
Citation: | Cui, Z.Q., Zuo, H., Qiao, W. K., et al. 2024. Fuzzy Proportional Integral Derivative control of a voice coil actuator system for adaptive deformable mirrors. Astronomical Techniques and Instruments, 1(3): 179−186. https://doi.org/10.61977/ati2024025. |
Research on adaptive deformable mirror technology for voice coil actuators (VCAs) is an important trend in the development of large ground-based telescopes. A voice coil adaptive deformable mirror contains a large number of actuators, and there are problems with structural coupling and large temperature increases in their internal coils. Additionally, parameters of the traditional proportional integral derivative (PID) control cannot be adjusted in real-time to adapt to system changes. These problems can be addressed by introducing fuzzy control methods. A table lookup method is adopted to replace real-time calculations of the regular fuzzy controller during the control process, and a prototype platform has been established to verify the effectiveness and robustness of this process. Experimental tests compare the control performance of traditional and fuzzy proportional integral derivative (Fuzzy-PID) controllers, showing that, in system step response tests, the fuzzy control system reduces rise time by 20.25%, decreases overshoot by 78.24%, and shortens settling time by 67.59%. In disturbance rejection experiments, fuzzy control achieves a 46.09% reduction in the maximum deviation, indicating stronger robustness. The Fuzzy-PID controller, based on table lookup, outperforms the standard controller significantly, showing excellent potential for enhancing the dynamic performance and disturbance rejection capability of the voice coil motor actuator system.
Adaptive optics (AO) is a dynamic wavefront correction technique[1] with extensive applications in fields such as laser communication, ground-based optical telescopes, and imaging the retina of the human eye[2]. As one of the key components of an adaptive optics system, deformable mirrors driven by piezoelectric materials are widely used and are a relatively mature technology, but they face challenges such as hysteresis, high driving voltage, and limited stroke. Deformable mirrors driven by VCAs are used in telescopes such as the Multiple Mirror Telescope (MMT)[3], Large Binocular Telescope (LBT) [4], and Very Large Telescope (VLT)[5], owing to their advantages of fast response, no hysteresis, large stroke, and high precision. Internationally, upcoming next-generation large ground-based telescopes such as the Giant Magellan Telescope (GMT) in the United States and the Extremely Large Telescope (ELT) in Europe are adopting this voice coil adaptive deformable mirror technology. Currently, there are no instances of the application of this technology in large telescopes within China.
Research on voice coil adaptive deformable mirrors is already underway in China[6, 7], and the currently available literature primarily covers topics such as the structural design of voice coil motor actuators and the displacement detection of deformable mirror surfaces. However, there is a lack of relevant reports on the control algorithms employed in voice coil motor actuator systems. Currently, VCAs commonly employ PID control[8, 9], with parameters that are often determined through empirical tuning, but this approach presents challenges such as sub-optimal correction effects and generally extended tuning times.
Voice coil adaptive deformable mirrors, which contain a large number of actuators, face challenges such as structural coupling between actuators and a significant temperature rise in the actuator coils. During the control process, the characteristics of the actuators can be affected, and PID control parameters are unable to dynamically self-tune to adapt to system changes in real-time. In response to the aforementioned issues, we propose a Fuzzy-PID control algorithm. This combined approach is then applied to the control of voice coil motor actuators, allowing real-time self-tuning of PID control parameters during the control process. Fuzzy control has the advantage of not relying on an accurate model of the controlled object, making it effective for controlling objects for which it is difficult to establish precise mathematical models[10]. The Fuzzy-PID algorithm inherits the advantages of regular fuzzy control methods and also has the applicability and robustness of a PID control method. In addition, by employing a table lookup method instead of real-time calculations by the fuzzy controller, the computational complexity during the control process is reduced.
Here, we introduce the design of a Fuzzy-PID controller and the acquisition of a fuzzy control lookup table, and verify the effectiveness of the controller in improving the dynamic performance and disturbance resistance of voice coil motor actuators through both simulation and experimental approaches.
Adaptive deformable mirrors with numerous actuators face challenges in implementing centralized control methods and lack general design approaches for fully decentralized cooperative control [11]. Here, we focus on the Fuzzy-PID control algorithm using a voice coil motor actuator from a self-developed six-unit voice coil adaptive deformable mirror. A schematic diagram of this is shown in Fig. 1.
