Linear Parameter-varying Structure Research Articles

An Integrated Design Approach for Fault-Tolerant Control of Switched LPV Systems With Actuator Faults

In this article, the active fault-tolerant control (FTC) issue is addressed for switched linear parameter varying (LPV) systems in the discrete-time domain. A general dwell-time property is considered in the system setup to govern the switching dynamics between subsystems, and the parameter variations within each subsystem are subjected to the polytopic uncertainties. The main innovation of the developed active FTC approach is to effectively cope with switched LPV models where both input and output matrices can be of parameter-dependent form. By virtue of a novel Lyapunov function approach depending on both dwell time and parameter variations, the joint task for fault detection, estimation, and compensation is fulfilled via an integrated design scheme. The input-to-state stability (ISS) conditions are obtained for the augmented faulty system satisfying a given ISS-gain performance requirement. The desired effect of active FTC is achieved in three critical steps: 1) construct a fault detection filter in terms of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> norm; 2) design an observer-based estimator to estimate the system states and faults simultaneously; and 3) synthesize a fault-tolerant controller with the LPV structure using the estimated states and faults for fault compensation. Finally, an application example is utilized to illustrate the efficiency and availability of the proposed control approach.

A networked-based receding horizon scheme for constrained LPV systems

This paper deals with control problems for networked constrained polytopic Linear Parameter Varying (LPV) systems. A novel LPV customization of a recent Receding Horizon robust Control (RHC) scheme developed for polytopic uncertainty systems is here proposed for the case where command inputs and state measurement are subject to time-varying delays. By taking advantage of the flexibility of the LPV structure, families of precomputed one-step controllable sets are off-line computed which result less conservative with respect to their robust counterparts. Finally, simulation results involving the constrained tracking problem of an unicycle-type mobile robot are reported to show the effectiveness and the benefits of the proposed control scheme.

H∞Loop Shaping Control of Input Saturated Systems with Norm-Bounded Parametric Uncertainty

This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem ofH∞loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-blockH∞synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV) system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter.

Modeling and control of tubular solid-oxide fuel cell systems: II. Nonlinear model reduction and model predictive control

This paper describes a systematic method for developing model-based controllers for solid-oxide fuel cell (SOFC) systems. To enhance the system efficiency and to avoid possible damages, the system must be controlled within specific operating conditions, while satisfying a load requirement. Model predictive control (MPC) is a natural choice for control implementation. However, to implement MPC, a low-order model is needed that captures the dominant dynamic behavior over the operating range. A linear parameter varying (LPV) model structure is developed and applied to obtain a control-oriented dynamic model of the SOFC stack. This approach effectively reduces a detailed physical model to a form that is compatible with MPC. The LPV structure includes nonlinear scheduling functions that blend the dynamics of locally linear models to represent nonlinear dynamic behavior over large operating ranges. Alternative scheduling variables are evaluated, with cell current being shown to be an appropriate choice. Using the reduced-order model, an MPC controller is designed that can respond to the load requirement over a wide range of operation changes while maintaining input–output variables within specified constraints. To validate the approach, the LPV-based MPC controller is applied to the high-order physical model.

Parameter dependent freeway modelling

The problem of modelling the complex behaviour of freeway flow leads to a nonlinear macroscopic model. Unfortunately, high dimensional non-linear characteristics could not be performed easily. The paper´s purpose is to introduce a new, general modelling formalism for freeway traffic flow modelling, respectively control. Linear Parameter Varying (LPV) systems represent a numerically tractable class of complex non-linear systems. The main idea is to derive some arbitrary, time dependent parameters by capturing the nonlinearities in the system. Even if the transformation of the full nonlinear model to affine and quasi Linear Parameter Varying (qLPV) system is not unique, an appropriate qLPV model is presented and a computationally low demanding form is given. More, the paper investigates the problem of selecting the adequate scheduling variables, endogenous parameters and some linear approximations giving a novel way to describe freeway traffic systems. An important aspect of the model selection is the feasibili ty of the resulted system throughout the controller and observer design. The paper describes the problem of quadratic stabilizability and detectability for LPV flow models. The Linear Matrix Inequality (LMI) conditions are developed to verify these important properties. Finally, a numeric example suggests the application of the LPV structure for a general freeway section with on- and off-ramps. The comparison of the simulation response of the non-linear and the derived nominal LPV model has also been investigated.

An Optimal Inverse Systems for Max-Plus Linear Systems with Linear Parameter-Varying Structure

This paper proposes an optimal inverse system for a max-plus linear system with a linear parameter-varying structure. For the design of inverse systems of max-linear systems, the prediction equation using max-plus linear systems and the greatest subsolution for the linear algebraic equation are required. Hence, this paper newly gives a prediction equation and the greatest sub-solution for the linear parameter-varying system. In addition to those, this paper shows an optimization method for the system parameters in the inverse systems, and this optimization problem can be reduced to the linear programming. Finally, the proposed method is applied to a two-inputs, two-outputs production system with four machines, and the efficiency of the proposed method is demonstrated by using numerical simulations.

ROBUST CONTROL OF NONLINEAR PROCESSES USING MULTIPLE MODELS

This paper addresses the problem of controlling a nonlinear process when linear models have been identified at different operating points. A multimodel approach is used to to identify and control highly nonlinear process. The internal linear model representation of the nonlinear plant for conventional robust controller is replaced by the linear parameter varying (LPV) model, which introduces transparency while offering distinct advantages for nonlinear model-based control. For this LPV structure a robust controller is then designed based on H∞ techniques. Simulation results for a CSTR process are used to illustrate the performance benefits of multimodel approach.