Two-phase vibration mode control method based on open-closed loop PID type iterative learning
Patent Information
- Application Number
- CN202311794106.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-12-25
- Publication Date
- 2026-09-22
- Estimated Expiration
- 2043-12-25
AI Technical Summary
[0030](1)、本发明通过开闭环PID型迭代学习控制振动模态。在第k次迭代、第t时刻振动模态与第k-1次迭代、第t时刻振动模态的差值为第k次迭代的输出误差ek(t)。且由于本算法采用的是开闭环结构,因此根据反馈可同时计算第k+1次的输出误差ek+1(t)。根据两项误差及第k次迭代时的输入电压可以计算出第k+1次迭代时的输入电压。如此循环控制,直到获得等幅正交的两相振动模态。采用开闭环PID型迭代学习算法,与其他迭代学习算法相比,开闭环PID型迭代学习算法具有更快的收敛速度和更高的鲁棒性,通过较少迭代次数就可以精准跟随给定,从而达到精准控制振动模态的效果。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of ultrasonic motor stator vibration mode control technology, specifically a two-phase vibration mode control method based on open-loop and closed-loop PID iterative learning. This method is used to synthesize an ideal traveling wave from the two-phase vibration modes of a traveling wave ultrasonic motor based on open-loop and closed-loop PID iterative learning. Background Technology
[0002] Traveling-wave ultrasonic motors (TWUSMs) utilize the inverse piezoelectric effect to excite the stator to vibrate in a microscopic traveling wave manner, which in turn drives the macroscopic motion of the rotor through contact friction. They offer advantages such as low speed and high torque, immunity to magnetic field interference, flexible design, and excellent position and speed control. They are primarily used in high-precision fields such as robotics, precision instruments, medical devices, aerospace, and advanced weaponry.
[0003] However, even after its development, TWUSM still suffers from drawbacks such as low output power, low efficiency, large torque ripple, and unstable control precision. The main reasons for this are the presence of strong nonlinearity, strong coupling, and parameter uncertainties during its operation, which are detrimental to control. Therefore, in-depth research into the control performance of TWUSM remains of significant practical importance.
[0004] Chen Ning, Zheng Jieji, et al. (Chen Ning, Zheng Jieji, Fan Shixun, et al. High-precision control of speed and position of ultrasonic motor [J]. Optics and Precision Engineering, 2020, 28(04):790-799) used a dual-loop composite control algorithm to improve the speed control stability of TWUSM and achieved high-resolution position control of the motor through drive parameter optimization. Shi Jingzhuo's team at Henan University of Science and Technology (Shi Jingzhuo, Wenwen Huang and Zhao Liuqing. Improved Indirect Iterative Learning MIT Control Method for Ultrasonic Motor [J]. IEEE Access, 2021, PP. (9):100308-100318.) improved the control performance of the motor based on the nonlinear Hammerstein model of ultrasonic motor by combining the traditional control algorithm with the idea of iterative learning and improving iterative learning control. However, existing control studies have mostly focused on the external characteristics of motor speed and position, neglecting the internal operating mechanism of TWUSM. From the perspective of motor operating principles, controlling the two-phase vibration modes to be of equal amplitude and orthogonal is a crucial condition for synthesizing an ideal traveling wave. Synthesizing an ideal traveling wave plays a vital role in reducing losses, improving operating efficiency, minimizing torque ripple, and enhancing control accuracy. However, current technologies for controlling the two-phase vibration modes to be of equal amplitude and orthogonal primarily achieve this by controlling the duty cycle and phase. Due to the asymmetry of the motor's structure, parameter uncertainties, and deviations in the drive circuit parameters, the two-phase vibration modes cannot achieve complete equal amplitude and orthogonality, thus failing to obtain a "pure" traveling wave. Consequently, the aforementioned defects persist during motor operation. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a two-phase vibration mode equal-amplitude orthogonal control method based on open-loop and closed-loop PID iterative learning. This method can fundamentally solve the problem of impure traveling waves, completely converting the excited standing waves into traveling waves, thereby improving motor efficiency, reducing motor losses, and enhancing control accuracy.
