Reference Management for Fault-Tolerant Model Predictive Control

Abstract

This work presents a reference management technique for fault-tolerant model predictive control. The reference value to be tracked is first filtered through a set of statically admissible commands. This set expresses the airframe's physical ability to achieve a new equilibrium point, and it is constructed by considering the limitations of the inputs and states of the system under control. The set has a polyhedral form defined by linear inequalities. State and control vectors are obtained at steady state to guarantee the feasibility of the constrained numerical problem faced by the model predictive control regulator. The proposed method has been evaluated using a linear model of a fighter aircraft, and it demonstrated adequate performance with a computational burden compatible with real-time applications.augmented observation matrix e = model following error H = tracking matrix I = identity matrix J = cost function K d = feedback gain matrix k ss , k N = linear inequalities vectors L, L d , L x = observer gain matrices L d , H = auxiliary observer matrices L ss , M x , M x ss , M u ss , M d = linear inequalities matrices N = control horizon O 1 = invariant set O 1 = tracking invariant set P = terminal weighting matrix P m = set of statically admissible commands given the current disturbance P ss = steady-state polyhedron P w = set of statically admissible commands p, q, r = aircraft angular rates, rad=s Q, W, R = weighting matrices Q d , W d , R d = discrete weighting matrices Q m , W m , R m = implicit model following weighting matrices Q ss , R ss = constrained target calculator weighting matrices r c = command (demand) vector r ss = statically admissible command vector T = rotation matrix T s = sampling time, s t = time, s u max , u min = bounds over control vector w = performance output vector w m = reference model state vector X, U = admissible state and control sets X N = set of admissible extended state vectors X ss N = set of admissible steady-state control and state vectors x, u = state and control vectors x a = augmented state vector x max , x min = bounds over state vector x ss , u ss = state and control vectors at steady state x 0 = initial state vector x,d = estimated state and disturbance vectors x,ũ = tracking state and control vectors y = observed vector z = controlled output vector z ss = feasible command vector ,= angles of attack and sideslip, rad c , r = canard and rudder deflections, rad r e , l e = right and left elevon deflections, rad x , z = tolerance vectors = projection operator = slice operator , , d = discrete-time state-space matrices = auxiliary discrete state-space matrix a , a = augmented discrete state-space matrices

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

“…It has long been advocated that model predictive control (MPC) has advantages in the field of reconfigurable and fault tolerant control [1][2][3][4][5][6][7][8][9][10]. In MPC, at each time step, the control input applied to the plant is obtained by solution of an optimisation problem [11,12], which minimises a function of future inputs and states over a finite horizon, subject to physical and operational constraints.…”

Offline Model Predictive Control Based on Weighted Projection over Polytopes

“…The simulations were performed on a PC with a 3.20 GHz Intel Core i5 CPU and 4 GB of RAM. A previous work [11] presented larger runtimes, in the range of milliseconds. Recently, Hartley et al [2] presented numerical simulations of MPC with execution times in the range of microseconds, but using iterative solvers that demand specific initialization tuning.…”

“…This is achieved by proposing a new form to solve quadratic convex optimization problems and applying it on the feasible target tracking model predictive control (FTT-MPC) method [11], producing a new form of offline MPC. Based on the assumption of the existence of priority among controlled outputs and manipulated variables (inputs), the traditional quadratic programming problem is replaced by offline computation and projection of polyhedral sets.…”

“…In addition, even if feasibility is found, closedloop stability may not be assured because the constraints are active not only at the time instant of the input computation, but also at all future instants. Previous work presented the feasible target tracking MPC technique [11], a three-stage control method where each part comprises a quadratic programming problem. In the present work, the offline feasible model predictive control method (OFF-MPC) is proposed, replacing each optimization of the FTT-MPC by prioritized projections on polytopes that comprises the relevant system constraints.…”

Distributed predictive control with minimization of mutual disturbances

“…Reconfigurable terminal sets have been proposed in the context of setpoint, reference or target tracking and fault tolerant forms of MPC [22][23][24][25][26]; the idea is to parameterize an invariant, admissible set in terms of a steady-state target equilibrium pair, so that when the target changes the terminal set can be adjusted accordingly and automatically. In [27], a novel reconfigurable terminal set that is an inner approximation to the maximal admissible set (MAS) [28], parameterized by the right-hand side of the polytopic input constraint set (i.e., here b i ), is proposed; the context is fault-tolerant control, wherein the failure of an actuator may be modelled as a change in the input constraint set.…”