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Anti-windup PI controller for millimeter-wave adaptive optics: a Nobeyama 45 m radio telescope simulation

This paper proposes and validates an anti-windup proportional-integral (AWPI) controller for millimeter-wave adaptive optics, demonstrating through Nobeyama 45-m telescope simulations that it effectively suppresses distance variations between the primary reflector and receiver while respecting physical movement constraints.

Original authors: Ichiro Jikuya, Yoichi Tamura, Akio Taniguchi, Masaki Sakakibara, Akinobu Miyake, Masato Hagimoto, Kianhong Lee, Chihiro Imamura, Shion Takeno, Sachiko S. Okumura, Nozomi Okada

Published 2026-08-18

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CC BY 4.0

Original authors: Ichiro Jikuya, Yoichi Tamura, Akio Taniguchi, Masaki Sakakibara, Akinobu Miyake, Masato Hagimoto, Kianhong Lee, Chihiro Imamura, Shion Takeno, Sachiko S. Okumura, Nozomi Okada

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast silence of the radio sky, telescopes act as giant ears, listening for faint whispers from distant galaxies. To hear these whispers clearly, the telescope's dish must hold a perfect shape, focusing incoming radio waves onto a single receiver point. However, the massive metal structures of these telescopes are not rigid; they bend and shift as the sun heats them or as the wind pushes against them. This movement changes the distance between the main dish and the receiver, blurring the signal much like a camera lens that has gone out of focus. For decades, astronomers have relied on adaptive optics in optical telescopes to correct for the shimmering of Earth's atmosphere, but radio astronomers face a different problem: the physical stretching and shrinking of the telescope itself. The challenge is to keep the receiver in the exact right spot, moving it in real-time to counteract the telescope's own structural changes, ensuring the signal remains sharp.

A team of researchers has developed a new way to solve this problem for millimeter-wave radio telescopes, specifically testing their ideas on a simulation of the famous Nobeyama 45-meter Radio Telescope in Japan. The core of their work is a control system designed to manage a sub-reflector, a smaller mirror that sits in front of the main dish and directs signals to the receiver. This sub-reflector is mounted on a mechanism that can move it in two directions, up and down or side to side, to compensate for the shifting distance caused by the telescope's deformation. The researchers faced a difficult engineering hurdle: the motors that move this mirror have physical limits. If the telescope shifts too much, the motors might be asked to move faster or further than they physically can, a situation known as saturation. In standard control systems, when a motor hits this limit, the internal calculations can go haywire, causing the system to overshoot or become unstable once the limit is passed. The team needed a method that would keep the system stable even when the motors were working at their absolute maximum.

To address this, the researchers created a simulation based on the Nobeyama 45-meter telescope, which uses a system of five radiators to measure the exact distance changes in real-time. They applied a specific type of controller, known as an anti-windup proportional-integral controller, to the model. This controller acts like a vigilant driver who knows the car's speed limit. When the road is clear, it adjusts the steering smoothly. But when the car hits a wall of traffic and cannot go faster, the driver stops trying to push the accelerator harder, preventing the engine from revving uselessly and the car from lurching forward when the traffic clears. In the simulation, the researchers introduced various constant disturbances, representing sudden shifts in the telescope's structure, and tested the system under two conditions: one where the motors had plenty of room to move, and another where the required movement was so large that the motors were forced to hit their physical limits.

The results of the simulation showed that the new controller worked exactly as intended. When the motors were not at their limit, the system successfully corrected the distance errors, bringing the signal back to perfect focus. More importantly, when the motors were forced to their maximum capacity, the system did not break down or become unstable. Instead, the controller recognized the limit and adjusted its internal calculations to prevent the "windup" effect, keeping the system steady. Even while the motors were stuck at their maximum, the system maintained a stable state, and as soon as the disturbance lessened and the motors were free to move again, the system immediately resumed its precise corrections. The simulation confirmed that this approach could handle the complex, shifting forces acting on a large radio telescope without losing control.

This work provides a solid theoretical foundation for future large-scale radio astronomy projects, including the proposed AtLAST and LST telescopes, which will be even larger and more complex than current instruments. By proving that this control method can handle the physical limitations of real-world machinery in a simulated environment, the researchers have offered a reliable blueprint for keeping future telescopes in perfect focus. The next step for the team is to take these findings from the computer screen to the actual Nobeyama 45-meter telescope, where they plan to test the controller in the field to ensure it performs just as well in the real world as it did in their simulation.