[0006] The technical solution adopted by this invention to solve this technical problem is:
[0007] A two-phase vibration modal control method based on open-loop and closed-loop PID iterative learning is used to control a traveling wave ultrasonic motor to generate equal-amplitude orthogonal vibration modes, thereby synthesizing an ideal traveling wave; the control method includes the following:
[0008] The input voltage and current of the traveling wave ultrasonic motor are collected during the current vibration cycle to calculate the two-phase vibration modes of the ultrasonic motor during the current vibration cycle, using y k (t) represents;
[0009] The calculated two-phase vibration modes are stored in memory. The number of stored sequences must be greater than the number of sequences collected for one vibration cycle according to the sampling frequency.
[0010] Given a two-phase vibration mode y that satisfies the requirement of equal amplitude and orthogonality of phases A and B. d (t), the difference between the given two-phase vibration mode and the calculated vibration mode is used to calculate the input voltage of the next vibration cycle after passing through the open-loop PID iterative learning control algorithm;
[0011] The process of the open-loop and closed-loop PID iterative learning control algorithm is as follows: Define the output error e of the kth iteration. k (t) represents the given two-phase vibration mode y d (t) and the calculated two-phase vibration modes y k (t) is subtracted, and the output error e of the (k+1)th iteration is obtained. k+1 (t);
[0012] Based on the output error e k (t), e k+1 (t) and input voltage u k (t), calculate the input voltage u for the next iteration using formula (3). k+1 (t);
[0013]
[0014] Where, k p k i and k d For open-loop PID coefficients, Γ p ,Γ i and Γ d t represents the closed-loop PID coefficients; the open-loop and closed-loop PID coefficients satisfy the convergence condition of iterative learning.
[0015] The two-phase vibration modes obtained in the (k+1)th iteration are observed using a vibration mode sliding mode observer.
[0016] When the two-phase vibration mode obtained in the (k+1)th iteration matches the given two-phase vibration mode, the iteration stops to obtain the equal-amplitude orthogonal two-phase vibration mode, and the input voltage at this time is output.
[0017] The duty cycle is calculated based on the input voltage obtained from the open-loop PID iterative learning control algorithm to generate a PWM wave output to the full-bridge drive circuit; the square wave voltage u on the secondary side of the full-bridge drive circuit is... o (t) Perform a Fourier expansion:
[0018]
[0019] Among them, u on (t) represents the nth harmonic component of the square wave input voltage, u n =2U o [sinnαπ-sinnπ(α-1)] / nπ,U O Let α be the amplitude of the square wave voltage and α be the duty cycle. The square wave signal passes through a matching inductor and a TWUSM static capacitor to form an LC resonant circuit, and the sum of the harmonics of the motor input voltage, u, is obtained as follows:
[0020]
[0021] When matching inductor L and static capacitor C are selected to make ω0 close to ω, and considering only the fundamental wave effect, the driving voltage is approximately assumed to be as shown in formula (6):
[0022]
[0023] When a full-bridge drive circuit is used to drive the TWUSM, the terminal voltage u output by the open-loop and closed-loop PID iterative learning control algorithm is... k+1 (t) further considers the pulse width, amplitude, and phase of the square wave voltage, u o Keeping it constant, the duty cycle α is calculated according to formula (7):
[0024]
[0025] Where U is the terminal voltage amplitude of the open-loop PID iterative learning control algorithm, and Uo is the amplitude of the square wave voltage;
[0026] The PWM wave output is adjusted according to the obtained duty cycle α and sent to the full-bridge drive circuit to drive the motor.
[0027] k p =0.1, k d =90, k i =0.001; Γ p =0.01、Γ d =220、Γ i =0.01.
[0028] The equipment used in the method includes an ARM+FPGA core controller, a Hall current sensor, a high-speed ADC, a full-bridge drive circuit, and a traveling wave ultrasonic motor.