The voice coil actuator system primarily consists of a deformable mirror, voice coil actuator, capacitive sensor, controller, driver, and base part. The voice coil actuator used in this research is a counter-opposed voice coil actuator, where the rotor is a permanent magnet opposed to the coil. In this configuration, the coil is fixed to the base, and the rotor magnet is rigidly connected to the deformable mirror. The equivalent mechanical model and equivalent circuit diagram of the voice coil motor actuator are shown in Fig. 2.
According to Newton's laws of motion, the dynamic equilibrium equation for a voice coil motor actuator can be expressed as
md2xdt+cdxdt+kx=kmi | (1) |
and
F=kmi, | (2) |
where m is the total mass of the rotor, x is the displacement of the rotor, k is the spring elastic coefficient, c is the damping coefficient, i is the current in the coil, km is the motor force constant, and F is the electromagnetic force.
According to Kirchhoff's voltage law, the voltage equilibrium equation for the voice coil motor actuator can be expressed as
kEdxdt+Ldidt+iR=u | (3) |
and
Ef=kEdxdt, | (4) |
where kE is the back electromotive force (EMF) coefficient, L is the equivalent inductance, R is the equivalent resistance, u is the coil terminal voltage, and Ef is the back EMF.
By combining equations (1) and (3), and performing Laplace transformation, the transfer function of the voice coil motor actuator can be obtained as
X(s)U(s)=kmmLs3+(cL+mR)s2+(LR+cR+kmkE)s+kR. | (5) |
Using the LabVIEW programming environment, a data acquisition program was developed to collect data using a uniform white noise signal (pseudo-random signal) as the input signal and the displacement of the voice coil motor actuator as the output signal. The input signal frequency ranges are 0–120 Hz, 0–80 Hz, 0–50 Hz, and 0–40 Hz, with an amplitude of ±0.5 V. Given that engineering typically focuses on the accuracy of identification models within the working bandwidth and considering that the resonance frequency of the six-unit voice coil motor deformable mirror is low, high-frequency noise signals may affect the results of system identification. Therefore, the data were preprocessed using the MATLAB system identification toolbox by filtering, mean removal, and resampling, then selecting “transfer function model” as the model type to be identified. Following the structure specified in equation (5) with 3 poles and 0 zeros, system identification is performed on the voice coil actuator. Multiple adjustments to the initialization methods are made to select the optimal identification result. The resulting transfer function for the voice coil actuator is
X(s)U(s)=1.026×107s3+519.2s2+2.305×105s+3.499×107. | (6) |
A Fuzzy-PID controller consists of both PID and fuzzy control components, as illustrated in Fig. 3. This arrangement takes error and the rate of change of error as inputs and adjusts PID parameters in real-time using fuzzy control rules.
Here, the chosen input variables for the fuzzy controller are the position deviation e and the rate of change of position deviation ec of the voice coil actuator. The output variables are the increments of the PID control parameters, ∆kp, ∆ki, and ∆kd, together with the corresponding fuzzy variables (linguistic variables) are E, EC, ∆KP, ∆KI, and ∆KD. In Fig. 3, Ke and Kec are quantification factors, and Kup, Kui, Kud are proportionality factors for the increments of the PID control parameters.
Considering that this fuzzy control system is a multivariable system with a large number of input and output variables, we adopted a standardized design. The fuzzy set domains of E, EC, ∆kp, ∆ki, and ∆kd are all set to [−6, 6], and the linguistic values of fuzzy variables are NB, NM, NS, ZO, PS, PM, PB, where NB represents negative large, NM represents negative medium, NS represents negative small, ZO represents zero, PS represents positive small, PM represents positive medium, and PB represents positive large. Standardized design simplifies the complexity of fuzzy variable design, facilitates the understanding and formulation of fuzzy rules, and improves the universality of the control system, making it easy to extend the actuator control to other positions on the adaptive deformable mirror. Through multiple adjustments of quantification factors and proportionality factors in simulations, to optimize the controller performance, the domains for input and output variables are determined as e=[−4, 4], ec=[−30, 30], ∆kp=[−1.2, 1.2], ∆ki=[−4.8, 4.8], and ∆kd=[−
Fuzzy variables have multiple linguistic values, with each linguistic value corresponding to a membership function. Common membership functions include triangular, Gaussian, and trapezoidal[11]. In this study, the selection principle for membership functions is to use low-resolution fuzzy sets in regions with large errors and higher-resolution fuzzy sets in regions with smaller errors[12]. Considering the practicalities, the adaptive deformable mirror has a high frequency but a small amplitude of motion. When the input deviation is small, there is a high requirement for control accuracy, while the accuracy requirement is relatively lower when the input deviation is large. Different membership functions have varied effects on control characteristics. For the portions where the central error is relatively small, functions with sharper shapes are employed. These functions are less influenced by other membership functions, resulting in higher control sensitivity. In contrast, for portions with larger errors, smoother-shaped functions are used, providing better stability performance. Considering both control sensitivity and stability, the membership functions for input and output linguistic variables are adjusted based on simulation experiments, as illustrated in Fig. 4. The linguistic value ZO adopts a triangular membership function; NM, NS, PS, PM use Gaussian membership functions; NB uses a Z-shaped membership function; and PB adopts an S-shaped membership function.
