Adaptive fuzzy terminal sliding-mode control of MEMS z-axis gyroscope with extended Kalman filter observer

Figures & data

Figure 1. Dynamical model of MEMS z-axis gyroscope.

Figure 2. Membership functions (a) sliding surface, (b) derivative of sliding surface and (c) reaching control.

Figure 3. Membership functions (a) error, (b) rate of error and (c) reaching control gain.

Figure 4. Control forces by AFTSMC and comparison of adaptations by AFSMC and AFTSMC with EKF.

Table 1.  Rule base of AFSMC.

	NB	NM	NS	Z	PS	PM	PB
NB	NB	NB	NM	NS	PS	PS	PS
NM	NB	NM	NM	NS	PS	PS	PS
NS	NM	NM	NS	NS	PS	PS	PM
Z	NM	NM	NS	Z	PS	PM	PM
PS	NM	NS	NS	PS	PS	PM	PM
PM	NS	NS	NS	PS	PM	PM	PB
PB	NS	NS	NS	PS	PM	PB	PB

Table 2.  Rule base for adaptation of the reaching control gain K_f.

	NB	NM	NS	Z	PS	PM	PB
NB	M	MS	S	Z	S	MS	M
NM	MB	M	MS	S	MS	M	MB
NS	B	MB	M	MS	M	MB	B
Z	VB	B	MB	M	MB	B	VB
PS	B	MB	M	MS	M	MB	B
PM	MB	M	MS	S	MS	M	MB
PB	M	MS	S	Z	S	MS	M

Table 3.  The MEMS gyroscope parameters used in simulation.

Parameter	Value	Unit
M		kg
dx		Ns/m
dxy		Ns/m
dy		Ns/m
kx	80.98	N/m
kx3		N/m^3
kxy	5	N/m
ky	71.62	N/m
ky3		N/m^3
w0	1	kHz
q0		m