Linear Parameter Varying Filter Research Articles

Resilient energy-to-peak filtering for linear parameter-varying systems under random access protocol

In this paper, we consider the energy-to-peak filtering issue for a class of linear parameter-varying (LPV) systems with time delays subject to certain communication regulation under which only one sensor is allowed to transmit its measurement data at each transmission instant. The data communication is regulated by the random access protocol (RAP) for the purpose of avoiding data collisions. The main purpose of this paper is to design an LPV filter such that the resultant filtering error system is asymptotically stable and also satisfies the prescribed - performance in the mean square. Taking into account both the LPV nature and the possible gain perturbations, a parameter-dependent resilient filter is constructed according to the plant dynamics and scheduling behaviour of the RAP. The desired filter gain matrices are obtained by solving a set of linear matrix inequalities. Finally, a simulation example is given to validate the effectiveness and correctness of the filter design scheme.

A Linear Parameter Varying Approach for Robust Dead-Time Compensation

Abstract This paper proposes a novel method for the design of time-varying dead-time compensators. The presented approach is a modified version of Filtered Smith Predictor (FSP), extended with a delay estimator and a Linear Parameter Varying (LPV) feedback filter. Just as with the FSP, this scheme can be tuned for an adequate trade-off between perfomance and robustness, as well as for unstable and integrative processes. The LPV filter (scheduled by the estimation of the dead-time) is used to overcome the time-varying delay as it autonomously adapts itself and imposes, accordingly, more/less robustness to the closed-loop. Simulation results considering the temperature control of a Solar Collector Field are given to illustrate the method’s performance towards reference tracking, disturbance rejection and uncertainty.

Discrete time H∞ synthesis conditions for LPV filter design

Abstract We are interested in H∞ synthesis conditions for Linear Parameter Varying (LPV) filter design. We prove that an existing class of sufficient conditions for poly-quadratic H∞ filter synthesis is in fact necessary as well. We develop alternative conditions based on a new theory of duality for poly-quadratic Lyapunov functions. We use these results to show how poly-quadratic H∞ state feedback synthesis conditions can be used for poly-quadratic H∞ LPV filter synthesis.

Trapped Unburned Fuel Estimation and Robustness Analysis for a Turbocharged Diesel Engine With Negative Valve Overlap Strategy

Turbocharger and negative valve overlap (NVO) strategy are widely used among advanced combustion modes for internal combustion engines. In order to achieve well emission performance, the NVO can be as large as 100 crank angle (CA) degrees, such that the residual gas fraction can be up to 40%. With such amount of residual gas in the cylinder, the trapped unburned fuel is not trivial. It has a significant impact on the combustion process. However, the trapped unburned fuel mass is hard to be measured directly. In this paper, a novel method based on the signals of oxygen fraction is proposed to estimate it. By analyzing the combustion process, dynamic equations for the intake/exhaust manifolds and in-cylinder oxygen fractions, as well as actual fuel mass in the cylinder are constructed. A smooth variable structure filter (SVSF) was designed to estimate oxygen fractions and further the trapped unburned fuel. As a comparison, Kalman filter (KF) and linear matrix inequality (LMI) based linear parameter-varying (LPV) filter were also applied. Robustness properties of the three observers are analyzed based on the theory of input-to-state (ISS) stability. The proposed models and methods and theoretical analysis are validated and compared through a set of simulations in high-fidelity GT-Power environment. The simulation results match well with theoretical analysis that the SVSF has good properties of strong robustness (with a root mean square error (RMSE) of 0.24, comparing with 0.4 of LPV filter and 0.49 of KF, for the unburned fuel estimation).

Sensor fault detection and isolation filter for polytopic LPV systems: A winding machine application

In this paper, a fault diagnosis method is developed for a particular class of nonlinear systems described by a polytopic linear parameter varying (LPV) formulation. The main contribution consists in the synthesis of an accurate fault detection and isolation (FDI) filter and also a sensor fault magnitude estimation with a quality factor. This quality factor of the filter underlines if the fault estimation can be used or not. Stability conditions of the polytopic LPV filter are studied by ensuring poly-quadratic stability with Linear Matrix Inequality (LMI) representation. The effectiveness of this global FDI scheme through LPV modelization, filter design and stability analysis, is illustrated on a real winding machine under multiple sensor faults.

Parameter-dependent H∞ filter design for LPV systems and an autopilot application

This paper considers the design problem of parameter dependent H ∞ filters for linear parameter varying (LPV) systems whose parameters are measurable. Conditions for existence of parameter-dependent Lyapunov function are proposed via parametrical linear matrix inequality (LMI) constraints. Based on the solutions to the LMIs, an algorithm for the gain matrices of LPV filter is presented. The design method is applied to a missile system to demonstrate the effectiveness.

Formula omitted] filtering for discrete-time linear systems with bounded time-varying parameters

In this paper, the problem of linear parameter varying (LPV) filter design for time-varying discrete-time polytopic systems with bounded rates of variation is investigated. The design conditions are obtained by means of a parameter-dependent Lyapunov function and extra variables for the filter design, expressed as bilinear matrix inequalities. An LPV filter, which minimizes an upper bound to the H ∞ performance of the estimation error, is obtained as the solution of an optimization problem. A convex model to represent the parameters and their variations as a polytope is proposed in order to provide less conservative design conditions. Robust filters for time-varying polytopic systems can be obtained as a particular case of the proposed method. Numerical examples illustrate the results.

A simple approach to direct LPV filter design from data for nonlinear systems

A simple approach to the design of Linear Parameter Varying (LPV) filters for nonlinear systems is proposed. The approach relies on individuating several working conditions of the system. For each of these conditions, an almost optimal Linear Time Invariant (LTI) filter is directly identified from data. The designed LTI filters are then suitably combined to give an LPV filter. The identification of a nonlinear model and the design of a nonlinear filter are thus avoided. The direct filter design approach is applied to a problem involving real data, regarding the estimation of vehicles yaw rate.