Fuzzy control rules have a direct impact on the performance of the fuzzy inference system. We comprehensively consider the control effectiveness of the three parameters kp, ki and kd in the PID control algorithm, and the influence of the dynamic performance of the system when these three parameters change, such as the settling time and overshoot of the system's step response. Simultaneously, expert control experience is incorporated into the formulation of fuzzy rules. A fuzzy control rules table for ΔKP, ΔKI, ΔKD is formulated as shown in Table 1.
E | ΔKP,ΔKI,ΔKD | ||||||
EC=NB | EC=NM | EC=NS | EC=ZO | EC=PS | EC=PM | EC=PB | |
NB | PB, NB, PS | PB, NB, NS | PM, NM, NB | PM, NM, NB | PS, NS, NB | ZO, ZO, NM | ZO, ZO, PS |
NM | PB, NB, PS | PB, NB, NS | PM, NM, NB | PS, NS, NM | PS, NS, NM | ZO, ZO, NS | NS, ZO, ZO |
NS | PM, NM, ZO | PM, NM, NS | PM, NS, NM | PS, NS, NM | ZO, ZO, NS | NS, PS, NS | NS, PS, ZO |
ZO | PM, NM, ZO | PM, NM, NS | PS, NS, NS | ZO, ZO, NS | NS, PS, NS | NM, PM, NS | NM, PM, ZO |
PS | PS, NM, ZO | PS, NS, ZO | ZO, ZO, ZO | NS, PS, ZO | NS, PS, ZO | NM, PM, ZO | PM, PB, ZO |
PM | PS, NO, PB | ZO, ZO, NS | NS, PS, PS | NM, PS, PS | NM, PM, PS | NM, PB, PS | NB, PB, PB |
PB | ZO, NO, PB | ZO, ZO, PM | NM, PS, PM | NM, PM, PM | NM, PM, PS | NB, PB, PS | NB, PB, PB |
The Mamdani method[13] is employed for fuzzy inference in this study, and the centroid method is used for de-fuzzification of fuzzy output. The centroid method assumes that the fuzzy set of fuzzy output is a two-dimensional plane, and the centroid of the plane is the weighted average of all points on that plane, with weights determined by the membership degrees of each point in the fuzzy set. These weights can be determined based on the membership functions and fuzzy rules obtained in subsection 2.2. Using the centroid method, precise outputs ΔKP, ΔKI and ΔKD under the inputs e and ec are obtained.
The PID control parameters used in practical applications are obtained based on equation (7), where kp, ki, and kd are the real-time PID control parameters; kp0, ki0 and kd0 are the initial PID control parameters, and Kup, Kui, Kud are the proportion factors of PID control parameter increments determined through multiple simulation experiments. The proportion factors are multiplied by the fuzzy controller outputs Δkp, Δki, Δkd to obtain real-time changes in PID control parameters. The relationship between these values can be mathematically expressed as
{kp=kp0+KupΔkpki=ki0+KuiΔkikd=kd0+KudΔkd. | (7) |
These changes are then added to the initial PID control parameters to obtain real-time PID control parameters.
With the development of voice coil adaptive deformable mirror technology, the number of voice coil motor actuators is increasing. Consequently, their control programs are becoming more complex, requiring high computational capabilities for the controllers. To reduce costs and decrease the computational load on the controller in real-time, this study adopts a table lookup method to replace the real-time calculation of the fuzzy controller. This means offline computation of a fuzzy control lookup table representing the relationship between input variables Ke⋅e, Kec⋅ec and output variables Δkp, Δki, Δkd. The compiled fuzzy control lookup table is then embedded in the controller. During on-site control, the software only needs to query the control table to obtain the required control quantities, which are then output to control the actual object[14].
