new control approach is proposed for the transient stabilization of a single-machine infinite-bus power system. The proposed method is based on an LPV (linear parameter varying) modelling of the nonlinear power system and gain-scheduled output feedback control. It is well-known that when large disturbances or a fault occurs, the nonlinearity inherent in power systems can no longer be ignored. The proposed method can handle the nonlinear model directly. First, we show that the nonlinear model can be transformed equivalently into an LPV system with the rotor angle as the scheduling parameter. Then, a gain-scheduled output feedback controller is designed based on robust pole placement and L2-gain minimization. Simulation results verify that the proposed method is better than well-tuned conventional PSS control.

System or process identification is a mathematical modeling of systems (processes) from test or experimental data. Process models obtained from identification process can be used for operator training simulator, analysis and design of safety systems, and design of process and control systems. This paper presents the Linear Parameter Varying (LPV) model identification for Industrial boiler furnace. LPV model is the development of linear time invariant models of different operating conditions along the overall operating trajectory and interpolation of linear models. The LPV model is adopted by considering the fact that boiler furnace in the thermal power plant has several operating conditions. By assuming that on every operating condition there are parameters changes, the LPV model is suitable for covering all operating conditions. The boiler furnace is modeled as LPV systems with Linear transfer function model structure. Identification algorithm used in the identification process is Prediction error method. Data needed for identification is taken from first principle model of the process with sampling time of 1 second. The identification result is simulated and validated with the measured data. The simulation result shows better accuracy for Linear Parameter Varying model.

A linear parameter-varying (LPV) model of the Benchmark Active Controls Technology (BACT) windtunnel model is developed to facilitate the synthesis and analysis of flutter suppression controllers. The BACT wind-tunnel model is a part of NASA Langley Research Center's Benchmark Models Program initiated to study aeroelastic phenomena and flutter suppression. The LPV model developed in this paper is a function of both Mach number and dynamic pressure and accurately represents the BACT wind-tunnel model over a large flight envelope. This LPV model makes it possible to rigorously investigate the robustness properties of flutter suppression controllers developed for the BACT wing. Furthermore, it enables the use of recent results in LPV control theory to develop robust, automatically gain-scheduled flutter suppression controllers.

A model order reduction method is proposed for models of aeroservoelastic vehicles in the linear parameter-varying (LPV) systems framework, based on state space interpolation of modal forms. The dynamic order of such models is usually too large for control synthesis and implementation since they combine rigid body dynamics, structural dynamics and unsteady aerodynamics. Thus, model order reduction is necessary. For linear timeinvariant (LTI) models, order reduction is often based on balanced realizations. For LPV models, this requires the solution of a large set of linear matrix inequalities (LMIs), leading to numerical issues and high computational cost. The proposed approach is to use well developed and numerically stable LTI techniques for reducing the LPV model locally and then to transform the resulting collection of systems into a consistent modal representation suitable for interpolation. The method is demonstrated on an LPV model of the body freedom flutter vehicle, reducing the number of states from 148 to 15. The accuracy of the reduced order model (ROM) is confirmed by evaluating the ν-gap metric with respect to the full order model and by comparison to another ROM obtained by state-of-the-art LPV balanced truncation techniques.

In this paper, we consider the fault Detection and isolation (FDI) problem for faulty linear parameter-varying (LPV) systems subject to disturbances and propose a observer-based solution by using multiobjective optimization techniques. To simply the design process, a general faulty LPV system will be constructed from standard LPV description by converting actuator/system component faults into sensor faults at first. Then a bank of LPV FDI filters will be designed to identify each fault. Each FDI filter could generate a residual signal to track individual fault with minimum error and suppressing the effects of disturbances and other fault signals. The design of FDI filters will be formulated as multiobjective optimization problems in terms of linear matrix inequalities (LMIs) and can be solved efficiently. Two numerical examples are also presented to demonstrate the proposed fault detection and isolation approach on both LPV and LTI systems.

Shape Memory Alloys (SMAs) actuators operate via a nonlinear and hysteretic relationship between input power and mechanical motion. This nonlinearity presents a serious challenge when developing methods for controlling these actuators. Because this hysteresis and nonlinearity is caused by the crystal phase transformation however, the SMA constitutive and kinetic models can be written in Linear Parameter Varying (LPV) form, with the partial derivative of crystal phase fraction with respect to temperature as the varying parameter. This allows a SMA system to be written in a state-space format where the coefficients in the state matrices vary as a function of the state variables, allowing for the application of powerful linear system analysis tools to this model without simplifying assumptions. This LPV model can then be used to create an estimator for the system, allowing for real-time approximations of the system states, including temperature and phase fraction. This paper presents the derivation of one such LPV model and explores its ability to accurately represent a physical SMA actuator system by comparison with an instrumented SMA muscle system.

Linear parameter-varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different representations it appears that the time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics. In order to construct a parametrization-free description of LPV systems that overcomes these difficulties, a behavioral approach is introduced that serves as a basis for specifying system theoretic properties. LPV systems are defined as the collection of trajectories of system variables (like inputs and outputs) and scheduling variables. LPV kernel, input-output, and state-space system representations are introduced with appropriate equivalence transformations.

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

This paper investigates the guaranteed cost control problem for a class of linear parameter-varying (LPV) systems with Markovian switching under partly known transition rates. A key point of this work relaxes Markovian jump systems whose subsystems are described by linear time-invariant (LTI) dynamics to LPV systems with Markovian switching whose subsystems are described by LPV dynamics. Meanwhile, the special assumption of completely known transition rates is relaxed to more general case that transition rates are partly known. Moreover, the proposed control technique for the LPV systems with Markovian switching is used to solve the guaranteed cost control problem of turbofan-engine. Firstly, a guaranteed cost controller is designed, and the design problem can be reduced to a set of linear matrix inequalities (LMIs) feasibility problem. Then, a turbofan-engine example is given to demonstrate the applicability of the main results.

High performance positioning devices exhibit position dependent dynamics in the form of varying flexible modes, which are expected to dominate the dynamic behavior in the new generation of lightweight positioning structures. To handle such position-dependent behavior, the framework of Linear Parameter-Varying (LPV) systems offers powerful tools in terms of control synthesis with many successful practical applications. However, to achieve the desired performance, a low complexity but accurate LPV model of the underlying plant is of crucial importance. Obtaining LPV models for positioning devices based on first principle laws is a rigorous and costly process often resulting in models with inadequate accuracy. Therefore a data driven-modeling approach using Orthonormal Basis Functions (OBF's) is studied for the control oriented modeling of xy-positioning table dynamics. Through a simulation study it is demonstrated that the proposed modeling procedure, using only measurement data, can provide models whose accuracy is very close to the analytic models derived with the full knowledge of the system.

A linear parameter varying (LPV) flight dynamics model (FDM) is proposed to cater for atmospheric disturbance analysis in special flight conditions. A novel FDM which is capable of addressing the influence of turbulent wind is derived under the wind frame. An affine parameter dependent LPV model with wind effects is built based on function substitution method. The optimal solution for the decomposing function of the LPV FDM is obtained by genetic algorithm (GA). The analysis of dynamic response indicates that the genetic-optimized LPV FDM approximates the nonlinear FDM evidently, since it identifies the instantaneous dynamics and flight states varying in a wide range. The simulations of approach and landing against wind shear show that the genetic-optimized LPV FDM captures the instantaneous dynamic response when flying through turbulent wind, indicating that the LPV model can be further applied to turbulent wind special flight analysis and control law design.