Linear Fractional Transformation Systems Research Articles

Robust Impedance-Matching of Manipulators Interacting With Uncertain Environments: Application to Task Verification of the Space Station's Dexterous Manipulator

A systematic design method is developed for the identification and control of a simulating robot in order to adjust its contact force and impact dynamics to match those of a reference robot when both robots couple to a similar physical environment with unknown impedance. The control architecture, which is based on closed-loop impedance matching between two robots, is utilized by a hydraulic robot testbed facility for high-fidelity task verification of the space station's dexterous manipulator without requiring contact dynamics modeling. First, the uncertain environment is modeled in terms of parameter uncertainty bounds for a class of environment impedances. Then, the control goal is specifically defined as to minimize the contact-force error between the two robots, where the contact force is caused either by time-varying operator commands or impacts due to a nonzero preimpact velocity. Next, a hierarchical control architecture is formulated in the general framework of linear fractional transformation system by making use of the frequency-domain specifications of the robots together with the environment's parameter uncertainty bounds. It is shown that the overall system uncertainty can be represented by a perturbation block in the feedback form, which can be specified by a block structure array by making use of a unitary transformation. Subsequently, a $\mu$-synthesis-based controller is developed and implemented to achieve the dynamical similarity while maintaining contact stability. Experimental results demonstrate that the simulating robot can generate high-fidelity contact-force profile and impulsive force for different environments without contact dynamics modeling.

Robust output regulation of uncertain linear fractional transformation systems with application to non‐linear Chua's circuit

This study deals with the robust H ∞ output regulation problem for a class of uncertain systems in a linear fractional transformation form. The problem is addressed under a measurement output-feedback framework, i.e. no full information of both plant and exosystem states is assumed for feedback control use. A new robust control law with a novel output regulator structure is proposed, based on which sufficient conditions for robust output regulability and L 2 stability are established in terms of linear matrix equations plus a set of linear matrix inequalities. As a result, the optimal H ∞ output regulation control solution can be synthesised effectively via convex optimisation. Finally, the proposed robust output regulation design scheme will be applied to solve the chaos tracking control problem for the non-linear Chua's circuit.

Almost output regulation of LFT systems via gain-scheduling control

ABSTRACTOutput regulation of general uncertain systems is a meaningful yet challenging problem. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective design mechanism. In this paper, we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation (LFT) with time-varying parametric uncertainties and unknown external perturbations. A novel semi-LFT gain-scheduling output regulator structure is proposed, such that the associated control synthesis conditions guaranteeing both output regulation and disturbance attenuation performance are formulated as a set of linear matrix inequalities (LMIs) plus parameter-dependent linear matrix equations, which can be solved separately. A numerical example has been used to demonstrate the effectiveness of the proposed approach.

Hybrid Switched Gain-Scheduling Control for Missile Autopilot Design

This paper presents a new hybrid switched gain-scheduling control method for missile autopilot design via dynamic output feedback. For controller design purpose, the nonlinear missile plant model is first converted to a switched linear fractional transformation system. Then, the new hybrid switched gain-scheduling autopilot is designed, which consists of a switching dynamic output–feedback linear fractional transformation controller and a supervisor enforcing a controller state reset at each switching time instant. The proposed hybrid control scheme is shown to provide a systematic yet simple framework for missile autopilot design. Specifically, the control synthesis conditions that guarantee weighted stability performance are formulated in terms of a finite number of linear matrix inequalities, which can be solved effectively via convex optimization without parameter-space gridding. Furthermore, stringent controlled performance and strong robustness against parameter perturbations are achieved using this new control approach, whereas no parameter variation information is required for both controller synthesis and implementation. The advantages of the proposed design approach over existing methods will be shown through nonlinear simulations for the missile autopilot design over a wide range of operating conditions.

Output feedback control of linear fractional transformation systems subject to actuator saturation

ABSTRACTIn this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.

Linear fractional transformation gain-scheduling flight control preserving robust performance

In this article, a gain-scheduling flight controller design based on a blending/interpolating methodology and an optimal linear fractional transformation (LFT)-based control technique is proposed to achieve robust performances over a wide range of aircraft operating conditions. Representing the non-linear system dynamics into an uncertain LFT system form, our gain-scheduling strategy designs a limited number of robust linear controllers covering the whole range of operating conditions. Using these fixed controllers in a robust performance control set-up, we derive a blending/interpolating scheduling controller, which achieves the desired performance for the entire flight envelope. Our approach offers the benefit of facilitating controller design and provides proofs of robust stability and performance through an uncertain LFT robust performance formulation. In addition, tools analysing the robustness of the closed-loop gain-scheduling system are also provided. Non-linear simulations based on our proposed approach for a B1 flexible aircraft for a limited flight but reasonable flight envelope show very good performance results in both time and frequency domain responses.

Robust fault detection and isolation for parameter‐dependent LFT systems

AbstractIn this paper, we consider robust fault detection and isolation (FDI) problems for faulty linear systems with linear fractional transformation (LFT) parameter dependency and propose an observer‐based solution by using multiobjective optimization techniques. To simplify the design process, a general faulty LFT system will be constructed from the standard LFT description by converting actuator/system component faults into sensor faults first. Then a bank of parameter‐dependent FDI filters will be designed to identify each fault. Each FDI filter will generate a residual signal to track an individual fault with minimum error and to suppress the effects of disturbances, time‐varying parameters and other fault signals. The design of LFT parameter‐dependent FDI filters, as a multiobjective optimization problem, will be formulated in terms of linear matrix inequalities (LMIs) and can be solved efficiently. A numerical example is used to demonstrate the proposed fault detection and isolation approach for LFT systems with different parametric structures. Copyright © 2009 John Wiley & Sons, Ltd.

Almost output regulation for parameter-dependent linear fractional transformation systems

An important problem of output regulation for linear fractional transformation (LFT) systems is considered. This problem is mainly concerned about tracking and/or rejection of persistent signals produced by some external generator. Necessary and sufficient solvability condition for LFT systems as two linear matrix equations, which is an extension of the existing output regulation results for the linear time invariant and nonlinear systems will be presented. On the basis of the analysis condition, the LFT almost output regulation problem of approximately tracking/rejecting persistent signals will be studied by minimising the ℒ2 gain from perturbation of the signal to error output. Its synthesis condition will be formulated as two matrix equations plus a set of linear matrix inequalities. An example will be used to demonstrate the proposed approach.

Robust and gain-scheduling control of LFT systems through duality and conjugate Lyapunov functions

In this paper, we study stability and performance properties of linear fractional transformation (LFT) parameter-dependent systems using duality theory and tools from convex analysis. A pair of conjugate functions, the convex hull and the maximum of a family of quadratic functions, are used for analysis and synthesis of LFT systems. Sufficient synthesis conditions for both robust state feedback and gain-scheduling output feedback control problems are formulated as a set of linear matrix inequalities (LMIs) with linear search over scalar variables. Finally, a numerical example is used to demonstrate the advantages of the proposed approaches.

Gain-scheduling control of LFT systems using parameter-dependent Lyapunov functions

In this paper, we propose a new control design approach for linear fractional transformation (LFT) systems using parameter-dependent Lyapunov functions. Instead of assuming parameter dependency in LFT fashion, we consider general parameter-dependent controllers to achieve better closed-loop performance. Using full-block multipliers, new LPV synthesis conditions have been derived in terms of finite number of linear matrix inequalities (LMIs). Both continuous- and discrete-time cases are discussed. A ship steering example has been used to demonstrate advantages and benefits of the proposed approach.