For ease of engineering implementation, in this paper, the range of variations for the input variables Ke⋅e and Kec⋅ec is discretized into a set of 13 integers, specifically {−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6}. The discretization method involves dividing the range of variations for Ke⋅e and Kec⋅ec into 13 sub-intervals. Within each sub-interval, the values of Ke⋅e or Kec⋅ec are assigned the same value. The assignment of values in different intervals is given in Table 2.
Input | Interval | ||||||||||||
(−∞, −5.5) | [−5.5, −4.5) | [−4.5, −3.5) | [−3.5, −2.5) | [−2.5, −1.5) | [−1.5, −0.5) | [−0.5, 0.5) | [0.5, 1.5) | [1.5, 2.5) | [2.5, 3.5) | [3.5, 4.5) | [4.5, 5.5) | [5.5, +∞) | |
Ke⋅e | −6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Kec⋅ec | −6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
The MATLAB Fuzzy Logic Toolbox provides a graphical user interface. After completing the design of the fuzzy system using this interface, all combinations of discretized Ke⋅e and Kec⋅ec are input, and the corresponding values of Δkp, Δki, Δkd are recorded. Subsequently, a fuzzy control lookup table can be obtained, representing the relationship between the input variables Ke⋅e, Kec⋅ec and the output variables Δkp, Δki, Δkd[13]. Through the above process, we can obtain the fuzzy control lookup table for Δkp as shown in Table 3. Similarly, lookup tables for Δki and Δkd can be formulated.
Ke⋅e | Kec⋅ec | ||||||||||||
−6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |
−6 | 5.16 | 5.08 | 4.88 | 4.19 | 3.95 | 3.56 | 3.66 | 2.98 | 1.72 | 1.02 | −0.121 | −0.407 | −0.411 |
−5 | 5.08 | 5.08 | 4.8 | 4.19 | 3.95 | 3.06 | 3.11 | 2.95 | 1.67 | 0.995 | −0.297 | −0.969 | −0.987 |
−4 | 4.88 | 4.8 | 4.88 | 4.19 | 3.95 | 3.06 | 2.31 | 2.31 | 1.35 | 0.732 | −0.286 | −1.12 | −1.57 |
−3 | 4.19 | 4.19 | 4.19 | 4.19 | 3.94 | 3.06 | 2.02 | 1.01 | 0.688 | 0 | −0.732 | −1.04 | −1.66 |
−2 | 3.95 | 3.95 | 3.95 | 3.94 | 3.95 | 3.06 | 2.02 | 0.978 | 0 | −0.688 | −1.35 | −1.67 | −1.72 |
−1 | 3.92 | 3.91 | 3.67 | 3.06 | 3.06 | 2.12 | 0.994 | −0.0132 | −1.33 | −2 | −2.73 | −2.94 | −2.94 |
0 | 3.76 | 3.73 | 3.52 | 2.9 | 2.14 | 0.994 | 0.293 | −0.794 | −2.14 | −2.9 | −2.67 | −2.69 | −2.78 |
1 | 2.98 | 2.95 | 2.74 | 2 | 1.33 | 0 | −0.794 | −1.08 | −2.4 | −3.03 | −1.26 | 0 | 0.102 |
2 | 1.72 | 1.67 | 1.35 | 0.688 | 0 | −1.33 | −2.14 | −2.4 | −2.31 | −3.08 | −1.75 | 0.278 | 2.42 |
3 | 1.66 | 1.04 | 0.732 | 0 | −0.688 | −2 | −2.9 | −3.03 | −3.08 | −3.08 | −1.41 | −0.551 | 0.152 |
4 | 1.57 | 1.11 | 0.00784 | −1.27 | −1.86 | −2.74 | −3.52 | −3.67 | −3.76 | −3.72 | −2.8 | −3.17 | −3.27 |
5 | 0.987 | 0.962 | 0.00812 | −2.01 | −2.83 | −2.98 | −3.73 | −3.91 | −3.93 | −4.15 | −4.2 | −4.2 | −4.59 |
6 | 0.411 | 0.399 | −0.167 | −2.04 | −3.3 | −3.53 | −3.76 | −3.92 | −3.95 | −4.19 | −4.78 | −4.69 | −4.78 |
To compare the performance of the fuzzy and regular PID controllers, a simulation diagram was created in the MATLAB/Simulink environment, as shown in Fig. 5. The transfer function used in the simulation diagram is given by equation (6), with quantization factors Ke=1.5 and Kec=0.2, and proportionality factors Kup=0.2,Kui=0.8,Kud=0.0001.
