Stability analysis of Fuzzy-Model-Based control systems and its application to control of continuum manipulators

Student thesis: Doctoral ThesisDoctor of Philosophy


This thesis is to investigate the stability analysis problem of fuzzy-model-based (FMB) control systems and its application to continuum manipulator. The stability analysis of T-S FMB control system is conducted on the basis of Lyapunov stability theory relaxed by membership-function-dependent (MFD) approach and extended to some practical control problems, such as control input saturation and guaranteed cost of system indexes, where numerical examples are raised to verify the effectiveness of each proposed fuzzy control method. An example of continuum manipulator is developed to show the process and advantage of applying fuzzy logic and fuzzy-model- based control method to a real complex practical system. The main works and contributions of the thesis are summarized in the following three parts: 
1) The first part of work is presented in Chapter 3. It aims to consider the output feedback tracking control with control input saturation problem under the framework of Takagi-Sugeno (T-S) FMB control. A fuzzy controller is employed to close the feedback loop, which aims to drive the system states to follow those of a stable reference model subject to H∞ performance. To enhance the fuzzy controller design flexibility, the number of rules and premise membership functions are not necessarily required to be the same as those of fuzzy model. To address the control input saturation problem, linear sectors are created by local upper and lower bounds to include the possible control area such that the nonlinear saturation problem can be tackled. Then, the membership-function-dependent (MFD) technique is used to embed the information of membership functions to the stability conditions in the form of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of proposed method dealing with different levels of control input saturation problems. 
2) The second part of the thesis work is presented in Chapter 4. It considers the guaranteed cost stability analysis in the T-S FMB control system. A weighted quadratic cost function is considered as the cost index to measure the performance of the closed-loop system in terms of the system states, system outputs and control signals. The stability of the FMB control system is investigated by the Lyapunov stability theory subject to the minimization of cost index for performance realization. An MFD approach using the piece-wise linear membership 3 functions (PLMFs) technique is employed to include the information of membership functions into the stability analysis. MFD stability conditions in terms of LMIs are obtained to determine the system stability and feedback gains with the consideration of the system performance measured by the cost function. An numerical example is raised to demonstrate the effectiveness and merits of proposed method. 
3) The third part of the work focuses on applying fuzzy logic and FMB control to a practical example of nonlinear systems. Based on the curve geometry of a continuum manipulator, the kinetic and potential energies can be calculated as the integration of the energies regarding to each slice perpendicular to the backbone of the manipulator. By applying Euler-Lagrangian equation of motion, we can obtain the dynamic model of continuum manipulator with the capabilities of bending and contractile. Two traditional nonlinear control methods, namely inverse dynamic control and sliding mode control, are implemented to drive the system states to follow the desired trajectory of a stable reference system. In order to improve the tracking performance and solve the chattering problem particularly in sliding mode control, a fuzzy sliding mode controller is proposed by applying fuzzy logic theory, which varies the value of feedback gains adaptively to the manipulator configurations and successfully attenuates the chattering problem in the traditional sliding mode control method. In order to further apply the FMB control on the practical example of nonlinear systems, the dynamic model of continuum manipulator needs to be transformed to a polynomial fuzzy model, where the fuzzy model of two-link rigid body manipulator is developed preparatively as a relatively simple practical nonlinear system. Then the development polynomial fuzzy model of continuum manipulator is proceeded with necessary simplifications.
Date of Award1 Oct 2019
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorHak-Keung Lam (Supervisor) & Hongbin Liu (Supervisor)

Cite this