Results

The system responses for trajectory and force control have been obtained as results. 

The terminologies involved in the system response curve are as follows:

• Peak-Time: The time required for the response to reach the first peak of the overshoot.   

• Settling-Time: The time required for the response curve to reach and stay within a range of about 2% or 5% the setpoint value.   

• Rising Time: The time required for the response to rise from 10% to 90% of the setpoint value.    

Position Control Results

 The responses of the position of the slider-nut to step and sinusoidal inputs are recorded at different PID control gains (Kp, Ki, and Kd) to ensure the system responds in a desired (tuned) manner.  

Perfect Tuning implies:   

• Zero Overshoot   

• No Oscillations   

• Fast Response (small Rising Time)   

• Small Settling Time  

The system block diagram for position control is shown as follows:

To tune the PID controller, the following steps were used:  

1. Set all gains to zero.  

2. Increase the P gain (Kp) until the response to a disturbance is a steady oscillation.  

3. Increase the D gain (Kd) until the oscillations go away (i.e., it's critically damped).  

4. Repeat steps 2 and 3 until increasing the D gain (Kd) no longer stops the oscillations.  

5. Set Kp and Kd to the last stable values.  

6. Increase the I gain (Ki) until it brings you to the setpoint with the number of oscillations desired (normally zero, but a quicker response can be had if you don't mind a couple of oscillations or overshoot).  

Tuned Response for sampling time 0.05 s  

System Response for Sinusoidal Input

Force Control Results