Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Various optical actuators and control methods suitable for various optical applications have been proposed and developed^1,2. These optical actuators are able to control the optical path; galvanometer mirrors especially offer a good balance in terms of accuracy, speed, mobility, and cost^3,4,5. Actually, the advantage offered by the speed and accuracy of galvanometer mirrors has led to the realization of a variety of optical applications, such as target tracking and drawing, scanning control, and motion-blur compensation^{6,7,8,9,10,11,12}. However, in our previous motion-blur compensation system, a galvanometer mirror using a proportional-integral-differential (PID) controller provided a small gain; hence, it was difficult to achieve a higher frequency and a faster speed¹¹.

On the other hand, PID control is a widely-used method, as it satisfies a certain level of tracking accuracy¹³. A variety of methods have been proposed to correct the gain in PID control. As a typical solution, PID control parameter tuning is conducted manually. However, it takes time and special skill to maintain. A more sophisticated method, an auto-tuning function to automatically determine the parameters, has been proposed and is widely used¹⁴. The tracking accuracy for high-speed operations is improved using the auto-tuning function when the proportional gain value P increases. However, this also increases the convergence time and noise in the low-speed range. Hence, the tracking accuracy is not necessarily improved. Although a self-tuning controller can be tuned to set suitable parameters for PID control, the tuning introduces a delay because of the need to obtain suitable parameters; therefore, it is difficult to adopt this method in real-time applications¹⁵. An extended PID controller^16,17 and an extended predictive controller¹⁸ have been proposed to extend general PID control and to enhance the tracking performance of galvanometer mirrors for a variety of tracking paths, such as triangular waves, sawtooth waves, and sine waves. However, in those systems, the galvanometer system was regarded as a black box, whereas a model of the control system was required, and the control system was not regarded as a black box. Hence, those methods require that their model for each galvanometer mirror be updated. Moreover, although Mnerie et al. validated their method of focusing on a detailed output wave and phase, their research did not include the attenuation of the entire wave. In fact, in our previous research¹¹, the gain was significantly decreased when the sinusoidal frequency was high, thereby indicating the necessity to compensate for the gain of the entire wave.

In this research, our procedure for gain compensation with PID control¹² is based on the pre-emphasis technique^19,20,21—a method to enhance the quality or speed of communication in communications engineering—which enables the construction of an experimental system using existing equipment. Figure 1 shows the flow structure. The pre-emphasis technique is able to obtain in advance the desired output value from an input value, where PID control is not effective, even if the galvanometer mirror and its controller are regarded as black boxes. This enables them to expand the frequency and amplitude range in which a gain of 0 dB can be obtained without tuning the PID control parameters.

When the gain is amplified, the response characteristics of the galvanometer mirror generally differ at different frequencies, and therefore, we need to amplify each frequency with amplification coefficients. Thus, a sine wave is suitable for the pre-emphasis technique, as there is only one frequency in each sine wave. In this research, because we apply gain compensation to accomplish motion-blur compensation, the control signal is limited to sine-wave scanning, and the sine-wave signal constitutes a single frequency, unlike other waves, such as triangular and sawtooth waves. Further, the input signal into the galvanometer mirror is updated immediately within the next cycle because of the open loop after the pre-emphasis coefficients are set. In other words, we need to know only the input-to-output ratio to regard the controller as a black box, and detailed modeling is not required. This simplicity allows our system to be easily embedded in applications.

The overall goal of this method is to establish an experimental procedure of motion-blur compensation as an application by gain compensation using the pre-emphasis technique. Multiple hardware devices are used in these procedures, such as a galvanometer mirror, a camera, a conveyor belt, illumination, and a lens. Central software user-developed programs written in C++ also constitute part of the system. Figure 2 shows a schematic of the experimental setup. The galvanometer mirror rotates with gain-compensated angular velocity, thereby making it possible to evaluate the amount of blur from the images.