Performance Guarantee of a Class of Continuous LPV System with Restricted-Model-Based Control

This paper considers the problem of the robust stabilisation of a class of continuous Linear Parameter Varying (LPV) systems under specifications. In order to guarantee the stabilisation of the plant with very large parameter uncertainties or variations, an output derivative estimation controller is considered. The design of such controller that guarantee desired  induced gain performance is examined. Furthermore, a simple procedure for achieving the  norm performance is proved for any all-poles single-input/single-output second order plant. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. Finally, the effectiveness of the proposed method is verified via a numerical example

Adaptive Control of MEMS Gyroscope Based on T-S Fuzzy Model

A multi-input multioutput (MIMO) Takagi-Sugeno (T-S) fuzzy model is built on the basis of a nonlinear model of MEMS gyroscope. A reference model is adjusted so that a local linear state feedback controller could be designed for each T-S fuzzy submodel based on a parallel distributed compensation (PDC) method. A parameter estimation scheme for updating the parameters of the T-S fuzzy models is designed and analyzed based on the Lyapunov theory. A new adaptive law can be selected to be the former adaptive law plus a nonnegative in variable to guarantee that the derivative of the Lyapunov function is smaller than zero. The controller output is implemented on the nonlinear model and T-S fuzzy model, respectively, for the purpose of comparison. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme and the correctness of the T-S fuzzy model

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS) approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method

Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

Intelligent adaptive control for nonlinear applications

The thesis deals with the design and implementation of an Adaptive Flight Control technique for Unmanned Aerial Vehicles (UAVs). The application of UAVs has been increasing exponentially in the last decade both in Military and Civilian fronts. These UAVs fly at very low speeds and Reynolds numbers, have nonlinear coupling, and tend to exhibit time varying characteristics. In addition, due to the variety of missions, they fly in uncertain environments exposing themselves to unpredictable external disturbances. The successful completion of the UAV missions is largely dependent on the accuracy of the control provided by the flight controllers. Thus there is a necessity for accurate and robust flight controllers. These controllers should be able to adapt to the changes in the dynamics due to internal and external changes. From the available literature, it is known that, one of the better suited adaptive controllers is the model based controller. The design and implementation of model based adaptive controller is discussed in the thesis. A critical issue in the design and application of model based control is the online identification of the UAV dynamics from the available sensors using the onboard processing capability. For this, proper instrumentation in terms of sensors and avionics for two platforms developed at UNSW@ADFA is discussed. Using the flight data from the remotely flown platforms, state space identification and fuzzy identification are developed to mimic the UAV dynamics. Real time validations using Hardware in Loop (HIL) simulations show that both the methods are feasible for control. A finer comparison showed that the accuracy of identification using fuzzy systems is better than the state space technique. The flight tests with real time online identification confirmed the feasibility of fuzzy identification for intelligent control. Hence two adaptive controllers based on the fuzzy identification are developed. The first adaptive controller is a hybrid indirect adaptive controller that utilises the model sensitivity in addition to output error for adaptation. The feedback of the model sensitivity function to adapt the parameters of the controller is shown to have beneficial effects, both in terms of convergence and accuracy. HIL simulations applied to the control of roll stabilised pitch autopilot for a typical UAV demonstrate the improvements compared to the direct adaptive controller. Next a novel fuzzy model based inversion controller is presented. The analytical approximate inversion proposed in this thesis does not increase the computational effort. The comparisons of this controller with other controller for a benchmark problem are presented using numerical simulations. The results bring out the superiority of this technique over other techniques. The extension of the analytical inversion based controller for multiple input multiple output problem is presented for the design of roll stabilised pitch autopilot for a UAV. The results of the HIL simulations are discussed for a typical UAV. Finally, flight test results for angle of attack control of one of the UAV platforms at UNSW@ADFA are presented. The flight test results show that the adaptive controller is capable of controlling the UAV suitably in a real environment, demonstrating its robustness characteristics