Technical Summary: Anti-windup PI Controller for Millimeter-wave Adaptive Optics

Problem Definition
This work addresses the control challenge inherent in Millimeter-wave Adaptive Optics (MAO) for radio astronomy. Unlike conventional optical adaptive optics that correct for atmospheric turbulence, MAO is defined here as the compensation for distance variations between the primary reflector (M1) and the receiver. The specific problem is formalized as an asymptotic constant disturbance suppression task. The system must drive an optical driving system (specifically a two-axis translating sub-reflector, M2) based on real-time measurements of distance variations, while strictly adhering to the physical movement constraints (saturation limits) of the actuators.

Methodology
The authors propose a control framework utilizing an Anti-Windup Proportional-Integral (AWPI) controller. The methodology is built upon the following components:

System Modeling: The sub-reflector drive system is modeled as a decoupled first-order system with a time constant matrix $T_s$ . The measurement system, based on an Excess Path Length (EPL) setup using five radiators, provides real-time data $y(t)$ . This measurement is modeled as the sum of the desired optical path length (dependent on elevation angle), optical path length changes at measurement points, and a disturbance vector $w(t)$ representing unmodeled factors.
Control Law Formulation: The AWPI controller maps the estimated residual $\hat{q}(t)$ $\overset{q}{^} (t)$ (the difference between measured EPL and the desired path) to control inputs $u(t)$ $u (t)$ . The control law includes:
- A standard PI structure with integral gain $K_i$ and proportional gain $K_p$ .
- An anti-windup mechanism involving a gain matrix $K_a$ and a saturation function $sat(\cdot)$ . This mechanism prevents the internal integrator variable $v(t)$ from diverging when the control input hits physical limits.
- The use of the Moore-Penrose pseudo-inverse ( $M^\dagger$ ) to map measurements to actuation coefficients, effectively decoupling the system.
Theoretical Framework: The control design ensures that the suppressible component of the disturbance (the projection of $w$ onto the image of the measurement matrix $M$ ) is asymptotically suppressed. The system is proven to be internally stable provided the integral and proportional gains remain positive.

Key Contributions

Formalization of MAO Control: The paper formalizes the MAO problem as an asymptotic constant disturbance suppression problem, distinct from atmospheric turbulence correction.
AWPI Implementation for Radio Telescopes: The authors adapt the general AWPI theory to the specific parameters of the Nobeyama 45-m Radio Telescope, calculating specific gain matrices ( $K_i, K_p, K_a$ ) and the measurement matrix $M$ derived from electromagnetic field analysis.
Handling Saturation: The work explicitly addresses the physical limitations of the optical driving system, demonstrating how the anti-windup mechanism maintains stability and prevents integrator divergence during input saturation.

Simulation Results
The authors validated the proposed approach through simulations using the Nobeyama 45-m Telescope model with a piecewise constant disturbance function. The simulations tested four scenarios involving two distinct disturbance vectors ( $w_1$ and $w_2$ ) and two amplitude levels (10 and 20) to simulate unsaturated and saturated conditions, respectively.

Unsaturated Conditions: When the disturbance amplitude was 10, the control input did not saturate. In cases where the disturbance was fully suppressible, the residual converged to zero. In cases of partial suppressibility (due to dimensional mismatch between 5 measurements and 2 actuators), the suppressible components were rejected, leaving a constant residual corresponding to the insuppressible disturbance.
Saturated Conditions: When the disturbance amplitude was increased to 20, the control input reached saturation limits. The simulation confirmed that the anti-windup mechanism successfully prevented the internal integrator variable $v(t)$ from diverging. While the estimated expansion coefficients did not converge to zero during saturation, they settled to stable constant values.
Overall Performance: The closed-loop system demonstrated asymptotic stability and effective disturbance suppression in the low-frequency range, consistent with the theoretical predictions of the decoupled sensitivity function $S(s)$ .

Significance and Claims
The paper claims that the proposed AWPI approach provides a robust solution for the MAO control problem, effectively balancing disturbance suppression with the physical constraints of the optical driving system. The simulation results validate that the system operates as designed, maintaining stability even when actuators saturate.

The authors position this work as establishing the theoretical baseline and control framework for future field experiments at the Nobeyama 45-m Radio Telescope. They state that these outcomes are intended to serve as a technical foundation for future large-aperture telescope projects, specifically citing AtLAST and the Large Aperture Telescope (LST). The paper does not claim immediate deployment but rather presents the necessary control theory and simulation verification required before practical implementation.

Technical Summary: Anti-windup PI Controller for Millimeter-wave Adaptive Optics

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