Proof。 Substituting (27) into (26), a chain of interconnected track- ing error dynamics can be derived
ity using a recursive procedure from the strict feedback nonlinear
where xi "i 2 [1, n], y, and u are the state, the output and the input of i þ
system, respectively, and gi(x), "i 2 [1, n] is nonzero for all x。
Using giei+1 as the input and ei as the output in (30) gives
770 W。 Kim et al。 / Mechatronics 22 (2012) 766–777
PMSM, controller, and observer parameters。
|ifflffln{pzuffltffl} o|u{tpzu}t
|P{z0}
Parameter Value Parameter Value
Then (31) shows that the relationship between ei and ei+1 is
strictly output passive [34] and e_ i ¼ —ki ei 8i 2 ½1; 4] is zero-state
observable。 Therefore, each subsystem is bounded input bounded output (BIBO) stable for "i 2 [1, 4]。 Serial interconnections of BIBO stable system are also BIBO stable。 Further, the 5th tracking error dynamics becomes
k 5。651 × 105 b 0
h1 7。1693 × 109 h2 3。2569 × 1010
h3 2。1456 xn 950
f 0。5 Kv 1。3333 × 10—5
k1 3000 k2 2500
k3 2300 k4 50
e_ 5 ¼ —k5e5: ð32Þ
Consequently e5 converges exponentially to zero at the conver- gence rate k5 and ei converges to zero "i 2 [1, 4]。 h
Remark 3。 The tracking performance of the proposed controller
(27) requires parameters。 Therefore, it is important to know the accuracy values of parameters。 The tracking performance of the proposed controller (27) is most sensitive to the ratio of hydraulic parameters h2/h1 [38]。 If we obtain the information of full state, the parameters h1 and h2 can be easily estimated using the adaptation algorithms [38,39]。 More detailed analysis is beyond the scope of this paper, but is given in [40]。
From (23), the control law (27) can be rewritten as
u ¼ u。x; xd 。;
8
k5 100 l1 837。7153
l2 3。5088 × 105 l3 8。5148 × 1010
l4 0。3188 l5 0。3162
KP 1500 KI 20
Kff 100
> 4 ¼ h1 pffiPffisffiffi—ffiffitffiaffiffinffiffihffiffiðffirffixffi4ffiffiÞffixffiffi3ffi 电液系统的输出反馈非线性控制英文文献和中文翻译(6):http://www.youerw.com/fanyi/lunwen_96540.html