《智能控制》课程教学资源（试卷习题）Exercise 2-4 Inverted Pendulum：Rule-Base Modifications

Exercise 2. 4(Inverted Pendulum: Rule- Base Modifications ): In this problem we will study the effects of adding rules to the rule- base. Suppose that we use seven triangular membership functions on each universe of discourse and make them uniformly distributed in the same manner as how we did in Exercise 2.3. In particular make the points at which the outermost input membership functions for e saturate at +r/2 and for e at tr/4 For u make the outermost ones have their peaks at#20 (a)Define a rule-base (ie, membership functions and rules) that uses all possible rules, and provide rule-base table to list all of the rules(make an appropriate choice of the linguistic-numer ic values for the premise terms and consequents ) There should be 49 rules b) Use triangular membership functions and repeat Exercise 2.3(a),(b),(c),(d),(e)(but provide the impl ie fuzzy sets for the four rules that are on), (f),(g)(but use all four imp lied fuzzy sets in the CoG computat ion),(h), (a)、 23322 2 02210122 3 122333 (b) 0 1.5 error 05 0 0.5 ource 520-15-105

Exercise 2.4 (Inverted Pendulum: Rule-Base Modifications): In this problem we will study the effects of adding rules to the rule-base. Suppose that we use seven triangular membership functions on each universe of discourse and make them uniformly distributed in the same manner as how we did in Exercise 2.3. In particular, make the points at which the outermost input membership functions for e saturate at  /2 and for e at  /4 . For u make the outermost ones have their peaks at ±20. (a) Define a rule-base (i.e., membership functions and rules) that uses all possible rules, and provide a rule-base table to list all of the rules (make an appropriate choice of the linguistic-numeric values for the premise terms and consequents). There should be 49 rules. (b) Use triangular membership functions and repeat Exercise 2.3 (a), (b), (c), (d), (e) (but provide the implied fuzzy sets for the four rules that are on), (f), (g) (but use all four implied fuzzy sets in the COG computation), (h), and (i). Exercise2.4 （a）、 error -3 -2 -1 0 1 2 3 -3 3 3 3 2 2 1 0 -2 3 3 2 2 1 0 -1 -1 3 2 2 1 0 -1 -2 0 2 2 1 0 -1 -2 -2 1 2 1 0 -1 -2 -2 -3 2 1 0 -1 -2 -2 -3 -3 3 0 -1 -2 -2 -3 -3 -3 （b）、 a

0.5 0.4 2 0 0.E 5 -05 hange in error error 0.8 0.5 0.4 0.2 0 errol

b. c. d

规则1. Iferror is"o” and change- In-error Is"l” Then force is“-l” 规则2. If error is“o” and change- In-error Is“2” Then force is“-2 output =-7 74 5708 15708 07854 07854 66667 26666 其中 inputI为 error Inpu2为 change-in-error outputI为 force 规则: If error is"” and change-in- error Is"l” Then force is“-2”, If error is"I” and change- .in-error Is“2” Then force is“-2”, If error is"2” and change-in- error Is“" Then force is“-2” If error is"2” and change- In-error Is“2” Then force is“-3” 0.785 output =-167 15708 .7854 0.7854 26.6667 66667 所做结果如d图所示。 force=7.74 所做结果如e图所示。 force=-167

规则 1. If error is “0” and change-in-error is “1” Then force is “-1”; 规则 2. If error is “0” and change-in-error is “2” Then force is “-2”. 其中 input1 为 error input2 为 change-in-error output1 为 force e. 规则：If error is”1” and change-in-error is “1” Then force is “-2”; If error is”1” and change-in-error is “2” Then force is “-2”; If error is”2” and change-in-error is “1” Then force is “-2”; If error is”2” and change-in-error is “2” Then force is “-3”; f. 所做结果如 d 图所示。force=-7.74 g. 所做结果如 e 图所示。force=-16.7

10 inp input1 -10 0.5 input2 ut1

h. i