Nonlinear Dynamic Model-Based Adaptive Control of a Solenoid-Valve System

Table 1

Regression and parameter estimation terms.

No.	Terms	No.	Terms
𝑊101	𝑥̈𝑑	𝑊113	𝐶𝑅(𝛼)𝑥
𝑊102	𝑥̈𝑑𝑥	𝑊114	𝑇𝑐(𝛼)[𝑉𝐽(𝛼)/𝑉𝑂]^2𝑥^2
𝑊103	𝑥̈𝑑𝑥^2	𝑊115	𝐶𝑅(𝛼)𝑥^2
𝑊104	𝑥̇	𝑊116	𝑥̇𝑒̇
𝑊105	𝑥̇𝑥	𝑊117	𝑥̇𝑒
𝑊106	𝑥̇𝑥^2	𝑊118	𝑥𝑥̇𝑒̇
𝑊107	𝑥	𝑊119	𝑥𝑥̇𝑒
𝑊108	𝑥^2	𝑊120	𝑒
𝑊109	𝑥^3	𝑊121	𝜆1𝑒̇
𝑊110	𝑇𝑐(𝛼)[𝑉𝐽(𝛼)/𝑉𝑂]^2	𝑊122	𝜆1𝑥𝑒̇
𝑊111	𝐶𝑅(𝛼)	𝑊123	𝜆1𝑥^2𝑒̇
𝑊112	𝑇𝑐(𝛼)[𝑉𝐽(𝛼)/𝑉𝑂]^2𝑥	—	—
Θ101	𝑀𝑠2𝐶^21/(𝐶2𝑁^2)	Θ113	𝑇̂‌𝑏14𝐶1/(𝑟𝑔̂𝑁^2)
Θ102	𝑀𝑠4𝐶1/𝑁^2	Θ114	𝑇̂‌ℎ12𝐶2/(𝑟𝑔̂𝑁^2)
Θ103	𝑀𝑠2𝐶2/𝑁^2	Θ115	𝑇̂‌𝑏12𝐶2/(𝑟𝑔̂𝑁^2)
Θ104	𝐶𝑠2𝐶^21/(𝐶2𝑁^2)	Θ116	𝑀𝑠2𝐶1/𝑁^2
Θ105	𝐶𝑠4𝐶1/𝑁^2	Θ117	𝑀𝑠2𝐶1/𝑁^2
Θ106	𝐶𝑠2𝐶2/𝑁^2	Θ118	𝑀𝑠2𝐶2/𝑁^2
Θ107	𝑘̂‌2𝐶^21/(𝐶2𝑁^2)	Θ119	𝑀𝑠2𝐶2/𝑁^2
Θ108	𝑘̂‌4𝐶1/𝑁^2	Θ120	1/𝑟^2𝑔
Θ109	𝑘̂‌2𝐶2/𝑁^2	Θ121	𝑀𝑠2𝐶^21/(𝐶2𝑁^2)
Θ110	𝑇̂‌ℎ12𝐶^21/(𝑟𝑔̂𝐶2𝑁^2)	Θ122	𝑀𝑠4𝐶1/𝑁^2
Θ111	𝑇̂‌𝑏12𝐶^21/(𝑟𝑔̂𝐶2𝑁^2)	Θ123	𝑀𝑠2𝐶2/𝑁^2
Θ112	𝑇̂‌ℎ14𝐶1/(𝑟𝑔̂𝑁^2)	—	—