[0029] Compared with the prior art, the substantial advantages of the present invention are as follows:
[0030] (1) This invention uses open-loop and closed-loop PID iterative learning to control vibration modes. The difference between the vibration mode at time t in the k-th iteration and the vibration mode at time t in the (k-1)-th iteration is the output error e of the k-th iteration. k (t). Furthermore, since this algorithm employs an open-loop and closed-loop structure, the output error e of the (k+1)th iteration can be calculated simultaneously based on the feedback. k+1 (t). The input voltage at the (k+1)th iteration can be calculated based on the two errors and the input voltage at the kth iteration. This cyclic control continues until a two-phase vibration mode with equal amplitude and orthogonality is obtained. An open-loop PID iterative learning algorithm is adopted. Compared with other iterative learning algorithms, the open-loop PID iterative learning algorithm has a faster convergence speed and higher robustness. It can accurately follow the given condition with fewer iterations, thereby achieving the effect of precise control of the vibration mode.
[0031] (2) This invention directly addresses the vibration modes, utilizing an open-loop and closed-loop PID iterative learning algorithm to obtain the input voltages for controlling the two-phase vibration modes with equal amplitude and orthogonality. The input voltages are then converted into duty cycles and output to the two-phase full-bridge drive circuit, thereby generating two-phase vibration modes with equal amplitude and orthogonality, and ultimately synthesizing an ideal traveling wave. Compared to other research on the control of ultrasonic motors, this invention is directly applied to the control of the vibration modes of ultrasonic motors, fundamentally improving the motor's stability and operating efficiency, and effectively reducing torque ripple.
[0032] (3) This invention offers flexible control and can overcome the defect of unsatisfactory vibration modes caused by the asymmetry of the two phases of the traveling wave ultrasonic motor due to the manufacturing process. It can also overcome the nonlinear defects caused by the friction drive of the stator and rotor of the traveling wave ultrasonic motor. By using the previous vibration mode sliding mode observer, vibration mode estimation can be realized, solving the problem of observation difficulty. Attached Figure Description
[0033] Figure 1 This is the overall control block diagram of the two-phase vibration modal control method based on open-loop and closed-loop PID iterative learning according to the present invention.
[0034] Figure 2 This is a diagram of the full-bridge drive circuit in this invention.
[0035] Figure 3 This refers to the secondary voltage of the full-bridge drive circuit in this invention.
[0036] Figure 4The figures show the simulation curves of the two-phase vibration modes and two-phase input voltages obtained after control using an open-loop iterative learning algorithm. Figures (a) and (b) show the curves of the two-phase vibration modes after different iterations. From top to bottom, the curves in the two figures represent: the given vibration mode curve, the vibration mode curve after 200 iterations, the vibration mode curve after 100 iterations, and the vibration mode curve after 50 iterations. Figures (c) and (d) show the two-phase input voltages after different iterations. From top to bottom, the curves in the two figures represent: the input voltage after 200 iterations, the input voltage after 100 iterations, and the input voltage after 50 iterations.
[0037] Figure 5 Figure 1 shows the square wave input voltage, two-phase input current, two-phase input voltage, and two-phase vibration modes obtained after using an open-loop iterative learning algorithm for control. Figure (a) shows the square wave input voltage of phase A and phase B when the vibration modes are of equal amplitude and orthogonal; Figure (b) shows the input current of phase A and phase B when the vibration modes are of equal amplitude and orthogonal; Figure (c) shows the input voltage of phase A and phase B when the vibration modes are of equal amplitude and orthogonal; Figure (d) shows the experimentally obtained phase A and phase B vibration modes.
[0038] Figure 6 The torque comparison is shown in (a) before and after the adoption of the open-loop PID iterative learning control algorithm (b). Detailed Implementation
[0039] The present invention will be further explained below with reference to the embodiments and accompanying drawings, but this is not intended to limit the scope of protection of this application.
