Linear Parameter-varying Design Research Articles

Direct identification of continuous-time linear parameter-varying input/output models

Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuous time (CT) requiring accurate and low-order CT models of the system. However, identification of CT-LPV models is largely unsolved, representing a gap between the available LPV identification methods and the needs of control synthesis. In order to bridge this gap, direct identification of CT-LPV systems in an input–output setting is investigated, focusing on the case when the noise part of the data generating system is an additive discrete-time (DT) coloured noise process. To provide consistent model parameter estimates in this setting, a refined instrumental variable (IV) approach is proposed and its properties are analysed based on the prediction-error framework. The benefits of the introduced direct CT-IV approach over identification in the DT case are demonstrated through a representative simulation example inspired by the Rao–Garnier benchmark.

Leakage detection and location in gas pipelines through an LPV identification approach

A new approach to gas leakage detection in high pressure distribution networks is proposed, where two leakage detectors are modelled as a linear parameter varying (LPV) system whose scheduling signals are, respectively, intake and offtake pressures. Running the two detectors simultaneously allows for leakage location. First, the pipeline is identified from operational data, supplied by REN-Gasodutos and using an LPV systems identification algorithm proposed in [1]. Each leakage detector uses two Kalman filters where the fault is viewed as an augmented state. The first filter estimates the flow using a calculated scheduling signal, assuming that there is no leakage. Therefore it works as a reference. The second one uses a measured scheduling signal and the augmented state is compared with the reference value. Whenever there is a significant difference, a leakage is detected. The effectiveness of this method is illustrated with an example where a mixture of real and simulated data is used.

A local approach to LPV-identification of a Twin Rotor MIMO System

AbstractA local approach to LPV (Linear Parameter Varying) identification of a Twin Rotor MIMO System (TRMS) is considered via grey-box modeling. A white-box model of the TRMS is derived from the first principles, and black-box models at local operating points are given by a closed loop subspace identification method. Local black-box models that have consistent states are obtained by means of a frequency domain subspace method with the knowledge of the white-box model, and an LPV model is computed by interpolating the consistent local state-space models.

An LPV Modeling and Identification Approach to Leakage Detection in High Pressure Natural Gas Transportation Networks

In this paper a new approach to gas leakage detection in high pressure natural gas transportation networks is proposed. The pipeline is modelled as a Linear Parameter Varying (LPV) System driven by the source node massflow with the gas inventory variation in the pipe (linepack variation, proportional to the pressure variation) as the scheduling parameter. The massflow at the offtake node is taken as the system output. The system is identified by the Successive Approximations LPV System Subspace Identification Algorithm which is also described in this paper. The leakage is detected using a Kalman filter where the fault is treated as an augmented state. Given that the gas linepack can be estimated from the massflow balance equation, a differential method is proposed to improve the leakage detector effectiveness. A small section of a gas pipeline crossing Portugal in the direction South to North is used as a case study. LPV models are identified from normal operational data and their accuracy is analyzed. The proposed LPV Kalman filter based methods are compared with a standard mass balance method in a simulated 10% leakage detection scenario. The Differential Kalman Filter method proved to be highly efficient.

LPV design of adaptive integrated control for road vehicles

AbstractThe paper presents a multi-layer supervisory architecture for the design of adaptive integrated control systems in road vehicles. The performance specifications are guaranteed by the local LPV (Linear Parameter Varying) controllers, while the coordination of these components is provided by the supervisor. Monitoring components provide the supervisor with information needed to make decisions about the necessary interventions into the vehicle motion and guarantee the robust operation of the vehicle. In the proposed architecture the supervisor and the components communicate through a well-defined interface. This interface uses the monitoring signals as additional scheduling variables of the individual LPV controllers introduced to distinguish the performances that correspond to different operational modes. The advantage of this architecture is that local LPV controllers are designed independently provided that the monitoring signals are taken into consideration in the formalization of their performance specifications.

Robust identification/invalidation in an LPV framework

AbstractA robust linear parameter varying (LPV) identification/invalidation method is presented. Starting from a given initial model, the proposed method modifies it and produces an LPV model consistent with the assumed uncertainty/noise bounds and the experimental information. This procedure may complement existing nominal LPV identification algorithms, by adding the uncertainty and noise bounds which produces a set of models consistent with the experimental evidence. Unlike standard invalidation results, the proposed method allows the computation of the necessary changes to the initial model in order to place it within the consistency set. Similar to previous LPV identification procedures, the initial parameter dependency is fixed in advance, but here a methodology to modify this dependency is presented. In addition, all calculations are made on state‐space matrices which simplifies further controller design computations. The application of the proposed method to the identification of nonlinear systems is also discussed. Copyright © 2009 John Wiley & Sons, Ltd.