By using a trial-and-error method and performing multiple adjustments, the optimal initial parameters for the PID controller are selected as follows: kp0=0.01, ki0=420, kd0=0.008. In the simulation environment, a unit step signal is applied simultaneously to both control systems, with results shown in Fig. 6. According to Table 4, the fuzzy PID control system exhibits superior dynamic performance. Compared with the regular PID control system, the fuzzy PID controller has a 4.53% reduction in rise time, a 25.34% decrease in overshoot, and a 25.77% reduction in settling time.
Controller | Raising time /ms |
Overshoot /(%) |
Settling time /ms |
PID | 18.32 | 23.44 | 56.51 |
Fuzzy-PID | 17.49 | 17.50 | 41.95 |
Selecting another transfer function model obtained from system identification, for example equation (8), the fitting degree is lower compared to transfer function (6). By using transfer function (8), we conduct experiments again to compare the performance of PID controller and fuzzy PID controller. Per equation (8), givesa lower fitting degree compared with the transfer function (6). In the Simulink diagram above, without altering the controller parameters, the transfer function in the simulation diagram is replaced with equation (8) for simulation testing. The results are shown in Fig. 7.
X(s)U(s)=2.007×107s3+647.1s2+3.681×105s+7.67×107 | (8) |
As Table 5 shows, compared with the regular PID controller, although the rise time of the Fuzzy-PID controller increases by 0.92%, the overshoot decreases by 35.71%, and the settling time is shortened by 4.05%. When the transfer function of the voice coil motor actuator changes, the Fuzzy-PID controller demonstrates strong robustness, significantly improving the overshoot and settling time of the system response compared with a standard PID controller.
Controller | Raising time /ms | Overshoot /(%) |
Settling time /ms |
PID | 19.51 | 12.60 | 38.98 |
Fuzzy-PID | 19.69 | 8.10 | 37.40 |
We created a prototype, shown in Fig. 8, using an NI cRIO-9040 embedded controller for both the Fuzzy-PID controller and the standard PID controller. This controller is equipped with a 16-channel 16-bit synchronous analog input module
VCA1 (see Fig. 1) is initially set at 0 µm, while other actuators are in a constant-force maintenance state. The step response target position is 1 µm. The rise time and overshoot of the mirror reaching the target position are compared under different control methods. The response curves controlled by different methods are shown in Fig. 9. As shown in Table 6, the Fuzzy-PID control system exhibits improved dynamic performance. Compared with the regular PID control system, the Fuzzy-PID control has a rise time shortened by 20.25%, overshoot reduced by 78.24%, and settling time decreased by 67.59%.
Controller | Raising time /ms | Overshoot /(%) |
Settling time /ms |
PID | 79.00 | 19.39 | 307.00 |
Fuzzy- PID | 63.00 | 4.22 | 99.50 |
In the voice coil motor actuator system, to investigate the impact of quantization factors Ke and Kec, as well as the proportion factors Kup, Kui, and Kud (taking Kup as an example), on the performance of the Fuzzy-PID controller, experimental studies are conducted through a controlled variable method, with results shown in Fig. 10. The results indicate that within a certain range, Ke has a noticeable effect on reducing the rise time of the system, with a larger Ke resulting in a shorter rise time. Kec has a significant effect on reducing the overshoot of the system, with a larger Kec leading to a smaller overshoot. A larger Kup strengthens the corrective effect on PID control, effectively reducing the overshoot.
The steady-state position of VCA1 is 1.25 µm. VCA2 (as shown in Fig. 2) is selected to compare the robustness performance of the two controllers. A step command of 0.5 µm is applied to actuator VCA2 on top of its current steady-state position of 1.25 µm. The displacement of the mirror at the position of voice coil motor actuator VCA1 is recorded, and the experiment is conducted with 10 averaged results. The system responses under different controllers are compared, and the results, given in Fig. 11, indicate that the maximum deviation for PID is 69.30 nm, while for Fuzzy-PID, it is 37.36 nm. This demonstrates that, in the presence of a step disturbance from adjacent actuators, the maximum deviation is reduced by 46.09% with the Fuzzy-PID controller, as compared with the regular PID controller, showing improved robustness.
