State-Feedback Output Tracking Via a Novel Optimal-Sliding Mode Control

This chapter describes a new framework for the design of a novel suboptimal state-feedback-sliding mode control for output tracking while H2/H∞ performances of the closed-loop system are under control. In contrast to most of the current sliding surface design schemes, in this new framework, the level of control effort required to maintain sliding is penalized. The proposed method for the design of optimal-sliding mode control is carried out in two stages. In the first stage, a state-feedback gain is derived using a linear matrix inequality (LMI)-based scheme that can assign a number of the closed-loop eigenvalues to a known value while satisfying performance specifications and ensuring that all the closed-loop poles are located in a preselected subregion. The sliding function matrix related to the particular state feedback derived in the first stage is obtained in the second stage by using one of the two different methods developed for this goal. We present a numerical example to demonstrate the remarkable performance of the proposed scheme

A Novel Optimal Sliding Mode Control for Multiple Time-Delay Systems

© 2018 AACC. This paper considers the problem of delay-independent optimal sliding mode control design for uncertain systems with multiple constant delays. An improved delay-independent framework for the design of SMC is established in terms of a linear matrix inequality for time-delay systems, in which multi-channel H 2 performances of the closed-loop system are under control. Unlike most of the existing methods, the required level of control effort to maintain sliding will be taken into account in this new framework. Our two-stage SMC is constructed as follows. Firstly, a certain state feedback gain is designed while assigning some of the closed-loop eigenvalues precisely to a predetermined stable location as well as ensuring a prescribed multi-channel H 2 performance level of the closed-loop system. In the second stage, we will find the optimal switching surface associated with the gain designed in the first stage via a novel approach developed for this goal while ensuring the stability of the reduced-order dynamics

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Novel frameworks for the design of fault-tolerant control using optimal sliding-mode control

Copyright © 2018 John Wiley & Sons, Ltd. This paper describes 2 schemes for a fault-tolerant control using a novel optimal sliding-mode control, which can also be employed as actuator redundancy management for overactuated uncertain linear systems. By using the effectiveness level of the actuators in the performance indexes, 2 schemes for redistributing the control effort among the remaining (redundant or nonfaulty) set of actuators are constructed based on an H2-based optimal sliding-mode control. In contrast to the current sliding-mode fault-tolerant control design methods, in these new schemes, the level of control effort required to maintain sliding is penalised. The proposed optimal sliding-mode fault-tolerant control design schemes are implemented in 2 stages. In the first stage, a state feedback gain is derived using an LMI-based scheme that can assign a number of the closed-loop eigenvalues to a known value whilst satisfying performance specifications. The sliding function matrix related to the particular state feedback derived in the first stage is obtained in the second stage. The difference between the 2 schemes proposed for the sliding-mode fault-tolerant control is that the second one includes a separate control allocation module, which makes it easier to apply actuator constraints to the problem. Moreover, it will be shown that, with the second scheme, we can deal with actuator faults or even failures without controller reconfiguration. We further discuss the advantages and disadvantages of the 2 schemes in more details. The effectiveness of the proposed schemes are illustrated with numerical examples

Robust control of redundantly actuated dynamical systems

The eigenstructure assignment scheme for robust multivariable feedback control is extended to redundantly actuated dynamical systems. It is shown that an orthonormal set of close loop eigenvectors is always exactly assignable in the case of redundant actuation proving the inherent robustness in the control design methodology. A choice of close loop eigenvector set to minimize the feedback gain matrix is suggested. Partial Eigenstructure Assignment methodology is proposed for second order mechanical systems. A methodology for coordinated actuation of redundant actuator sets by a trained weighted minimum norm solution is presented. To apply the methodology to hyper-redundant actuator arrays, for application to smart actuator arrays, a novel adaptive discretization algorithm is proposed. The adaptive aggregation strategy, based on the physics of the system, introduces nodes, to optimize a performance index of the overall plant model. The dimensionality of the inputs thus reduces to a finite number, making it a candidate plant for control by the robust redundant control scheme. The adaptive aggregation together with robust redundant control methodology is demonstrated on a finite element model of a novel morphing wing. This schema unifies the traditionally disparate methods of modeling and controller design

Active vibration control in linear time-invariant and nonlinear systems

Active vibration control techniques are widely used in linear time-invariant and nonlinear systems. However, there still exist many difficulties in the application of conventional active vibration control techniques, including the following: (1) In application, some of the degrees of freedom may not be physically accessible to actuation and sensing simultaneously; (2) large flexible structures are difficult in terms of isolating one substructure from the vibration of another; (3) the incomplete understanding of the effects of softening nonlinearity may put conventional active controllers at risk; and (4) global stability of under-actuated nonlinear aeroelastic systems, resulting from actuator failure or motivated by weight and cost constraints imposed on next-generation flight vehicles, is extremely challenging, especially in the case of uncertainty and external disturbances. These intellectual challenges are addressed in this research by linear and nonlinear active control techniques. A new theory for partial pole placement by the method of receptances in the presence of inaccessible degrees of freedom is proposed. By the application of a new double input control and orthogonality conditions on the input and feedback gain vectors, partial pole placement is achieved in a linear fashion while some chosen degrees of freedom are free from both actuation and sensing. A lower bound on the maximum number of degrees of freedom inaccessible to both actuation and sensing is established. A theoretical study is presented on the feasibility of applying active control for the purpose of simultaneous vibration isolation and suppression in large flexible structures by block diagonalisation of the system matrices and at the same time assigning eigenvalues to the chosen substructures separately. The methodology, based on eigenstructure assignment using the method of receptances, is found to work successfully when the open-loop system, with lumped or banded mass matrix, is controllable. A comprehensive study of the effects of softening structural nonlinearity in aeroelastic systems is carried out using the simple example of a pitch-flap wing, with softening cubic nonlinearity in the pitch stiffness. Complex dynamical behaviour, including stable and unstable limit cycles and chaos, is revealed using sinusoidal-input describing functions and numerical integration in the time domain. Bifurcation analysis is undertaken using numerical continuation methods to reveal Hopf, symmetry breaking, fold and period doubling bifurcations. The effects of initial conditions on the system stability and the destabilising effects of softening nonlinearity on aerodynamic responses are considered. The global stability of an under-actuated wing section with torsional nonlinearity, softening or hardening, is addressed using a robust passivity-based continuous sliding-mode control approach. The controller is shown to be capable of stabilising the system in the presence of large matched and mismatched uncertainties and large input disturbance. With known bounds on the input disturbance and nonlinearity uncertainty, the continuous control input is able to globally stabilise the overall system if the zero dynamics of the system are globally exponentially stable. The merits and performance of the proposed methods are exemplified in a series of numerical case studies

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling