# Steering Mirror System with Closed-Loop Feedback for Free-Space Optical Communication Terminals
## 3 Control Feedback  
The stick slip piezo actuators used in this design exhibit significant hysteresis, with the size of the forward and reverse steps differing by approximately 16%, as illustrated in Figure 3a. With the actuator unloaded, the mean forward step size was measured as 24.1 nm, and the mean reverse step size as 20.3 nm. Consequently, counting the number of commanded steps does not provide an accurate measure of actuator position, as the 16% positioning error will accumulate with multiple changes in direction. An example of this is shown in Figure 3b, which depicts the position of the actuator tip over a series of forwards and backward movements, highlighting the forward drift of the 0 step position with each successive pass.  
For accurate positioning of the actuators, a form of closed-loop control is essential. One option would be to use a mechanically coupled feedback sensor such as a linear variable differential transformer, with the pushrod attached to the back of the mirror. The downside of these feedback sensors is that a malfunction or jamming could mechanically lock the actuator in place. A more robust method employs non-contact sensors, such as optical encoders. The sensor receives the light directed onto a coded reflective pattern to track movement. Single-channel encoders can monitor movement speed, while quadrature encoders can be used to also track the direction of motion.  
While some commercial products come with built-in optical encoders, they are generally much bulkier and heavier, weighing 200 g compared to the 55 g PIA13 VFs. This increased size and weight makes these actuators less practical for use in CubeSats. Therefore, an in-house solution was developed, integrating optical encoder feedback into the COTS Thorlabs actuators. The chosen optical encoder for this setup is the AEDR-8300-1K2 quadrature encoder (Broadcom, Palo Alto, CA, USA). A critical specification for these encoders is the reflectance of the coded pattern. Rather than requiring a simple black-and-white barcode-style pattern, the brighter areas of the pattern must have a specular reflectance of over 60%. To achieve this, a fine straight knurled knob was diamond-turned, providing a highly reflective surface on the raised portions of the knurling. An image of the encoder wheel is displayed in Figure 4a. The knob features 72 grooves, corresponding to 288 pulses per revolution with the quadrature encoder. Along with the 1/4'' \(\times\) 80 fine thread lead screw on the actuators, the encoder should provide a resolution of 1.1 um. Since these inertial actuators require a mass on the screw thread, the only additional weight for this system is the encoder PCB, adding just 6 g to the actuator's mass. Figure 4b  
Figure 3: (**a**) Real position of piezo actuator head as a function of piezo step count. (**b**) Forward drift of 0 step position as the actuator is driven successively between 0 and 40,000 steps.  
displays a plot of the actuator tip position against the encoder counts for 20 successive movements, using the encoder feedback for position control. This can be compared to Figure 3b, where the commanded piezo steps are used for feedback. The 12 \(\upmu\)m spread on the actuator position originates partially from the backlash of the measurement probe, and partially from the delay in communication between the prototype encoder electronics and the motor controller.