To address the issues of time-consuming adjustment of PID control parameters for voice coil motor actuators in adaptive deformable mirrors, as well as the inability to change parameters once they are determined, we propose the application of a Fuzzy-PID control algorithm. The fuzzy controller allows real-time self-tuning of PID control parameters. Considering the large number of voice coil motor actuators used in the adaptive deformable mirrors for large-aperture telescopes and the potential computational resource constraints faced by the controller hardware, our proposed system uses a table lookup method to replace the fuzzy controller calculations in actual control to save computational resources, as verified here by experimentation.
Our results show that, compared with standard PID control, Fuzzy-PID control reduces the rise time by 20.25%, decreases overshoot by 78.24%, and shortens the settling time by 67.59%. In disturbance rejection experiments, the maximum deviation under fuzzy control is reduced by 46.09% compared with standard PID control, showing stronger robustness. Additionally, we explore the influence of quantization factors and proportionality factors on the performance of the Fuzzy-PID controller.
In summary, the Fuzzy-PID control algorithm based on table lookup provides a reference for improving the dynamic performance and disturbance rejection capability of voice coil motor actuator systems for adaptive deformable mirrors. It also offers a method to mitigate the impact of changes in actuator system characteristic parameters, showing excellent potential for practical applications in future large telescopes.
Ziqiang Cui designed the Fuzzy-PID control algorithm and conducted experimental research. Weikang Qiao analyzed the experimental data and evaluated the effectiveness of the algorithm. Hao Li played a significant role in the construction of the experimental platform. Fujia Du validated the effectiveness of the experimental platform. Yifan Wang has improved some of the hardware of the experimental platform. Jinrui Guo organized the experimental results. Heng Zuo provided guidance for the experiment and proofread the manuscript, improving the overall quality of the manuscript. All authors have read and approved the final manuscript.
Heng Zuo is an editorial board member for Astronomical Techniques and Instruments and was not involved in the editorial review or the decision to publish this article. The authors declare no competing interests.
[1] |
Guo, Y. M., Zhong, L. B., Min, L., et al. 2022. Adaptive optics based on machine learning: a review. Opto-Electronic Advances, 5(7): 200082-1−200082-20. doi: 10.29026/oea.2022.200082
|
[2] |
Burns, S. A., Elsner, A. E., Sapoznik, K. A., et al. 2019. Adaptive optics imaging of the human retina. Progress in Retinal and Eye Research, 68: 1−30. doi: 10.1016/j.preteyeres.2018.08.002
|
[3] |
Wildi, F. P., Brusa, G., Riccardi, A., et al. 2003. Towards first light of the 6.5m MMT adaptive optics system with deformable secondary mirror. In Proceedings of SPIE. 4839: 155–163.
|
[4] |
Esposito, S., Riccardi, A., Fini, L., et al. 2010. First light AO (FLAO) system for LBT: final integration, acceptance test in Europe, and preliminary on-sky commissioning results. In Proceedings of SPIE. 7736: 107–118.
|
[5] |
Arsenault, R., Biasi, R., Gallieni, D., et al. 2006. A deformable secondary mirror for the VLT. In Proceedings of SPIE. 6272: 284–295.
|
[6] |
Zuo, H., Liu, Z. M. 2018. Design of microdisplacement measurement system for large aperture adaptive mirror. Optics and Precision Engineering, 26(7): 1612−1620. (in Chinese) doi: 10.3788/OPE.20182607.1612
|
[7] |
Zhang, Z. G., Hu, Q. L., Ma, W. C., et al. 2022. Design and performance research of high efficiency variable reluctance voice coil actuator. Chinese Journal of Liquid Crystal & Displays, 37(1): 21−28. (in Chinese) doi: 10.37188/CJLCD.2021-0272
|
[8] |
Biasi, R., Gallieni, D., Mantegazza, P. 1996. Control law design for electromagnetic actuators at the secondary mirror. In Adaptive Optics. ESO Conference and Workshop Proceedings. 54: 221−227.
|
[9] |
Deshmukh, P. G., Mandal, A., Parihar, P. S., et al. 2018. Design, development, and validation of a segment support actuator for the prototype segmented mirror telescope. Journal of Astronomical Telescopes, Instruments, and Systems, 4(1): 014005. doi: 10.1117/1.JATIS.4.1.014005
|
[10] |
Dai, J. K., Jiang, H. M., Zhong, Q. R., et al. 2014. LD temperature control system based on self-tuning fuzzy PID algorithm. Infrared and Laser Engineering, 43(10): 3287−3291. (in Chinese)
|
[11] |
Xu X., Li T., Bo, X., C., et al. 2000. Matlab Toolbox Application Guide-Control Engineering. Beijing: Publishing House of Electronics Industry. (in Chinese)
|
[12] |
Wang, J. F., Lu, Z. D. 2000. The determine method of membership function in fuzzy control. Henan Science, 18(4): 348−351. doi: 10.13537/j.issn.1004-3918.2000.04.005
|
[13] |
Xi, A. M. 2008. Fuzzy Control Technology. Xi'an: Xidian University Press. (in Chinese)
|
[14] |
Huangpu, H. Y., Zhang, X. Y. 2000. The design method of FUZZY controller–read table method and its application. Journal of Xinjiang Normal University(Natural Sciences Edition), 19(3): 29−33.
