【正文】 Control performance.2. IntroductionFuzzy control was first applied by Mamdani to control a steam engine and this served as the starting point for practical application. The fuzzy inference method used by Mamdani was the “direct inference method”, which is currently the most frequently used method. However, in this method, inference is timeconsuming because many calculations are involved in the fuzzy inference process, and the number of rules generally increases. Therefore, to solve this problem, fuzzy inference methods such as the “indirect inference method” proposed by Tsukamoto, which is capable of highspeed inference, and the “simplified indirect inference method” have been proposed for fuzzy control.The advantage of these fuzzy control methods is that improvement of the transient characteristic of control performance and control with excellent robustness can be easily realized. However, because fuzzy control is essentially nonlinear and a general design method for nonlinear control has not yet been established, it is extremely difficult to establish a systematic design method for fuzzy control. There is also a problem in that the stability and accuracy of fuzzy control systems are mot necessarily guaranteed.On the other hand, stability is theoretically guaranteed in PID control, which is a representative method of linear control, and it is said that highaccuracy control is possible, especially in the steadystate characteristic region. However, PID control has a problem in that it cannot take fully into account, for example, the influence of nonlinear characteristics when a controlled system is in the transient characteristic region.Therefore, in this paper, to solve these problems in fuzzy and PID controls and to utilize the advantages of both methods and their mutual pensation, a “hybrid control method” is proposed.It is proposed that fuzzy and PID controls are bined in parallel, using fuzzy control in the transient characteristic region and PID control in the steady state characteristic region. Moreover, smooth control during switching is guaranteed by executing the change using fuzzy inference (. fuzzy switching). Also, to increase the speed of control, the “simplified indirect inference method” which is capable of highspeed inference is used as the fuzzy inference method instead of the general “direct inference method”.Therefore, first, the “simplified indirect inference method” is explained, and then the configuration of the proposed hybrid control system is described. Next, the inference procedure in this hybrid control method is described, and it is shown that highspeed control is possible because the number of rules can be sharply contracted and the final inference result can be obtained in a functional form. Finally, using the results of simulations for first and secondorder lag systems with dead time, the effectiveness of this hybrid control method is pared with that of PID control.A method in which fuzzy and PD controls were bined in parallel was previously proposed by Matsunaga et al. However, in their method the changes were executed alternately (. crisp switching) and hence smooth control during switching was very difficult. Also, because there was no Icontrol in the configuration, the steadystate error remained. Moreover, because the “direct inference method” was used as the fuzzy inference method, the execution speed of control was limited. Besides the above method, Ishida also proposed a method in which fuzzy control using the “direct inference method” and PI control were bined in parallel. However, the control performance was limited because there was no Dcontrol in the configuration.3. Simplified indirect inference methodThe “simplified indirect inference method” is based on the original “indirect inference method” proposed by Tsukamoto to make it better suited to fuzzy control. The “simplified indirect inference method” uses the monotonic membership functions, where an arctan is function and is a linear function. Normally, the arctan functions are used in the antecedent part of the control rules, and the linear functions are used in the consequent part. E is the error, and △U is the onelevel difference of the manipulated variable. P. and N. indicate the positive and negative fuzzy variables, respectively.4. Configuration of hybrid control systemWhereas the “direct inference method” was used as the fuzzy inference method by Matsunaga et al., the “simplified indirect inference method” which is capable of highspeed inference is adopted here to increase the speed of the fuzzy controller. Also, the switching method between fuzzy and PID controls used in the scheme of Matsunaga et al. was crisp switching in a certain range of error and onelevel error difference, which the authors use fuzzy switching here in order to achieve smooth control during switching. The “fuzzy switching control rule” used to execute this fuzzy switching is shown below. This control rule is used to fuzzily switch the control to PID control in the steadystate characteristic region close to the target value, and to fuzzy control in the transient characteristic region as in the case of the rising of a control response.Here, is the onelevel difference of the manipulated variable, which is an output from the aped controller, and is that from the fuzzy controller. Also, the fuzzy variable ( i=1, 2) indicates the “fuzzy switching membership function”. This membership function and the execution region of fuzzy switching can be set by defining its shape in terms of the error E and the onelevel error difference.5. Simulation examplesUsing the results of a simulation in which first and secondorder lag systems with dead time are employed as the controlled system, the effectiveness of this hybrid control method is pared with that of PID control.Here, the transfer function given by the following equation is used as the firstorder lag syste