As per my understanding, you are trying to drive a DC machine using the control circuit made using NE555 timer. Your aim is to vary speed by turning the knob.
You can do this by using a buck converter that receives gate pulses from the control circuit. The output of buck converter drives the DC motor. I am suggesting one of the possible way to do it in the below screenshot.
Here, I have used the model “DC Motor” available in “Simscape > Electrical > Electromechanical > Brushed Motors”. I am using a frictional load to model mechanical load torque on the machine.
In the above Simulink model, I am turning the “duty Cycle control knob” and observing the speed output of the DC motor on the scope. Below scope shows the speed of the DC motor.
I have attached the Simulink model. To know more information about the block used, navigate to the ”help” tab of the “block parameters” for that particular block.