Fuzzy Gain Scheduling and Tuning of Multivariable Fuzzy Control—Methods of Fuzzy Computing in Control Systems

The thesis deals with fuzzy computing in control systems and particularly in multivariable control and gain scheduling. It addresses research problems as to how to apply methods of fuzzy set theory efficiently in control tasks, and how to tune a fuzzy controller. The problem is solved by analyzing properties of fuzzy sets and fuzzy systems, selecting a structure for the fuzzy system, and packaging the system in a compact parameterized presentation. The thesis has two main results. It proposes a multivariable fuzzy controller aimed to control a stable, two-input two-output system. Also a method to automate a rule base updating in a fuzzy gain scheduling scheme is developed. In the thesis, fuzzy logic is not considered as a logic, but as a computing method. Fuzzy systems are considered from two points of view. First the system has linguistic representation with linguistic variables and fuzzy if-then rules. On the other hand, fuzzy logic is used as a numerical method to create a nonlinear mapping between inputs and outputs. Some special properties of fuzzy systems are discussed in more detail. Transparency and locality of design parameters of the fuzzy system are important properties and it is not worthwhile to lose them with careless design of the system. Therefore a structure and a parameterization is proposed for fuzzy computing systems. Interpolation behaviour of different implementations in fuzzy reasoning is discussed. It is shown that under certain assumptions the fuzzy system is piece-wise multi-linear which ensures well-behaved interpolation. The assumptions are less restrictive than presented in earlier literature. Practical advice for the design and tuning of fuzzy controllers are given. Input fuzzy sets should be placed according the nonlinearity needed. Each rule should have an individual fuzzy set as a consequence that clustering of the rules can be avoided and the controller can be tuned locally. A systematic method to tune a multivariable fuzzy controller for an unknown two-input two-output process is developed. The method groups the rules for two rule bases which are tuned with different objectives. Thus, a good control performance is obtained and also the total number of the rules can be kept small. The design is based on a scheme of dominant rules. The consequences of the rules are designed for a situation where the rule is dominant. Conventional control and fuzzy computing is combined together in the scheme of fuzzy gain scheduling. Tuning parameters of the controller are stored in a fuzzy rule base beforehand, and during control the fuzzy system gives suitable parameter values for the controller. In addition to the process output, the reference signal is also used as a scheduling variable in order to predict near future operation conditions. A method is proposed to keep the rule base up-to-date. When the controller is retuned