Linear Parameter-varying Design Research Articles

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.

Quasi-LPV Modeling of Guided Projectile Pitch Dynamics through State Transformation Technique

In this paper, we develop a reliable Linear Parameter-Varying (LPV) model of the pitch channel dynamics of a fin-stabilized projectile. Among the available LPV design approaches, the State Transformation is analyzed, being particularly suitable for a class of systems defined as output nonlinear, and compatible with the projectile dynamics formulation. The State Transformation provides a quasi-LPV representation, which corresponds to an exact transformation of the original nonlinear model, preserving relevant couplings that are usually lost through the classical approximation methods. Some important considerations regarding the limitations of this approach are also discussed and verified in the missile dynamics. The accuracy of the obtained quasi-LPV model is assessed by means of open-loop simulations, comparing the performance to the original nonlinear model at selected flight conditions.

Discrete-time LPV Systems with Inexact Scheduling Parameters: an Unknown Input Observer Design approach

In this paper, a novel unknown input observer (UIO) design for discrete-time linear parameter-varying (LPV) with inexact scheduling parameters is addressed. The proposed approach is particularly relevant as most LPV design conditions require that the time-varying parameters of the system are completely known and real-time available. Therefore, such strategies do not present adequate formulations to deal with such types of uncertainty. Moreover, UIOs have significant applications in different areas, such as fault detection and isolation problems. Existence conditions for the UIO are provided in order to properly handle the mismatch along with the presence of unknown inputs in the LPV system. The design conditions are based on an input-to-state stability approach obtained from a parameter-dependent Lyapunov function and are cast in the form of Linear Matrix Inequalities. The effectiveness of the proposed methods is illustrated using a numerical example.

Thermally degraded speed estimation of traction machine drive in electric vehicle

The speed of an induction machine drive (IMD) in the electrified powertrain of an electric vehicle (EV) suffers from thermal degradation caused by EV loading, driving cycle schedules, EV operating conditions, traffic state and temperature. It is necessary to estimate this thermal degradation in order to design appropriate control methodologies to address this significant issue that directly affects the EV performance. This study proposes a robust linear parameter varying (LPV) observer to estimate this degradation in IMD as well as EV speed under various thermal and loading conditions in steady state and during large transients. The stability and robustness of LPV methodology is ensured by optimal gains of H ∞ control and linear matrix inequalities using convex optimisation techniques. The weighting functions in LPV design are optimised by genetic algorithms. The proposed observer performance is compared with that of conventional sensorless field-oriented control and sliding mode observer. An improved speed performance during EV operation is also presented to validate the robustness of the proposed LPV observer against New European Driving Cycle. The performance analysis is conducted through NI myRIO 1900 controller-based electrical drive set-up.

The VEGA launcher atmospheric control problem: A case for linear parameter‐varying synthesis

This article presents the design of an atmospheric control system for the VEGA launcher using Linear Parameter-Varying (LPV) synthesis techniques, both non-rate and rate-bounded. Following the Space industry traditional approach, the control problem is first formulated to design a rigid-body controller. Subsequently, it is shown how the launcher control problem can be systematically augmented to obtain the rigid-body controller and bending filters in one single procedure. The resulting LPV controller is analyzed in terms of classical linear stability margins and compared with the VEGA baseline controller via Monte-Carlo analyses using a high-fidelity, nonlinear simulator developed by industry. In addition, the LPV design is benchmarked using extended uncertainty ranges against two other advanced controllers: a structured H∞ and an adaptive augmented design. The results show that the LPV controller provides satisfactory stability margins and excellent performance and robustness characteristics, with the advantage of the design technique offering a systematic and methodological design framework.

LPVcore: MATLAB Toolbox for LPV Modelling, Identification and Control

This paper describes the LPVcore software package for MATLAB developed to model, simulate, estimate and control systems via linear parameter-varying (LPV) input-output (IO), state-space (SS) and linear fractional (LFR) representations. In the LPVcore toolbox, basis affine parameter-varying matrix functions are implemented to enable users to represent LPV systems in a global setting, i.e., for time-varying scheduling trajectories. This is a key difference compared to other software suites that use a grid or only LFR-based representations. The paper contains an overview of functions in the toolbox to simulate and identify IO, SS and LFR representations. Based on various prediction-error minimization methods, a comprehensive example is given on the identification of a DC motor with an unbalanced disc, demonstrating the capabilities of the toolbox. The software and examples are available on www.lpvcore.net.

Vehicle sideslip estimation via kernel-based LPV identification: Theory and experiments

Many vehicle control systems depend on the body sideslip angle, but robust and cost-effective direct measurement of this angle is yet to be achieved for production vehicles. Estimation from indirect measurements is thus the only viable option. In the paper, a sideslip estimator is obtained through the identification of a linear parameter varying (LPV) model. Although inspired by physical insights into the vehicle lateral dynamics, the structure of the LPV estimator is not parametrized beforehand. Instead, the estimator is learned by means of a state-of-the-art non-parametric method for linear parameter varying identification, namely least-squares support vector machines (LS-SVM). Its performance is assessed over an extensive and heterogeneous set of experimental data, showing the effectiveness of the proposed estimator.