[0040] Figure 1 This is the overall control block diagram of the two-phase vibration modal control method based on open-loop PID iterative learning of the present invention. Taking one phase as an example, combined with a given vibration mode w dA (t) and the vibration mode w calculated by the vibration mode sliding observer A The output error e is obtained by subtracting (t). kA (t). Output error e kA (t) and input voltage u kA (t) After the open-loop and closed-loop PID iterative learning control algorithm, the input voltage u for the next iteration can be obtained. (k+1)A (t), and then the duty cycle α is obtained through duty cycle calculation. Adjusting the duty cycle α, the four PWM signals are input to the full-bridge drive circuit. After being boosted by transformer T and passed through the LC resonant circuit, the input voltage u at the motor terminal is... (k+1) (t), Input current i (k+1) (t) The new vibration mode is calculated by the vibration mode sliding mode observer, and then the next iteration is performed.
[0041] Figure 2 This is a schematic diagram of the full-bridge drive circuit in this invention. The entire full-bridge drive circuit mainly consists of four MOSFETs M1-M4, a transformer, a matching inductor L, and a static capacitor C. d Composition: Each phase is connected to a full-bridge drive circuit.
[0042] This invention provides a two-phase vibration modal control method based on open-loop and closed-loop PID iterative learning. The equipment used to implement this method includes an ARM+FPGA core controller, a Hall current sensor, a high-speed ADC, a full-bridge drive circuit, and a traveling wave ultrasonic motor. The steps of the control method are as follows:
[0043] Step 1: Set the initial phase difference and initial drive voltage of the full-bridge drive circuit;
[0044] The phase difference between the two full-bridge drive circuits is set to π / 2, with phase A at π / 2 and phase B at 0. Since the drive voltage of the full-bridge drive circuit is proportional to the duty cycle, the drive voltage can be adjusted by changing the duty cycle. The initial duty cycle is set to d. A (0)=d B (0) = 30%. The phase difference of the full-bridge drive circuit has a certain functional relationship with the phase difference of the two-phase vibration modes, which satisfies the electromechanical coupling equation.
[0045] The second step is to collect the input voltage and input current of the traveling wave ultrasonic motor during the current vibration cycle to calculate the two-phase vibration mode of the ultrasonic motor during the current vibration cycle.
[0046] Using an FPGA-controlled high-speed ADC, the analog signal transmitted by the Hall current sensor and the voltage divider sampling resistor is sampled at a sampling frequency of 40kHz to obtain the input voltage u during the k-th iteration and the t-th oscillation period. k and input current i k And calculate the two-phase vibration mode y of the current vibration period according to formula (1). k (t).
[0047]
[0048] Among them, u k =[u kA ,u kB ], i k =[i kA i kB ], w = [w A ,w B ]; u kA ,u kB Let i be the input voltage of phases A and B at the k-th iteration.kA i kB R represents the input currents of phases A and B during the k-th iteration; d and C d These are the node loss resistance and static capacitance resistance of the two-phase piezoelectric ceramic, respectively. A and w B These are the vibration modes of phases A and B, respectively. and Let be the velocity of the vibration modes of phases A and B. Here, y k (t) = w. The calculated vibration modes are stored in memory. The number of stored sequences must be greater than the number of sequences collected at the sampling frequency for one vibration cycle, to ensure that a complete vibration cycle can be stored.
[0049] The third step involves subtracting the given two-phase vibration modes from the calculated vibration modes, and then using an open-loop PID iterative learning control algorithm to calculate the input voltage u for the next vibration cycle. k+1 (t).
[0050] Given two-phase vibration modes y d (t) Set the amplitude to 0.6 μm, and define the output error e of the k-th iteration. k (t) represents the given two-phase vibration mode y d (t) and the calculated two-phase vibration modes y k (t) is the difference, i.e.:
[0051] e k (t)=y d (t)-y k (t) (2)
[0052] Because of the closed-loop control, e can be calculated simultaneously. k+1 (t). Based on the output error e k (t), e k+1 (t) and input voltage u k (t), the input voltage u for the next iteration can be calculated using formula (3). k+1 (t)
[0053]
[0054] Where, k p k i and k d For open-loop PID coefficients, Γ p ,Γ i and Γ d These are the closed-loop PID coefficients.
