B. Readouts
The Matlab data readouts are shown in Figures VI.B.1 to VI.B.4. Each top plot shows the displacement of the payload from the target destination. Each middle plot shows the estimated force response of the solenoids. The leftward direction is positive on both the displacement and force response plots. Each bottom plot shows the voltage inputs to the VCCS for both the left and right solenoids. The blue trace represents the right solenoid while the red trace represents the left solenoid.
Payload moving towards right solenoid
Figure VI.B.1: Transient Response
(a) Position Readout, (b) Force Response, and (c) Solenoid Currents for the first 140 ms.
The leftward direction is positive on both the displacement and force response plots. On the bottom plot, the blue trace represents the right solenoid while the red trace represents the left solenoid. The currents in both solenoids go to their maximum value of 4 A.
Figure VI.B.2: Steady-State Response
(a) Position Readout, (b) Force Response, and (c) Solenoid Currents after the first 140 ms.
The direction of the force is rightward during steady state. There is a drift in the force response. Most of the time, the right solenoid is constantly adjusting its magnetic force while the left solenoid is pulling the minimum tension force.
Here are some control system characteristics of the step response.
Payload moving towards left solenoid
Figure VI.B.3: Transient Response
(a) Position Readout, (b) Force Response, and (c) Solenoid Currents for the first 140 ms.
The left solenoid pulls the payload first to get it moving to the left. The right solenoid then exerts a pulling force on the payload to get it to stop. The currents in both solenoids go to their maximum value of 4 A.
Figure VI.B.4: Steady-State Response
(a) Position Readout, (b) Force Response, and (c) Solenoid Currents after the first 140 ms.
The direction of the force is leftward during steady state. There is a drift in the force response. Most of the time, the left solenoid is constantly adjusting its magnetic force while the right solenoid is pulling the minimum tension force.
Here are some control system characteristics of the step response.
Analysis of the Steady-State Force Response Drift
Please look at the force response plots of Figures VI.B.2 and VI.B.4. There is a drift in the force response during steady-state. It is relatively low frequency and changing linearly over a period of a few seconds. This drift is caused by the presence of the springs on the linear potentiometer’s shaft. While the springs are needed to secure the payload to the plunger, they can compress and elongate. If the payload travels rightward, the right spring will compress, the left spring will elongate, and there will be an overall rightward force (as is shown in Figure VI.B.2). If the payload travels leftward, the left spring will compress, the right spring will elongate, and there will be an overall leftward force (as is shown in Figure VI.B.4). In both cases, the linear potentiometer’s plunger position might be delayed behind the actual displacement of the payload. This will exacerbate the measurement error and noise.
Note also that the resolution of displacement measurement is 4.15 μm. This quantization error means that the controller will never read the payload as being exactly at the destination. Even after the payload settles, the controller is still trying to use the solenoids to slightly move it to the precise destination. Remember, the Kalman Filter treats the exogenous force as an accumulation of the observed position error.