An LPV identification Framework Based on Orthonormal Basis Functions

Describing nonlinear dynamic systems by Linear Parameter-Varying (LPV) models has become an attractive tool for control of complicated systems with regime-dependent (linear) behavior. For the identification of LPV models from experimental data a number of methods has been presented in the literature but a full picture of the underlying identification problem is still missing. In this contribution a solid system theoretic basis for the description of model structures for LPV systems is presented, together with a general approach to the LPV identification problem. Use is made of a series-expansion approach, employing orthogonal basis functions.

Optimal experimental design for LPV identification using a local approach

A common approach for dealing with non-linear systems is to describe the system by a model with parameters that vary as a function of the operating point. Consequently, the non-linear system is seen as a combination of local Linear Time-Invariant (LTI) systems, one for each value of the operating point. Such representations are called Linear Parameter-Varying (LPV) models. Due to the importance of this representation for the control of nonlinear systems, numerous algorithms have recently been developed to identify LPV models. However, the optimal design of such identification experiments remains completely unexplored. In this paper, we consider the so-called local approach for the LPV identification. In the local approach, the local linear models, corresponding to a series of fixed operating points, are identified by performing one identification experiment at each of these operating points. The LPV nature of the system is then retrieved by interpolating the value of the parameters at other operating points for example with a polynomial function which is fitted through the parameters identified at the operating points considered. We present an approach to choose optimally the value of the operating-points at which the local identification experiments will be performed. By optimal, we mean that the value of the operating points are optimized in such a way that the LPV model obtained after interpolation has a maximum accuracy.

Closed‐loop identification of the time‐varying dynamics of variable‐speed wind turbines

AbstractThe trend with offshore wind turbines is to increase the rotor diameter as much as possible to decrease the costs per kWh. The increasing dimensions have led to the relative increase in the loads on the wind turbine structure. Because of the increasing rotor size and the spatial load variations along the blade, it is necessary to react to turbulence in a more detailed way: each blade separately and at several separate radial distances. This combined with the strong nonlinear behavior of wind turbines motivates the need for accurate linear parameter‐varying (LPV) models for which advanced control synthesis techniques exist within the robust control framework. In this paper we present a closed‐loop LPV identification algorithm that uses dedicated scheduling sequences to identify the rotational dynamics of a wind turbine. We assume that the system undergoes the same time variation several times, which makes it possible to use time‐invariant identification methods as the input and the output data are chosen from the same point in the variation of the system. We use time‐invariant techniques to identify a number of extended observability matrices and state sequences that are inherent to subspace identification identified in a different state basis. We show that by formulating an intersection problem all states can be reconstructed in a general state basis from which the system matrices can be estimated. The novel algorithm is applied on a wind turbine model operating in closed loop. Copyright © 2008 John Wiley & Sons, Ltd.

Modeling Waste Heat Recovery System of Industrial Ammonia Process Plant Using LPV Identification

This paper presents modeling of Waste Heat System of an industrial ammonia process plant. Linear Parameter Varying (LPV) identification is utilized to cover changes in process operating conditions, such as start-up, normal operation and shut-down. Recursive Least Square (RLS) based algorithm is employed in the LPV identification process. Experimental input-output signals required for identification process are taken from DCS historian data of the ammonia process plant during plant operations. The resulting LPV model is simulated and validated with respect to the measured data. Promising results are obtained in applying advanced LPV identification to cover variations of process operating conditions in an industrial process plant.

Transient lean burn air-fuel ratio linear parameter-varying control using input shaping

Transient air-fuel ratio control for lean burn engines is essential to achieve improved fuel economy and strict federal emission regulations. Unlike conventional Spark Ignition (SI) engines, lean burn engines are no longer operating in a narrow band around stoichiometric resulting in a very challenging air-fuel ratio tracking problem. An approach to combine an input shaping method together with Linear Parameter Varying (LPV) feedback control is proposed in this paper to solve the transient air-fuel ratio tracking problem. LPV air-fuel ratio control has been shown to regulate the air-fuel ratio at steady state engine operating conditions, reduce the variability of the closed-loop system, reject disturbance and guarantee robustness and stability in the presence of variable time delays. In this paper, an input shaping method is used to reduce the cost of feedback, and thereby enhance the air-fuel ratio tracking performance during engine transient operations. The prefilter is designed based on the closed-loop dynamics resulting from the LPV design. A systematic input shaping prefilter design process is developed. The designed prefilter successfully extends the closed-loop air-fuel ratio tracking bandwidth. Simulation results using Federal Test Procedure (FTP) drive cycle data are used to demonstrate the effectiveness of the input shaping prefilter. Moreover, the designed prefilter is structurally simple and computationally efficient.

