Speed Control Method for the Working Shaft of the Complex Hydraulic Drive System Based on IFE-WOA Improved Fuzzy PID Controller

Figures & data

Figure 1. The structure of the automatic drive and control part of the complex hydraulic drive system.

Table 1. The main parameters involved in the complex hydraulic drive system.

Parameters	Symbol	Unit	Value
Motor displacement	Dm	m^3·rad^−1	15×10^−6
Hydraulic bulk modulus	β	N·m^−2	20×10^8
Motor leakage coefficient	λ	N·s	5×10^−8
Triangular belt stiffness	k	N·m^−1	20
Radius of driven pulley	r1	m	0.1
Radius of driving pulley	r0	m	0.1
Load inertia	J1	N·m·s^2·rad^−1	50×10^−3
Motor inertia	J0	N·m·s^2·rad^−1	4×10^−3
Proportional valve current	I	mA	100
Supply pressure	p	N·m^−2	5×10^6
Valve front gain	Kv	m^3·s^−1·mA^−1	15×10^−3
Working shaft friction coefficient	f1	N·m·s·rad^−1	0.1
Motor equivalent viscosity coefficient	f0	N·m·s·rad^−1	30×10^−4

Figure 2. The principle of using fuzzy PID control to control the working shaft speed of a complex hydraulic drive system.

Table 2. Fuzzy set partition of linguistic values.

Symbol	Fuzzy Linguistic
S	Small
MS	Medium small
M	Medium
MB	Medium big
B	Big
NB	Negative big
N	Negative
Z	Zero
P	Positive
PB	Positive big

Figure 3. The affiliation function curves of E, EC, ΔKp, ΔKi and ΔKd.

Table 3. Fuzzy rules of ΔK_p.

E	EC
	NB	N	Z	P	PB
NB	S	S	S	MS	M
N	S	MS	MS	MS	M
Z	S	MS	MB	MB	M
P	M	MB	M	MB	B
PB	S	MB	B	B	B

Table 4. Fuzzy rules of ΔK_i.

E	EC
	NB	N	B	Z	PB
NB	B	B	S	B	S
N	B	MB	N	MB	S
PB	MB	MB	MB	MB	S
P	M	MB	MB	MB	B
Z	M	S	MB	B	B

Table 5. Fuzzy rules of ΔK_D.

E	EC
	NB	N	Z	P	PB
NB	S	S	S	MB	B
N	S	MS	MS	M	B
Z	MS	MS	M	MB	B
P	M	MS	MB	MB	B
PB	M	MB	M	B	B

Figure 4. Response sensitivity test results: (a) IFE-WOA-based improved fuzzy PID controller; (b) Fuzzy PID controller.

Figure 5. Random variation speed tracking test results: (a) IFE-WOA-based improved fuzzy PID controller; (b) Fuzzy PID controller.

Figure 6. Tracking input signal variation at randomly varying speeds.