## Direct Torque Control Stability Conditions and Compensation Methods

**Veysel T. Buyukdegirmenci with advisor P. T. Krein**

Our research goal is to obtain a highperformance, well-conditioned induction machine control with wide operating speed ranges. Direct torque control (DTC) gives the least parameter dependency but exhibits erratic behavior under high-speed and highload operation. Algorithms to correct this introduce parameter sensitivity and mismatch. A robust asymptotic approach with reasonable parameter sensitivity is proposed.

Obtaining an analytical derivation of DTC using singular perturbation theory and sliding mode control provides the grounds to solve the problem. The stability condition requires the machine leakage factor to be under certain limits available only in high performance machines. As the load and speed increase, the impact of the non-zero leakage factor introduces coupling effects between stator flux, rotor speed and electromagnetic torque, causing erratic behavior. Compensator schemes are investigated for the singularly perturbed model.

An input-output decoupling (IOD) method guarantees decoupling but introduces parameter dependencies that result in nonrobust operation under parameter uncertainties. Furthermore, high controller complexity requires expensive signal processors and increases the susceptibility to numerical calculation errors. Asymptotic input-output decoupling (AIOD) is proposed to avoid injecting torque and flux ripples back into the system, reduce the computational complexity and minimize parameter sensitivity.

Experimental results shown in Figures15- 18 confirm that decoupling is achieved at high speeds and torques. A wider operating speed range is achieved compared to conventional DTC drives. In addition, the peak torque capability of a conventional DTC drive is extended with AIOD implementation and a 140% improvement is achieved at 30% above the rated speed. Figures 16 and 18 show that the maximum speed range of conventional DTC is enhanced by 30%.

This research is supported by the Grainger Center for Electric Machinery and Electromechanics.