For inrush, in transformer, 30 yrs. back, I developed, solid state, fast one cycle relay and used it successes fully. For soft starting of induction motor SSR are used, for long time, you can used it.

Mr. Desai do you have an appropriate reference or source files about SSR in machine drives? 

Siemen's solid state relay for induction motors, along with solid state starter for soft start....

you can use it if you have the required solid state relay rated