Design and Experimental Assessment of an Active Fault-Tolerant LPV Vertical Dynamics Controller

This article addresses the design of an active fault-tolerant full-vehicle semi-active suspension controller by linear parameter-varying (LPV) control methods. The restrictive force constraints of the semi-active damper are modeled by saturation indicator parameters and treated as scheduling parameters in the LPV design. The synthesized LPV controller is subsequently augmented by a damper force reconfiguration exploring the weak input redundancy provided by four dampers in a full-vehicle application. In this way, the controller compensates for damper forces lost in the case of saturation or failure by the remaining dampers. The performance of the proposed LPV controller is validated by experiments on a four-post test-rig. The results show the improved tradeoff between ride comfort and road-holding of the full-vehicle LPV controller compared with a quarter-vehicle LPV controller and a Skyhook-Groundhook controller.

LPV Modeling and Identification of Unsteady Aerodynamics for Fast Maneuvering Aircrafts

Fast maneuvers at large angles of attack are necessary for modern fighter aircrafts. The aerodynamic coefficients in this situation are unsteady, with the characteristics of hysteresis and fast time-varying. We propose an identification method based on the linear parameter varying (LPV) model. The model takes into account the hysteresis with respect to the angle of attack, and fast time varying with respect to the motion of post-stall maneuvers. By introducing the angular velocity as an exogenous variable, the model can guarantee the tracking ability of fast time-varying variations. We use the instrumental variable least squares (IVLS) algorithm to deal with the estimation problem. Finally, the experimental data obtained from maneuvers at large angles of attack from wind tunnel tests are used to validate the applicability and effectiveness of the proposed method.

Robust model predictive control for stratospheric airships using LPV design

Wind and time delays are two major factors that affect the stability and control for an unmanned stratospheric airship. A Robust Model Predictive Control (RMPC) approach is proposed to track desired trajectory for linear parameter-varying (LPV) systems of the airship with state delay and wind disturbances. The RMPC design problem of the studied LPV systems can be interpreted as a semi-definite programming (SDP) via Lyapunov stability theory and linear matrix inequality (LMI) technique. The performance of the proposed controller is illustrated using three scenarios. The results of trajectory tracking control for a YEZ-2A stratospheric airship and a Zhiyuan small-scale low-altitude one show the RMPC design feasible and effective.

A Varying Frequency LPV-Based Control Strategy for Three-Phase Inverters

Grid-connected inverters have drawn a lot of attention in the integration of distributed generation systems and microgrids, as they are an effective interface for renewable and sustainable energy sources. Several strategies, including repetitive and resonant controllers, have been implemented in order to achieve low distortion and high-quality power. However, it has been proved that their performance decreases substantially when the grid frequency varies. This paper proposes a resonant control strategy based on a linear parameter varying (LPV) design, which is able to deal with changes in the network frequency. Controller aim is associated with injecting a clean sinusoidal current to the grid, even in the presence of nonlinear/unbalanced loads and/or grid-voltage distortions. Main emphasis is focused on presenting an applied LPV design procedure that covers plant modeling, controller synthesis, stability analysis, and experimental results that show the feasibility and effectiveness of the proposed scheme.

A Non-Parametric Linear Parameter Varying Approach for Identification of Linear Time-Varying Systems

This paper presents a novel, non-parametric, linear parameter varying (LPV) algorithm for identification of linear time-varying systems. The method estimates the timevarying impulse response function as a LPV Laguerre basis expansion whose coefficients are functions of a scheduling variable (SV). Unlike many parametric LPV identification techniques, the method requires no a priori knowledge of the system order. Monte Carlo simulations of a time-varying, second-order system mimicking variations of reex stiffness dynamics with ankle position demonstrated that the method performs very well. It will be a valuable tool for identification of physiological and engineering systems in conditions where the system order is unknown and its parameters change with a SV.

A Combined Global and Local Identification Approach for LPV Systems

This paper tackles the problem of identifying linear parameter-varying (LPV) systems by combining data originating from global and local identification experiments into a nonlinear leastsquares problem. One extreme of the approach results in a model optimal with respect to the system behavior under varying scheduling parameter conditions, while the other gives a model being a good approximation of system behavior for fixed scheduling parameter. When measurements from global and local experiments are available, a compromise between the two objectives is achieved. Numerical and experimental validations, accompanied by comparisons with existing LPV identification methods show the potential of the developed approach.

