[Paper Review] Exploring closed-loop feedback control using experiments in optics

Kai Jensen, R. J. Larson+2 more|ArXiv.org|Jun 27, 2001

Advanced Frequency and Time Standards1 references3 citations

TL;DR

This paper presents two hands-on optics experiments for junior and senior physics students to teach closed-loop feedback control: a laser pointer tracker and a Michelson interferometer stabilizer. Using simple electronics—DC motors, photodetectors, op-amps, and PZT actuators—the experiments demonstrate proportional and integral feedback control, achieving stable locking of the laser beam or interference fringe position through real-time error correction.

ABSTRACT

We present two experiments in closed-loop feedback control. In the first experiment, students control the pointing angle of a laser to "lock" the laser onto a "target." In the second, students stabilize the pathlength difference in two arms of a Michelson interferometer. These experiments are appropriate for electronics and optics laboratory classes for junior and senior level students.

Motivation & Objective

• To provide an intuitive, laboratory-based introduction to feedback control principles for upper-division physics and engineering students.
• To bridge the gap between abstract mathematical models of feedback control and tangible physical systems by using accessible optical and electronic components.
• To demonstrate how proportional and integral feedback control can stabilize dynamic systems such as laser beam pointing and interferometer pathlength.
• To support student learning through experiential, low-cost experiments that emphasize system behavior over complex mathematical modeling.

Proposed method

• Construct a laser tracker using a DC motor to steer a laser pointer, with a two-segment photodetector to sense angular deviation from a target.
• Use a difference amplifier to generate an error signal proportional to the laser's angular offset, which is then amplified and fed back to adjust the motor input.
• Implement a closed-loop system where the feedback gain (H) and forward gain (G) determine system stability and accuracy, with the closed-loop transfer function y ≈ x/H when GH ≫ 1.
• Stabilize a Michelson interferometer by using a quadrant photodetector to monitor fringe position, with the error signal driving a piezoelectric (PZT) actuator to adjust mirror position.
• Use operational amplifiers (741s) in a difference amplifier and integrator configuration to process the detector signal, with a feedback capacitor and resistor to prevent saturation.
• Engage feedback by opening a switch to enable the control loop, allowing students to observe real-time stabilization of the interference pattern.

Experimental results

Research questions

• RQ1 How can closed-loop feedback control be effectively taught using low-cost, hands-on optics experiments in an upper-division laboratory setting?
• RQ2 What are the key design and tuning parameters that affect the stability and performance of a feedback system in a laser tracking or interferometer stabilization setup?
• RQ3 How does the feedback gain (H) influence the system's ability to maintain the laser beam or fringe at a desired position?
• RQ4 What role does the integrator play in eliminating steady-state error in the feedback loop, and how can it be tuned to avoid saturation?
• RQ5 What are the common failure modes in feedback systems, and how can they be diagnosed and corrected by students during experimentation?

Key findings

• The laser tracker experiment successfully demonstrated closed-loop control, with the system stabilizing the laser beam at the target center when feedback gain was sufficiently high.
• The Michelson interferometer stabilization achieved real-time locking of a bright fringe to the center of a two-segment photodetector, with the PZT actuator compensating for pathlength drift.
• Students observed that increasing the feedback amplifier gain improved error signal magnitude, but excessive gain caused integrator saturation and loss of lock.
• The use of a 1MΩ resistor in parallel with the integrator capacitor prevented output saturation due to op-amp offset currents, enabling stable operation.
• When the system failed to lock, reversing the detector inputs or polarity of the error signal often restored functionality, indicating the importance of correct feedback polarity.
• The PZT actuator, driven at ±10 V, provided ~0.8 μm of mirror displacement, sufficient to stabilize the interference pattern over a limited but observable range.