Mathematical Models of the Simplest Fuzzy Two-Term (PI/PD) Controllers Using Algebraic Product Inference

Table 1

(a) Outcomes of antecedent part of control rules: using ap AND. (b) Outcomes of antecedent part of control rules: using mn AND. (c) Outcomes of antecedent part of control rules: using ap/mn AND.

(a)

Region	𝑅1	𝑅2			𝑅3
	𝜇−	𝜇0 using			𝜇+
		bs OR	as OR	mx OR
1, 2	𝜇𝐷−⋅𝜇𝑉−	𝜇𝐷−⋅𝜇𝑉++𝜇𝐷+⋅𝜇𝑉−	𝜇𝐷−⋅𝜇𝑉++𝜇𝐷+⋅𝜇𝑉−−𝜇𝐷−⋅𝜇𝐷+⋅𝜇𝑉−⋅𝜇𝑉+	𝜇𝐷+⋅𝜇𝑉−	𝜇𝐷+⋅𝜇𝑉+
3, 4	𝜇𝐷−⋅𝜇𝑉−	𝜇𝐷−⋅𝜇𝑉++𝜇𝐷+⋅𝜇𝑉−	𝜇𝐷−⋅𝜇𝑉++𝜇𝐷+⋅𝜇𝑉−−𝜇𝐷−⋅𝜇𝐷+⋅𝜇𝑉−⋅𝜇𝑉+	𝜇𝐷−⋅𝜇𝑉+	𝜇𝐷+⋅𝜇𝑉+

(b)

Region	𝑅1	𝑅2			𝑅3
	𝜇−	𝜇0 using			𝜇+
		bs⋅OR	as⋅OR	mx⋅OR
1	𝜇𝐷−	𝜇𝐷−+𝜇𝑉−	𝜇𝐷−+𝜇𝑉−−𝜇𝐷−⋅𝜇𝑉−	𝜇𝑉−	𝜇𝑉+
2	𝜇𝐷−	𝜇𝐷++𝜇𝑉+	𝜇𝐷++𝜇𝑉+−𝜇𝐷+⋅𝜇𝑉+	𝜇𝐷+	𝜇𝑉+
3	𝜇𝑉−	𝜇𝐷++𝜇𝑉+	𝜇𝐷++𝜇𝑉+−𝜇𝐷+⋅𝜇𝑉+	𝜇𝑉+	𝜇𝐷+
4	𝜇𝑉−	𝜇𝐷−+𝜇𝑉−	𝜇𝐷−+𝜇𝑉−−𝜇𝐷−⋅𝜇𝑉−	𝜇𝐷−	𝜇𝐷+

(c)

Region	𝑅1	𝑅2	𝑅3
	𝜇−	𝜇0 using	𝜇+
		bs/as/mx OR
5	0	𝜇𝑉−	𝜇𝑉+
6	𝜇𝐷−	𝜇𝐷+	0
7	𝜇𝑉−	𝜇𝑉+	0
8	0	𝜇𝐷−	𝜇𝐷+
9	0	0	1
10, 12	0	1	0
11	1	0	0