In order to consider saturation in electric motor, the antiwindup algorithm presented selleck screening library in Figure 8 also applies to the adaptive antiwindup PID sliding mode control scheme.The PID sliding surface �� for the design of the adaptive sliding mode control system is defined as [29�C32]��=k1e+k2��e?dt+k3e�B,(18)where the tracking error of the position e = xd ? x, x is the displacement of hydraulic cylinder and k1, k2, and k3 are positive design parameters. The sliding mode control law consists of equivalent and robust control term; that is,��p=��p,eq+��p,robust.(19)By combining (11) and (18) with consideration of the noise term in the jerk x?=x?m+x?n, the derivative of the sliding surface �ƨB can be written as�ƨB=?k3ADp��eBV0+CTDpM��e��p+k3MV0BV0+CTDpM��e(x?m+x?n)+k3(A2+BCTDp)��eBV0+CTDpM��ex�B+k3x��d+k1e�B+k2e+k3BV0+CTDpM��ef,(20)where f=f1+(CT/A)f2+(V0/ADp��e)f�B2 is lumped uncertain nonlinearities of the EHA system and the subscripts m and n denote the nominal and noisy values, respectively.

To determine the equivalent control term ��p,eq, the noise term in the jerk is neglected, and it is assumed that the sliding surface �� is at steady-state, that is, �ƨB=0, and then the equivalent control law can be +k1k3e�B+k2k3e+x��d}.(21)Thus,??determined as��p,eq=BV0+CTDpM��eADp��e��+K0>+D��+Ksgn(��).