- Title
- A set-theoretic approach to sensor fault tolerant control of constrained linear parameter varying systems
- Creator
- McCloy, Ryan
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2018
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- One of the traditional motivators for the use of constrained optimisation in control systems has been its ability to handle safety constraints and equipment limitations over conventional control technologies, whereby operation close to such constraints is often most profitable or efficient. Driven by this, combined with advances in computing power and the development of analytical tools, academic interests have paved the way for expanding practical applications. In competitive markets where efficiency and performance are key, optimisation based control techniques are becoming increasingly popular. Although linear analysis and control tools have been widely studied, nonlinear solutions are still largely under development. The linear parameter varying framework is attractive as it allows for the use of powerful linear design tools to a wide range of complex nonlinear systems. Linear parameter varying models also have a close relationship with gain-scheduling control, which is a well-defined control strategy for a large class of nonlinear systems. The development of techniques to assess linear parameter varying system stability has also motivated the use of this modelling paradigm. Many of these techniques allow for the use of efficient computation methods, such as linear matrix inequality based routines. Whilst performance requirements are essential, another key feature to modern control system design is the robustness and stability of the design. With a heavy reliability upon the plant model in optimised control, it is significantly important to be able to efficiently handle a range of possible system faults/failures. With this in mind, exploration of new methodologies to ensure closed-loop stability, constraint satisfaction and robustness of design to system faults is a lively, interesting and useful topic for modern control system designers. The problems of stability, robustness, and fault tolerance, especially in model predictive control, are very much open problems for nonlinear systems, with no well-defined solution. As such, there is a great realm of opportunity for research and contribution to these areas. This thesis is then concerned with the development of sensor fault tolerant control strategies for mulitsensor constrained linear parameter systems. Fault tolerance is achieved via an invariant set-theoretic approach, in which, appropriately selected residual variables converge to sets based on the healthy or faulty behaviour of corresponding sensors. The established methodologies incorporate this set-based fault detection and isolation strategy combined with an estimate-based controller reconfiguration. Full mathematical description and proof for the robust stability of systems with convex polytopic uncertainty through the construction of attractive invariant sets is obtained. This result is an adaptation from switched systems and is particularly useful for systems modelled using the linear parameter varying framework. Initially, faulty sensors are detected and discarded from the control law utilising the developed analytical tools. The problem and comparison of several solutions of estimating convergence times to invariant sets is investigated as an extension of the set-theoretic tools. Using convergence time estimates, the overall approach is then naturally progressed to permit sensor reintegration, by detecting and tracking the transitions and set-membership of residual signals associated with faulty and recovered sensor behavior. Continuing with the set-theoretic nature of the overall approach, a tube-based model predictive controller is then integrated into the design methodology to provide constraint satisfaction. Driven by a tube-based model predictive control generated reference, conditions are formulated which guarantee satisfaction of hard constraints by defining tubes with cross sections that will contain the predicted state trajectory. Under this approach, bounded disturbances and model uncertainty can also be accounted for by forcing the nominal system to adhere to tighter constraints. Hence, this thesis provides certificates for assessing the robust stability of constrained linear parameter varying systems, in the presence of disturbances, model uncertainty, sensor faults and sensor recovery. Capabilities for instantaneous fault detection and guaranteed closed-loop stability in the presence of hard constraints is provided, whilst permitting the reintegration of recovered sensors with guaranteed convergence times. Simulated and experimental verification of the developed strategies is provided to demonstrate the performance characteristics and preservation of closed-loop stability through the implementation and testing of targeted applications. Although linear analysis and control tools have been widely studied, nonlinear solutions are still largely under development. The linear parameter varying framework is attractive as it allows for the use of powerful linear design tools to a wide range of complex nonlinear systems. Linear parameter varying models also have a close relationship with gain-scheduling control, which is a well-defined control strategy for a large class of nonlinear systems. The development of techniques to assess linear parameter varying system stability has also motivated the use of this modelling paradigm. Many of these techniques allow for the use of efficient computation methods, such as linear matrix inequality based routines. Whilst performance requirements are essential, another key feature to modern control system design is the robustness and stability of the design. With a heavy reliability upon the plant model in optimised control, it is significantly important to be able to efficiently handle a range of possible system faults/failures. With this in mind, exploration of new methodologies to ensure closed-loop stability, constraint satisfaction and robustness of design to system faults is a lively, interesting and useful topic for modern control system designers. The problems of stability, robustness, and fault tolerance, especially in model predictive control, are very much open problems for nonlinear systems, with no well-defined solution. As such, there is a great realm of opportunity for research and contribution to these areas. This thesis is then concerned with the development of sensor fault tolerant control strategies for mulitsensor constrained linear parameter systems. Fault tolerance is achieved via an invariant set-theoretic approach, in which, appropriately selected residual variables converge to sets based on the healthy or faulty behaviour of corresponding sensors. The established methodologies incorporate this set-based fault detection and isolation strategy combined with an estimate-based controller reconfiguration. Full mathematical description and proof for the robust stability of systems with convex polytopic uncertainty through the construction of attractive invariant sets is obtained. This result is an adaptation from switched systems and is particularly useful for systems modelled using the linear parameter varying framework. Initially, faulty sensors are detected and discarded from the control law utilising the developed analytical tools. The problem and comparison of several solutions of estimating convergence times to invariant sets is investigated as an extension of the set-theoretic tools. Using convergence time estimates, the overall approach is then naturally progressed to permit sensor reintegration, by detecting and tracking the transitions and set-membership of residual signals associated with faulty and recovered sensor behavior. Continuing with the set-theoretic nature of the overall approach, a tube-based model predictive controller is then integrated into the design methodology to provide constraint satisfaction. Driven by a tube-based model predictive control generated reference, conditions are formulated which guarantee satisfaction of hard constraints by defining tubes with cross sections that will contain the predicted state trajectory. Under this approach, bounded disturbances and model uncertainty can also be accounted for by forcing the nominal system to adhere to tighter constraints. Hence, this thesis provides certificates for assessing the robust stability of constrained linear parameter varying systems, in the presence of disturbances, model uncertainty, sensor faults and sensor recovery. Capabilities for instantaneous fault detection and guaranteed closed-loop stability in the presence of hard constraints is provided, whilst permitting the reintegration of recovered sensors with guaranteed convergence times. Simulated and experimental verification of the developed strategies is provided to demonstrate the performance characteristics and preservation of closed-loop stability through the implementation and testing of targeted applications.
- Subject
- LPV; linear parameter varying systems; FTC; fault tolerant control; invariant sets; MPC; model predictive control; thesis by publication
- Identifier
- http://hdl.handle.net/1959.13/1398743
- Identifier
- uon:34484
- Rights
- Copyright 2018 Ryan McCloy
- Language
- eng
- Full Text
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