Research On Intelligent Fuzzy Control Theory For Monotone Inertia Systems

Intelligent fuzzy control theory significantly lags behind the development of the techniques at present. That can be seen in several aspects as follows. The properties of the fuzzy control methods themselves need deep studying. Since most results on fuzzy control stability derive from the modeling methods, it is difficult to use them analyzing practical systems with no available models. There are no effective methods to analyze the dynamic and steady features of the system; Besides, most of various control methods based upon the Mamdani stagnate on the level which is only limited to some specific plants controlled, but lack systematic designing and analyzing methods. This paper focuses on some in-depth discussions in the several aspects toward some objects dealt with frequently.To study control systems whose control variables change in the form of steps, the function of system response process is proposed, which is defined with the parameters of the control jumping sequence. Based on the response process function, the "Monotone Inertia System" is put forward. It is abstracted from a kind of objects frequently dealt with in which the relation between the output and the input is of monotone and time inertia.For a monotone inertia system, the monotonicity of a control algorithm is naturally requested, which is important in analyzing the stability of the monotone inertia fuzzy control system. Based on the concept of monotone rulebase proposed in this paper, the monotonicity of the conventional fuzzy control algorithm is discussed in detail with direct analysis methods. Analysis shows that as long as the rulebase is monotone and the output fuzzy sets of the rules in the rulebase are fuzzy numbers in the shape of bending isoceles triangle, the one dimensional conventional Mamdani fuzzy control algorithm (conventional Mamdani fuzzy control algorithm, written as CMA for short) is monotone. The two dimensional CMA based on monotone rulebase may not be monotone, but is rough monotone if the output fuzzy sets of the rules in the rulebase are bending isoceles triangles. Rough monotone means that the monotonicity of the algorithm holds if the distance between the two input states is long enough. From the practical point of view, a sufficient condition for the monotonicity of the two dimensional CMA is presented. The influence of the input and output fuzzy sets used in the rulebase on the monotonicity of the control algorithm and on the output of the control algorithm is discussed. Research shows that the influence of the grading fuzzy numbers of the input universe on the output of the control algorithm is only in relation to the relatively "fat" or "thin" of the adjoiningfuzzy numbers. The research also shows that the monotonicity of the two dimensional CMA may also be destroyed if the grading fuzzy numbers of the output universe are set improperly. As to the monotone inertia system, a theorem for the existence of the exact grading fuzzy numbers is obtained: for any monotone control function of the system with single variable, there exists an one dimensional CMA equivalent to the function. Furthermore, by means of the matching between the base points of the rules and the object controlled, an estimation to the maximum error between the system and the control algorithm is presented. An operational quantitative analysis method to determine the density of the rules is proposed.In this paper, a method to analyze and design the stability of fuzzy control systems is presented for the monotone inertia systems. It does not depend on the development of an accurate mathematics model. The polestar of this method is to learn from human control,which means to improve and generalize the simple control rule------"If system state is Athen the control action is B" to one with more information, which also means to estimate the dynamic range of the systems controlled only by the rulebase with the help of experimental data (crisp or fuzzy) so as to deduce and estimate the dynamic features of the fuzzy control systems; then, the quantitative description for compelling stable strategy can be made by means of the qualitative model of the systems and the analysis of response trend of the systems. What is more, the intelligent fuzzy control strategy is presented which integrates the fuzzy control algorithm with the compelling stable strategy organically. With the help of the strategy, the intelligent human-like control ideas can be actualized, and the stability of the intelligent fuzzy control system can be guaranteed.Based on the ideas above, the full information control rule (which includes not only the fuzzy relation between system state and proper control input but also the acting time of the rule, the transition shape of the state within the acting time and the prospective state after the acting time as well as the measures dealing with some abnormal cases) is brought forward. Some concepts derived from the full information control rule are also introduced, such as the effectual rule (the result state of the rule differs distinctly from its input state), the hegemony rule, the input and output hegemony regions of a rule, the rule chain ( i.e. a sequence of rules that the former' resulting region intersects with the latter's input hegemony region) etc. By means of these concepts, the OK resonant stability of rulebase control systems is discussed in detail. A sufficient and necessary condition for the OK resonant stability of the rulebase control system is obtained. It is proved that a rulebase control system is OK resonance stable if and only if the length of any rule chain starting from any state in the state universe is finite and the last rule of the chain is theOK rule (which keeps its own resonance region and input hegemony region). A method is presented to judge the stability of a rulebase control system. Based on the acting time of the rules, both the settling time starting from an bounded initial state and the maximum settling time are obtained for the rulebase control system. The steady state error is also obtained by means of the hegemony region of the OK rule. Besides, to find the dynamic features of a system controlled by the CMA, the concept of compatibility between a fuzzy algorithm and its rulebase is proposed. After discussing adequately the compatibility between the CMA and the rulebase control method, by using of the "mere stone" function of the base points in the rulebase, the dynamic range and the steady state error are obtained for the monotone inertia system controlled by a monotone fuzzy control algorithm. So that some important parameters used to describe the performances of the fuzzy control system can be quantitatively described.To actualize the idea of intelligent human-like control, two concepts characterizing the response features of the system are proposed. They are the curve shape function vector and the aberrant point of the curve states. The dynamic trend features concerning the output of the monotone inertia system is discussed in detail when its control input changes in steps. The number and the attribute as well as the arranging sequence of the aberrant points in the normal response process of the monotone inertia system are also pointed out. Those can be used to construct an easy way to distinguish the normal process from abnormal process for the computer program of the intelligent fuzzy control algorithm. Based on the above work, the compelling stable control strategy is introduced. Analysis shows that the monotone inertia systems controlled by the strategy are stable. Combine the strategy with the CMA, an intelligent fuzzy control method (written as IFM for short) for the monotone inertia systems is presented. The method has some good features such as control period selected intelligently, the algorithm output adjusted intelligently and intrinsic control stability as well as steady state error-free, etc.To verify the theories proposed in this paper, the IFM and the CMA are applied to a fast gas-fired water heater respectively and the output response curves and data are recorded. Testing results shows the measuring data coincide with theory analysis. Comparison between the system output curves controlled by the IFM and that controlled by the CMA obtained under same working conditions gives that the IFM is superior to the CMA distinctly. The testing results also indicate that the intelligent fuzzy control method has strong resistance to periodical disturbances.