A local approach for the LPV identification of an actuated beam using piezoelectric actuators and sensors

This paper considers the identification of structural dynamics by identifying its frequency response functions (FRFs) – a mathematical representation of the relationship between the vibration response at one location and excitation at the same or another location. The spatially-varying characteristics of the FRFs at various input and output locations are explored, and lead to a spatial linear parameter varying (LPV) representation. A local LPV identification technique for lumped systems is adapted here to spatially-interconnected systems. The identification of a spatial LPV model facilitates the experimental work, and also simplifies the controller synthesis. The proposed approach is applied to identify an actuated beam equipped with an array of collocated piezoelectric actuators and sensors for performance illustration.

LPVIOID- A LPV IDENTIFICATION TOOLBOX FOR MATLAB: RECENT AND NOVEL TECHNIQUES

In this paper a system identification toolbox for MATLAB is introduced, including a user friendly graphical user interface. The toolbox is appropriate for the identification of systems in discrete-time linear parameter varying (LPV) form. Using LPVIOID1 it is possible to identify input-output models in open-loop and closed-loop settings based on experimental data. It comprises several recent LPV identification techniques. Furthermore, a novel method for identifying unstable plants in closed-loop is proposed. The toolbox is equipped with several tools for model validation. Examples for illustration are included.

LPV identification of the glucose-insulin dynamics in Type I diabetes

In this paper we address the problem of identifying a linear parameter varying (LPV) model of the glucose-insulin dynamics in Type I diabetic patients. First, the identification problem is formulated in the framework of bounded-error identification, then an algorithm for parameter bounds computation, based on semidefinite programming, is presented. The effectiveness of the proposed approach is tested in simulation by means of the widely adopted nonlinear Sorensen patient model.

Nonparametric Identification of LPV Models Under General Noise Conditions: An LS-SVM Based Approach

Parametric identification approaches in the Linear Parameter-Varying (LPV) setting require optimal prior selection of a set of functional dependencies, used in the parametrization of the model coefficients, to provide accurate model estimates of the underlying system. Consequently, data-driven estimation of these functional dependencies has a paramount importance, especially when very limited a priori knowledge is available. Existing overparametrization and nonparametric methods dedicated to nonlinear estimation offer interesting starting points for this problem, but need reformulation to be applied in the LPV setting. Moreover, most of these approaches are developed under quite restrictive auto-regressive noise assumptions. In this paper, a nonparametric Least-Squares Support Vector Machine (LS-SVM) approach is extended for the identification of LPV polynomial models. The efficiency of the approach in the considered noise setting is shown, but the drawback of the auto-regressive noise assumption is also demonstrated by a challenging LPV identification example. To preserve the attractive properties of the approach, but to overcome the drawbacks in the estimation of polynomial LPV models in a general noise setting, a recently developed Instrumental Variable (IV)-based extension of the LS-SVM method is applied. The performance of the introduced IV and the original LS-SVM approaches are compared in an identification study of an LPV system with unknown noise dynamics.

MIMO LPV State‐Space Identification of Open‐Flow Irrigation Canal Systems

Canal systems are complex nonlinear, distributed parameter systems with changing parameters according to the operating point. In this paper, a linear parameter‐varying (LPV) state‐space canal control model is obtained by identification in a local way using a multimodel approach. This LPV identification procedure is based on subspace methods for different operating points of an irrigation canal covering the full operation range. Different subspace algorithms have been used and compared. The model that best represents the canal behavior in a precise manner has been chosen, and it has been validated by error functions and analysis correlation of residuals in a laboratory multireach pilot canal providing satisfactory results.

Prediction error method for identification of LPV models

This paper is concerned with identification of linear parameter varying (LPV) systems in an input–output setting with Box–Jenkins (BJ) model structure. Classical linear time invariant prediction error method (PEM) is extended to the LPV PEM. Under the new LPV framework, identification of two types of input–output LPV models is considered: one is based on parameter interpolation and the other is based on model interpolation. The effectiveness of the proposed solution is validated by comparison with other existing LPV identification approaches through simulation examples and demonstrated by experiment studies.

Modelling and H∞ control of diesel engine boost pressure using a linear parameter varying technique

In this paper, a model-based boost pressure control of a turbocharged common-rail directed injected diesel engine is proposed. An advanced linear parameter varying (LPV) technique is adopted for model development and an H∞ control scheme is synthesized for control purposes. The LPV technique has an advantage in deriving a linear model from a complex non-linear system and guarantees higher linear model precision. The boost pressure model of the diesel engine is obtained as a simple second-order linear system and the parameters of the model are estimated by the LPV identification method. With the help of the LPV modelling method, the behaviour of boost pressure of the diesel engine is precisely characterized using a second-order linear model. Based on the simplified LPV boost pressure model, a robust H∞ controller is synthesized. The state-space representation is derived to follow the control design framework of an H∞ scheme, and weighting functions for improving control performance are added into the closed-loop control system. The experimental results show that the LPV model-based diesel engine boost pressure control allows better tracking performance than the production engine management system (EMS), which requires difficult calibration work.