Nonlinear $\mathcal {H}_2$ Control for a Nonlinear System With Bounded Varying Parameters: Application to PM Stepper Motors

We have designed a nonlinear <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> controller for permanent magnet stepper motors. The proposed method consists of a new torque modulation scheme, a passive nonlinear observer, and a nonlinear <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math> </inline-formula> controller. The nonlinear torque modulation is incorporated to generate desired torque. The <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> controller and a passive nonlinear observer are independently designed. The use of the passive nonlinear observer allows operation based on only angular position without requiring an additional sensor. The nonlinear <inline-formula><tex-math notation="LaTeX"> $\mathcal {H}_2$</tex-math></inline-formula> controller is developed to improve transient response in the position control. Tracking performance is evaluated in the view point of a linear system. The control gains are linearly scheduled by using interpolation parameters based on a linear matrix inequality approach. A stability of the passive nonlinear observer is proven by using a passivity theorem. The proposed method improves transient response in position tracking and allows evaluation of performance criteria. The performance of the proposed method was validated by means of experimental comparison with a previous method.

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