|
[1] | Zhimao Du, Qing Lin, Xuejun Rao, Yue Zhong, Jiawen Yao, Hua Bao, Libo Zhong, Yu Liang, Hui Zhang. The Educational Adaptive-optics Solar Telescope at the Shanghai Astronomy Museum [J]. Astronomical Techniques and Instruments, 2024, 1(3): 171-178. DOI: 10.61977/ati2024009 |
[2] | Shuai Yulin, Niu Dongsheng, Wang Hai, Pan Cong. Research on Micro-displacement Actuator for High Precision Mirror Position Control [J]. Astronomical Techniques and Instruments, 2023, 20(3): 250-257. DOI: 10.14005/j.cnki.issn1672-7673.20230320.003 |
[3] | Hu Kaiyu, Aili Yusup, Tan Lingxia. An Application of a Fuzzy Controller in the Adjustment System of the Sub-Reflector of the 25m Radio Antenna of the Xinjiang Astronomical Observatory [J]. Astronomical Research and Technology, 2015, 12(2): 149-158. |
[4] | Aili Yusup, Li Yongjiang, Sun Zengwu, Guo Shaoguang. An Automatic Control System for Changing Feeds Based on Fuzzy PID and Laser Ranging [J]. Astronomical Research and Technology, 2013, 10(2): 162-170. |
[5] | ZHOU Yu, XIONG Yao-heng. Analysis of Anisoplanatic Errors in Adaptive Optical Systems Based on Natural Guiding Stars [J]. Astronomical Research and Technology, 2009, 6(1): 8-12. |
[6] | WANG Xiang-feng, ZHANG Jin, Aili yu. The Fuzzy Control Policy Implementation of Software and Hardware Adopted in Automatically Changing Receiver System of 25m Radio Telescope [J]. Astronomical Research and Technology, 2005, 2(3): 162-169. |
[7] | XIONG Yao-heng, BAI Jing-ming. Astronomical Observation Results Using Adaptive Optical Telescopes [J]. Publications of the Yunnan Observatory, 2000, 0(2): 48-57. |
[8] | Zhang Bin, Li Wei, Song Guofeng, Jin Shengzhen. Presentation on the Electronic Control System of Space Solar Telescope [J]. Publications of the Yunnan Observatory, 1999, 0(S1): 130-133. |
[9] | Xiong Yaoheng, Jiang Chongguo, Wang Wu, Zheng Xianming, Zhang Yuncheng, Feng Hesheng. Adaptive Optics System and Its Application Predictions at 1.2m Telescope of Yunnan Observatory [J]. Publications of the Yunnan Observatory, 1999, 0(S1): 63-67. |
[10] | Zhang Chen. The Precision Test for the 1.2m Telescope Surface Applied to Adaptive Optics System [J]. Publications of the Yunnan Observatory, 1999, 0(1): 69-70. |
1. | Lu, W.. Optimization and design of electromechanical control automation based on dual motor control algorithm. Frontiers in Mechanical Engineering, 2024. DOI:10.3389/fmech.2024.1485041 |
E | ΔKP,ΔKI,ΔKD | ||||||
EC=NB | EC=NM | EC=NS | EC=ZO | EC=PS | EC=PM | EC=PB | |
NB | PB, NB, PS | PB, NB, NS | PM, NM, NB | PM, NM, NB | PS, NS, NB | ZO, ZO, NM | ZO, ZO, PS |
NM | PB, NB, PS | PB, NB, NS | PM, NM, NB | PS, NS, NM | PS, NS, NM | ZO, ZO, NS | NS, ZO, ZO |
