Linear parameter varying control for actuator failure

Abstract. A robust linear parameter varying (LPV) control synthesis is carried out for an HiMATvehicle subject to loss of control effectiveness. The scheduling t)ar;_met('r is selected to be a flmction of theestimates of the control effectiveness f_lctors. The estimates are provi, ted on-line by a two-stage Kalmanestimator. The inherent conservatism of the LPV design is reduced th, ough the use of a scaling factor onthe uncertainty block that represents the estimation errors of the eff(_ctiveness factors. Simulations of thecontrolled system with the on-line estimator show that a sut)erior fault-tolerance can be achiev('d.Key words, fault tolerant control system, fault parameter estimati()n, reconfigurable controllerSubject classification. Guidance and Control1. Introduction. One of control schemes for a nonlinear system is a gain-scheduled linear paraInetervarying control technique [13, 1, 7, 16]. This approach is particularly al,pealing in that a nonlinear plant istreated as a linear paraIneter varying (LPV) system whose state-space matrices are flmctions of a schedul-ing parameter vector. This allows linear control techniques to b(, applied to a nonlinear system. Severalresearches on an LPV synthesis methodology allow the design of the gl,_t)al control law for an LPV systemover a parameter set which is bounded and measurable [13, 1, 7, l(i. An LPV controller synthesis is fl)rnnl-lated into a linear matrix inequality (LMI) optimization problem. Ther( are LPV control synthesis nletho(tsaccording to a flmctional fl)rm of an LPV system. The polytopic LPV control synthesis method [2] is usedfl)r an LPV system which is a polytopic function of a scheduling parameter vector. The affine LPV controlsynthesis inethod [1] is applied to an affine LPV system, whose LMI constraints are evaluated at only vertexpoints of an LPV system. The grid LPV control synthesis method [7, 16] is for an LPV system which is abounded function of a scheduling parameter vector. In the method, L_II constraints are evaluated at gridpoints over parameter spaces. These methods can be converted to each other by increasing conservatismto describe an LPV system. The grid LPV synthesis method h_s be,,n suecessflfily applied to synthesiscontrollers for the pitch-axis missile autopilots[l?, 12], F-14 aircraft lat,,ral-directional axis during poweredapproach[6, 4], turbofan engines [15, 5] and F-16 aircraft [14]. Sch(_duling parameters of these apt)licationsare physical parameters such as angle of attack, mach number, vt_locily, dynamic pressure, etc. Schedul-ing parameters in LPV control synthesis are required to be measural,le and the variations of schedulingparameters should be in a bounded set.In this paper, actuator failures are modeled as an LPV system a_, functions of actuator effectivenessparameters [9]. These paraineters are estimated as biases using an ;_ugmented Kahnan filter. A set ofeovariance-dependent forgetting factors is introduced into the filtering algorithm. As a result, the change inthe actuator effectiveness is accentuated to help achieve a more accur_te estimate more rapidly. The H_cbounds on parameter estimation errors are assessed through simulati(_ns, which are then used as boundsof real parameter uncertainty in the construction of a robust LPV c()ntrol law. Actuator faults can beparanteterized as estimated fault effectiveness parameters. Thus, it is p(_ssible to formulate a fault tolerancecontrol design problem as an LPV control synthesis problem based on ,,stimated faults parameters.Fault estimation errors and modeling uncertainties are tel)resented by an uncertainty block in tile con-struction of a robust LPV control law. The structure of an uncertainty bl(,ck is not included in an conventionalLPV control synthesis methodology [7, 16]. A sealing factor on a uncertainty block can reduce conservatismof the LPV synthesis [1]. In Ref.[1], it is formulated into a singh, optimization problem to find a scalingfactor and a control law to achieve a certain level of performance. The ( ptimization problem is not a convexproblem, which has unknown positive matrices X and Y related with .t control law and a scaling factor Srelated with tile uncertainty block structure. The problem is solved by an iteration method of fixing X and_" or a scaling factor S. In this paper, the problem is formulated into tw(. LMI optimizations: one is to design