An exhaust valve assembly includes a valve body supported on a shaft for rotation within an exhaust component. The shaft is coupled to a solenoid with a linkage assembly. A controller controls the solenoid to rotate the shaft via the linkage assembly. The solenoid includes a plunger that moves between an actuation position and a release position. The controller utilizes pulse width modulation to control actuation and release of the plunger. This significantly reduces operational noises generated as the solenoid is moved between the actuation position and the release position.