Stability and gain analysis of 𝐋𝟐 for non-small delay systems with inputoutputmethod on permanent magnet synchronous motor

In this paper, the drive efficiency of a permanent magnet synchronous motor withdirect torque control is improved through a new delay-dependent adjusting structure.The proposed structure is based on the gain controller L۲ non-small delay with inputoutputmethod, which is calculated with a feedback linear controller and by the smallgain theorem, the upper L۲ norm band of the system is calculated to ensure stability.The law of linear feedback also compensates for the nonlinear effect of motordynamics and makes it possible to use linear controllers for the flux and torque loops.The proposed hybrid structure is introduced by an indefinite delay and two delaymodes with finite and unlimited variations are considered. The proposed method isbased on Lyapunov's theory and its coefficients are optimally designed, all of whichtogether produce high torque at low speeds, reduce ripple flux and torque, and reducecurrent distortion in the motor drive. This method has been tested by simulation on aSiemens engine and compared with other similar methods based on direct torquecontrol.abstract appears before the keywords.