A semidefinite relaxation procedure for fault-tolerant observer design

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design

Fault-tolerant Wide-area Control for Power Oscillation Damping

The effectiveness of using both local and remote (wide-area) feedback signals for power oscillation damping (POD) controllers is first demonstrated. The challenge is then to guarantee a minimum level of dynamic performance with only the local signals following a sudden loss of remote signals. A case study on the Nordic equivalent system is presented to show that the closed-loop response could deteriorate if the remote signals are lost. A fault-tolerant control (FTC) design methodology is presented to solve this problem and ensure an acceptable performance level even in case of loss of remote signals. The FTC design methodology is based on simultaneous regional pole-placement for normal and loss of (remote) signals conditions. First the problem is solved non-iteratively using a Linear Matrix Inequality (LMI) approximation and then it is shown that, although this procedure is linear and easy to implement, it has a drawback: the value of one of the control matrices is fixed before calculating the others. An iterative procedure is presented instead to ameliorate this problem and potentially improve the damping of the system. Case studies on the Nordic equivalent system confirm that the proposed iterative fault tolerant controller (FTCit) is able to improve performance against the non-iterative fault tolerant controller (FTC) and produce acceptable performance in case of loss of the remote signals while the response with a CC is unacceptable if a fault occurs

Tracking control for directional drilling systems using robust feedback model predictive control

A rotary steerable system (RSS) is a drilling technology which has been extensively studied and used for over the last 20 years in hydrocarbon exploration and it is expected to drill complex curved borehole trajectories. RSSs are commonly treated as dynamic robotic actuator systems, driven by a reference signal and typically controlled by using a feedback loop control law. However, due to spatial delays, parametric uncertainties and the presence of disturbances in such an unpredictable working environment, designing such control laws is not a straightforward process. Furthermore, due to their inherent delayed feedback, described by delay differential equations (DDE), directional drilling systems have the potential to become unstable given the requisite conditions. This paper proposes a Robust Model Predictive Control (RMPC) scheme for industrial directional drilling, which incorporates a simplified model described by ordinary differential equations (ODE), taking into account disturbances and system uncertainties which arise from design approximations within the formulation of RMPC. The stability and computational efficiency of the scheme are improved by a state feedback strategy computed offline using Robust Positive Invariant (RPI) sets control approach and model reduction techniques. A crucial advantage of the proposed control scheme is that it computes an optimal control input considering physical and designer constraints. The control strategy is applied in an industrial directional drilling configuration represented by a DDE model and its performance is illustrated by simulations

Robust moving horizon state estimation for uncertain linear systems using linear matrix inequalities

This paper investigates the problem of state estimation for linear-time-invariant (LTI) discrete-time systems subject to structured feedback uncertainty and bounded disturbances. The proposed Robust Moving Horizon Estimation (RMHE) scheme computes at each sample time tight bounds on the uncertain states by solving a linear matrix inequality (LMI) optimization problem based on the available noisy input and output data. In comparison with conventional approaches that use offline calculation for the estimation, the suggested scheme achieves an acceptable level of performance with reduced conservativeness, while the online computational time is maintained relatively low. The effectiveness of the proposed estimation method is assessed via a numerical example

A real-time robust ecological-adaptive cruise control strategy for battery electric vehicles

This work addresses the ecological-adaptive cruise control problem for connected electric vehicles by a computationally efficient robust control strategy. The problem is formulated in the space-domain with a realistic description of the nonlinear electric powertrain model and motion dynamics to yield a convex optimal control problem (OCP). The OCP is solved by a novel robust model predictive control (RMPC) method handling various disturbances due to modelling mismatch and inaccurate leading vehicle information. The RMPC problem is solved by semi-definite programming relaxation and single linear matrix inequality (sLMI) techniques for further enhanced computational efficiency. The performance of the proposed real-time robust ecological-adaptive cruise control (REACC) method is evaluated using an experimentally collected driving cycle. Its robustness is verified by comparison with a nominal MPC which is shown to result in speed-limit constraint violations. The energy economy of the proposed method outperforms a state-of-the-art time-domain RMPC scheme, as a more precisely fitted convex powertrain model can be integrated into the space-domain scheme. The additional comparison with a traditional constant distance following strategy (CDFS) further verifies the effectiveness of the proposed REACC. Finally, it is verified that the REACC can be potentially implemented in real-time owing to the sLMI and resulting convex algorithm

Maximally robust controllers for multivariable systems

Published versio

A STATE-SPACE ALGORITHM FOR THE SOLUTION OF THE 2-BLOCK SUPEROPTIMAL DISTANCE PROBLEM

Published versio

On the gap between the complex structured singular value and its convex upper bound

Published versio

Fault-tolerant Control Design to Enhance Damping of Inter-area Oscillations in Power Grids

SUMMARY In this paper passive and active approaches for the design of fault-tolerant controllers (FTCs) are presented. The FTCs are used to improve the damping of inter-area oscillations in a power grid. The effectiveness of using a combination of local and remote (wide-area) feedback signals is first demonstrated. The challenge is then to guarantee a minimum level of dynamic performance following a loss of remote signals. The designs are based on regional pole-placement using Linear Matrix Inequalities (LMIs). First, a passive FTC is proposed. It is shown that the computation of the controller reduces to the solution of bilinear matrix inequalities. An iterative procedure is then used to design the controller. Next, as an alternative to active, time varying controllers, one for each fault scenario, we propose an approach for the design of a 'minimal switching' FTC in which only one controller is designed, but where a simple switch is incorporated into the controller structure. A case study in a linear and nonlinear Nordic equivalent system is presented to show that the closed-loop response using a conventional control (CC) design could deteriorate the performance or even destabilize the system if the remote signals are lost and to demonstrate the effectiveness of the proposed FTC designs. KEY WORDS: Fault-tolerant control, regional pole-placement, simultaneous design, power oscillation damping, local and remote feedback

An explicit state-space approach to the one-block super-optimal distance problem

An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in (Jaimoukha and Limebeer in SIAM J Control Optim 31(5):1115–1134, 1993) which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work (Halikias et al. in SIAM J Control Optim 31(4):960–982, 1993; Limebeer et al. in Int J Control 50(6):2431–2466, 1989). The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control