José A. De Doná

Multisensor switching control strategy with fault tolerance guarantees

In this paper we propose a novel fault tolerant multisensor switching strategy for feedback control. Each sensor of the proposed multisensor scheme has an associated state estimator which, together with a state feedback gain, is able to individually stabilise the closed-loop system. At each instant of time, the switching strategy selects the sensor-estimator pair that provides the best closed-loop performance, as measured by a control-performance criterion. We establish closed-loop stability of the resulting switching scheme under normal (fault-free) operating conditions. More importantly, we show that closed-loop stability is preserved in the presence of faulty sensors if a set of conditions on the system parameters (such as bounds on the sensor noises, maximum and minimum values of the reference signal, etc.) is satisfied. This result enhances and broadens the applicability of the proposed multisensor scheme since it provides guaranteed properties such as fault tolerance and robust closed-loop stability under sensor fault. The results are applied to the problem of automotive longitudinal control.

Anti-windup and model predictive control: Reflections and connections.

Anti-windup strategies for dealing with input constraints date from the earliest stages of automatic control. They are ad-hoc procedures which achieve input saturation in an instantaneous fashion. Not surprisingly, anti-windup methods have a strong appeal to practitioners because of their simplicity. On the other hand, model predictive control (MPC) is a well established strategy for dealing with input constraint problems. The essential feature of the method is a receding horizon optimal quadratic control problem which is solved subject to input constraints. Both methods are known to perform well in practice and each has its strong advocates. In this paper, we explore connections between the methods for constrained single-input linear systems. In particular, we show that there are cases in which anti-windup schemes are identical to MPC schemes. In other cases, we show that anti-windup has performance which is close to that of MPC strategies. These comparisons are facilitated by formulating a general class of anti-windup algorithms in a form which highlights the connection with the state space formulations which are traditionally used in the MPC area.

Robust fault estimation and compensation for LPV systems under actuator and sensor faults

We propose a fault tolerant control scheme that compensates for actuator and sensor faults in linear parameter varying (LPV) systems by adjusting controller and observer gains based on estimates of the fault magnitude. The scheme consists of a plant in closed loop with an observer-based feedback tracking controller, which is adapted to the fault situation diagnosed by a fault detection and isolation (FDI) algorithm. Assuming the presence of unknown but bounded process and measurement disturbances, invariant sets are derived for the relevant system variables, and these sets are used to obtain error bounds in the fault estimate. Using these bounds, we provide conditions that ensure correct FDI and robust stability of the compensated closed-loop system even under errors in the fault magnitude estimation.

Actuator fault tolerant multi-controller scheme using set separation based diagnosis

We present a fault tolerant control strategy based on a new principle for actuator fault diagnosis. The scheme employs a standard bank of observers which match the different fault situations that can occur in the plant. Each of these observers has an associated estimation error with distinctive dynamics when an estimator matches the current fault situation of the plant. Based on the information from each observer, a fault detection and isolation (FDI) module is able to reconfigure the control loop by selecting the appropriate control law from a bank of controllers, each of them designed to stabilise and achieve reference tracking for one of the given fault models. The main contribution of this article is to propose a new FDI principle which exploits the separation of sets that characterise healthy system operation from sets that characterise transitions from healthy to faulty behaviour. The new principle allows to provide pre-checkable conditions for guaranteed fault tolerance of the overall multi-controller scheme.

Robust hybrid control incorporating over-saturation

A switching controller aimed at dealing with a class of uncertain systems subject to input saturation is presented. The switching strategy is such that a pre-specified level of over-saturation is allowed, forcing the input deliberately into saturation. The goal of this method is to use the full authority of the available control. The proposed scheme allows for, up to, 100% over-saturation. Under these conditions, robust stability of the hybrid scheme is established.

RECEDING HORIZON LINEAR QUADRATIC CONTROL WITH FINITE INPUT CONSTRAINT SETS

Abstract By exploring the geometry of the underlying constrained optimization, a finitely parameterized solution to the discrete time receding horizon linear quadratic control problem with a finite input constraint set is obtained. The resulting controller gives rise to a closed loop system which is piece-wise affine in the plant state. The switching regions are polytopes and are related to those obtained when dealing with ξ (saturation-like) constraint sets.

Lagrangian duality between constrained estimation and control

We show that the Lagrangian dual of a constrained linear estimation problem is a particular nonlinear optimal control problem. The result has an elegant symmetry, which is revealed when the constrained estimation problem is expressed as an equivalent nonlinear optimisation problem. The results extend and enhance known connections between the linear quadratic regulator and linear quadratic state estimation problems.

Sensor Fault Tolerant Control of Induction Motors

Abstract In this paper we propose a multiobserver switching control strategy for fault tolerant control of induction motors. The strategy combines three current sensors and associated observers that estimate the rotor flux. The estimates provided by the observers are compared at each sampling time by a switching mechanism which selects the sensors–observer pair with the smallest error between the estimated flux magnitude and a desired flux reference. The selected estimates are used by a field oriented controller to implement the control law. Pre-checkable conditions are derived that guarantee fault tolerance under an abrupt fault of a current sensor. Simulation results under realistic conditions illustrate the effectiveness of the scheme.

Solution of the input-constrained LQR problem using dynamic programming

The input-constrained LQR problem is addressed in this paper; i.e., the problem of finding the optimal control law for a linear system such that a quadratic cost functional is minimised over a horizon of length N subject to the satisfaction of input constraints. A global solution (i.e., valid in the entire state space) for this problem, and for arbitrary horizon N, is derived analytically by using dynamic programming. The scalar input case is considered in this paper. Solutions to this problem (and to more general problems: state constraints, multiple inputs) have been reported recently in the literature, for example, approaches that use the geometric structure of the underlying quadratic programming problem and approaches that use multi-parametric quadratic programming techniques. The solution by dynamic programming proposed in the present paper coincides with the ones obtained by the aforementioned approaches. However, being derived using a different approach that exploits the dynamic nature of the constrained optimisation problem to obtain an analytical solution, the present result complements the previous methods and reveals additional insights into the intrinsic structure of the optimal solution.

Control of constrained linear systems using fast sampling rates

Abstract This paper addresses the problem of optimal control of constrained linear systems when fast sampling rates are utilised. We show that there exists a well-defined limit as the sampling rate increases. An immediate consequence of this result is the existence of a finite sampling period such that the achieved performance is arbitrarily close to the limiting performance.