NS | PM, NM, ZO | PM, NM, NS | PM, NS, NM | PS, NS, NM | ZO, ZO, NS | NS, PS, NS | NS, PS, ZO |
ZO | PM, NM, ZO | PM, NM, NS | PS, NS, NS | ZO, ZO, NS | NS, PS, NS | NM, PM, NS | NM, PM, ZO |
PS | PS, NM, ZO | PS, NS, ZO | ZO, ZO, ZO | NS, PS, ZO | NS, PS, ZO | NM, PM, ZO | PM, PB, ZO |
PM | PS, NO, PB | ZO, ZO, NS | NS, PS, PS | NM, PS, PS | NM, PM, PS | NM, PB, PS | NB, PB, PB |
PB | ZO, NO, PB | ZO, ZO, PM | NM, PS, PM | NM, PM, PM | NM, PM, PS | NB, PB, PS | NB, PB, PB |
Input | Interval | ||||||||||||
(−∞, −5.5) | [−5.5, −4.5) | [−4.5, −3.5) | [−3.5, −2.5) | [−2.5, −1.5) | [−1.5, −0.5) | [−0.5, 0.5) | [0.5, 1.5) | [1.5, 2.5) | [2.5, 3.5) | [3.5, 4.5) | [4.5, 5.5) | [5.5, +∞) | |
Ke⋅e | −6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Kec⋅ec | −6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Ke⋅e | Kec⋅ec | ||||||||||||
−6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |
−6 | 5.16 | 5.08 | 4.88 | 4.19 | 3.95 | 3.56 | 3.66 | 2.98 | 1.72 | 1.02 | −0.121 | −0.407 | −0.411 |
−5 | 5.08 | 5.08 | 4.8 | 4.19 | 3.95 | 3.06 | 3.11 | 2.95 | 1.67 | 0.995 | −0.297 | −0.969 | −0.987 |
−4 | 4.88 | 4.8 | 4.88 | 4.19 | 3.95 | 3.06 | 2.31 | 2.31 | 1.35 | 0.732 | −0.286 | −1.12 | −1.57 |
−3 | 4.19 | 4.19 | 4.19 | 4.19 | 3.94 | 3.06 | 2.02 | 1.01 | 0.688 | 0 | −0.732 | −1.04 | −1.66 |
−2 | 3.95 | 3.95 | 3.95 | 3.94 | 3.95 | 3.06 | 2.02 | 0.978 | 0 | −0.688 | −1.35 | −1.67 | −1.72 |
−1 | 3.92 | 3.91 | 3.67 | 3.06 | 3.06 | 2.12 | 0.994 | −0.0132 | −1.33 | −2 | −2.73 | −2.94 | −2.94 |
0 | 3.76 | 3.73 | 3.52 | 2.9 | 2.14 | 0.994 | 0.293 | −0.794 | −2.14 | −2.9 | −2.67 | −2.69 | −2.78 |
1 | 2.98 | 2.95 | 2.74 | 2 | 1.33 | 0 | −0.794 | −1.08 | −2.4 | −3.03 | −1.26 | 0 | 0.102 |
2 | 1.72 | 1.67 | 1.35 | 0.688 | 0 | −1.33 | −2.14 | −2.4 | −2.31 | −3.08 | −1.75 | 0.278 | 2.42 |
3 | 1.66 | 1.04 | 0.732 | 0 | −0.688 | −2 | −2.9 | −3.03 | −3.08 | −3.08 | −1.41 | −0.551 | 0.152 |
4 | 1.57 | 1.11 | 0.00784 | −1.27 | −1.86 | −2.74 | −3.52 | −3.67 | −3.76 | −3.72 | −2.8 | −3.17 | −3.27 |
5 | 0.987 | 0.962 | 0.00812 | −2.01 | −2.83 | −2.98 | −3.73 | −3.91 | −3.93 | −4.15 | −4.2 | −4.2 | −4.59 |
6 | 0.411 | 0.399 | −0.167 | −2.04 | −3.3 | −3.53 | −3.76 | −3.92 | −3.95 | −4.19 | −4.78 | −4.69 | −4.78 |
Controller | Raising time /ms |
Overshoot /(%) |
Settling time /ms |
PID | 18.32 | 23.44 | 56.51 |
Fuzzy-PID | 17.49 | 17.50 | 41.95 |
Controller | Raising time /ms | Overshoot /(%) |
Settling time /ms |
PID | 19.51 | 12.60 | 38.98 |
Fuzzy-PID | 19.69 | 8.10 | 37.40 |
Controller | Raising time /ms | Overshoot /(%) |
Settling time /ms |
PID | 79.00 | 19.39 | 307.00 |
Fuzzy- PID | 63.00 | 4.22 | 99.50 |