LPV identification of a turbocharged diesel engine

This work proposes a methodology of identifying linear parameter varying (LPV) models for nonlinear systems. First, linear local models in some operating points, by applying standard identifications procedures for linear systems in time domain, are obtained. Next, a LPV model with linear fractional dependence (LFR) with respect to measured variables is fitted with the condition of containing all the linear models identified in previous step (differential inclusion). The fit is carried out using nonlinear least squares algorithms. Finally, this identification methodology will then be applied to a nonlinear turbocharged diesel engine.

Kernel methods for subspace identification of multivariable LPV and bilinear systems

Subspace identification methods for multivariable linear parameter-varying (LPV) and bilinear state-space systems perform computations with data matrices of which the number of rows grows exponentially with the order of the system. Even for relatively low-order systems with only a few inputs and outputs, the amount of memory required to store these data matrices exceeds the limits of what is currently available on the average desktop computer. This severely limits the applicability of the methods. In this paper, we present kernel methods for subspace identification performing computations with kernel matrices that have much smaller dimensions than the data matrices used in the original LPV and bilinear subspace identification methods. We also describe the integration of regularization in these kernel methods and show the relation with least-squares support vector machines. Regularization is an important tool to balance the bias and variance errors. We compare different regularization strategies in a simulation study.

Adaptive Linear Parameter Varying Control Synthesis for Actuator Failure

A robust linear parameter varying (LPV) control synthesis is carried out for a Highly Maneuverable Aircraft Technology (HiMAT) vehicle subject to loss of control effectiveness. The scheduling parameter is selected to be a function of the estimates of the control effectiveness factors. The estimates are provided online by a two-stage adaptive Kalman filter estimator. The inherent conservatism of the LPV design is reduced through the use of a scaling factor on the uncertainty block that represents the estimation errors of the effectiveness factors. Simulations of the controlled system with the online estimator show that a superior fault tolerance can be achieved.

LPV control for a wafer stage: beyond the theoretical solution

Although conventional PID-like SISO controllers are still most common in industry, there is a growing need for more advanced controller structures in order to comply with ever tighter performance requirements. In this paper we consider positioning devices in IC-manufacturing for which position-dependent plant dynamics are a performance limiting factor. We suggested to employ recently developed linear parameter varying (LPV) control techniques for designing position-dependent controllers that adapt themselves in order to achieve optimal closed-loop performance. Our main emphasis is on presenting a practical LPV design procedure which covers plant modeling, controller synthesis and actual implementation for an electromechanical positioning device, an advanced wafer-scanner. Our experimental results reveal that performance can be improved by LPV control if compared to a classical SISO design. We highlight a variety of troublesome aspects within the design cycle that lack a systematic theoretically founded solution and that limit the possible performance improvement achievable by LPV control.

Linear parameter varying controller for automated lane guidance: experimental study on tractor-trailers

Proposes a linear parameter-varying (LPV) controller design for automated lane keeping for vehicles. The lane keeping objective is to keep the vehicle centered with respect to the lane boundaries by applying appropriate steering action. Most current implementation of lane keeping controllers were based on linear synthesis techniques because linear techniques offer a direct tradeoff between steering action, passenger comfort, robustness, and tracking performance. However, linear methods assume constant longitudinal velocity of the vehicle for controller synthesis. It is known that the position response of the vehicle to the steering input varies significantly with the longitudinal velocity of the vehicle. The LPV design technique deals with this issue by synthesizing a velocity dependent controller. The controller minimizes the induced /spl Lscr//sub 2/ norm of the closed loop from the road curvature to the tracking error. The design has been successfully implemented on a tractor-trailer vehicle and experiments conducted up to longitudinal velocity of 60 mi/h are presented.

A generalized LPV system analysis and control synthesis framework

In this paper, a new approach for linear parameter-varying (LPV) system analysis and control synthesis is proposed. This unified framework combines two seemingly diversified methods in systematic gain-scheduling, LPV control theory, and extends the applicability of full block S -procedure to a general class of LPV systems. An example is used to demonstrate the proposed general LPV design approach, and to show its relative merits compared to other systematic gain-scheduling control techniques.