Robust Sliding Mode Observers for Large Scale Systems with Application to a Multimachine Power System

In this paper, a class of interconnected systems with structured and unstructured uncertainties is considered where the known interconnections and uncertain interconnections are nonlinear. The bounds on the uncertainties are employed in the observer design to enhance the robustness when the structure of the uncertainties is available for design. Under the condition that the structure distribution matrices of the uncertainties are known, a robust sliding mode observer is designed and a set of sufficient conditions is developed to guarantee that the error dynamics are asymptotically stable. In the case that the structure of uncertainties is unknown, an ultimately bounded approximate observer is developed to estimate the system states using sliding mode techniques. The results obtained are applied to a multimachine power system, and simulation for a two machine power system is presented to demonstrate the feasibility and effectiveness of the developed methods

Robust model-based fault estimation and fault-tolerant control : towards an integration

To maintain robustly acceptable system performance, fault estimation (FE) is adopted to reconstruct fault signals and a fault-tolerant control (FTC) controller is employed to compensate for the fault effects. The inevitably existing system and estimation uncertainties result in the so-called bi-directional robustness interactions defined in this work between the FE and FTC functions, which gives rise to an important and challenging yet open integrated FE/FTC design problem concerned in this thesis. An example of fault-tolerant wind turbine pitch control is provided as a practical motivation for integrated FE/FTC design.To achieve the integrated FE/FTC design for linear systems, two strategies are proposed. A H∞ optimization based approach is first proposed for linear systems with differentiable matched faults, using augmented state unknown input observer FE and adaptive sliding mode FTC. The integrated design is converted into an observer-based robust control problem solved via a single-step linear matrix inequality formulation.With the purpose of an integrated design with more freedom and also applicable for a range of general fault scenarios, a decoupling approach is further proposed. This approach can estimate and compensate unmatched non-differentiable faults and perturbations by combined adaptive sliding mode augmented state unknown input observer and backstepping FTC controller. The observer structure renders a recovery of the Separation Principle and allows great freedom for the FE/FTC designs.Integrated FE/FTC design strategies are also developed for Takagi-Sugeno fuzzy modelling nonlinear systems, Lipschitz nonlinear systems, and large-scale interconnected systems, based on extensions of the H∞ optimization approach for linear systems.Tutorial examples are used to illustrate the design strategies for each approach. Physical systems, a 3-DOF (degree-of-freedom) helicopter and a 3-machine power system, are used to provide further evaluation of the proposed integrated FE/FTC strategies. Future research on this subject is also outlined

Time Complexity of Decentralized Fixed-Mode Verification

Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem

An energy-based state observer for dynamical subsystems with inaccessible state variables

This work presents an energy-based state estimation formalism for a class of dynamical systems with inaccessible/ unknown outputs, and systems at which sensor utilization is impractical, or when measurements can not be taken. The power-conserving physical interconnections among most of the dynamical subsystems allow for power exchange through their power ports. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. This information is used in the design of an energybased state observer. Convergence stability of the estimation error for the proposed state observer is proved for systems with linear dynamics. Furthermore, robustness of the convergence stability is analyzed over a range of parameter deviation and model uncertainties. Experiments are conducted on a dynamical system with a single input and multiple inaccessible outputs (Fig. 1) to demonstrate the validity of the proposed energybased state estimation formalism

An Energy-Based State Observer for Dynamical Subsystems with Inaccessible State Variables

This work presents an energy-based state estimation formalism for a class of dynamical systems with inaccessible/ unknown outputs, and systems at which sensor utilization is impractical, or when measurements can not be taken. The power-conserving physical interconnections among most of the dynamical subsystems allow for power exchange through their power ports. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. This information is used in the design of an energybased state observer. Convergence stability of the estimation error for the proposed state observer is proved for systems with linear dynamics. Furthermore, robustness of the convergence stability is analyzed over a range of parameter deviation and model uncertainties. Experiments are conducted on a dynamical system with a single input and multiple inaccessible outputs (Fig. 1) to demonstrate the validity of the proposed energybased state estimation formalism

A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX

Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)