[0055] Both the open-loop and closed-loop PID coefficients must satisfy the following iterative learning convergence condition:
[0056] (1) Ensure that the initial conditions are the same for each iteration:
[0057] x k+1 (t)=x k (t)=x d (0), k = 0, 1, 2…,
[0058] in x is a state variable. d (0) represents the desired initial state;
[0059] (2) The selected parameters must satisfy the following equation:
[0060] ||(I+Γ d CB) -1 ||·||Ik d CB||<1
[0061] Where matrices C and B are coefficients derived from the state equation of the ultrasonic motor, and I is the identity matrix. In this embodiment, the coefficient k is set... p =0.1, k d =90, k i =0.001; Γ p =0.01、Γ d =220、Γ i =0.01.
[0062] Step 4: Calculate the duty cycle based on the obtained input voltage to generate a PWM wave output to the full-bridge driver circuit. The square wave voltage u on the secondary side of the full-bridge driver circuit... o (t) Perform Fourier expansion
[0063]
[0064] Where u on (t) represents the nth harmonic component of the square wave input voltage, u n =2U o [sinnαπ-sinnπ(α-1)] / nπ. The square wave signal passes through a matching inductor and a TWUSM static capacitor to form an LC resonant circuit, and the sum of the harmonics u of the motor input voltage is obtained as:
[0065]
[0066] Select matching inductor L and static capacitor C d By making ω0 close to ω, only the fundamental frequency of the voltage is amplified, while all other harmonics are attenuated. Considering only the fundamental frequency, the driving voltage can be approximated as...
[0067]
[0068] When a full-bridge drive circuit is used to drive the TWUSM, the terminal voltage u output by the open-loop and closed-loop PID iterative learning control algorithm is... k+1 (t) further considers the pulse width, amplitude, and phase of the square wave voltage, u o Keeping it constant, the duty cycle α is calculated according to formula (7):
[0069]
[0070] Where U is the terminal voltage amplitude of the open-loop PID iterative learning control algorithm, and Uo is the amplitude of the square wave voltage.
[0071] The duty cycle is calculated based on the voltage obtained from the open-loop PID iterative learning control algorithm. The PWM wave output is then adjusted according to the obtained duty cycle α and sent to the full-bridge drive circuit to drive the motor.
[0072] Step 5: Measure the vibration modes of the two-phase stator using a sliding mode observer. The voltage and current obtained from the motor side are input to the sliding mode observer, and the vibration modes obtained in the (k+1)th iteration are observed using the sliding mode observer. The sliding mode observer is as follows:
[0073]
[0074] in G represents the system state estimated by the observer, G is the parameter matrix with stable eigenvalues, v is the control input, A and B are the variables in the state equation of the ultrasonic motor, and y is the vibration mode w.
[0075] Step 6: Repeat steps 2 through 5 until two-phase vibration modes with equal amplitude and orthogonality are obtained.
[0076] An FPGA was used to control a Hall current sensor to sample the output voltage and current of a traveling wave ultrasonic motor at a sampling frequency of 40kHz. Based on the collected output voltage and current, the experimental vibration modes were calculated using simulation software.
[0077] When setting the parameters of the open-loop and closed-loop PID iterative learning algorithm and the motor parameters according to the above requirements, the motor parameters are measured based on the admittance circle method. The traveling wave ultrasonic motor selected is model TRUM60A, used in conjunction with a full-bridge drive circuit.
[0078] Depend on Figure 4 As shown in Figures (a) and (b), after a certain number of iterations, the amplitudes of phases A and B stabilize at 0.5838 μm and 0.5920 μm, respectively; the phase difference is π / 2. From... Figure 4Simulation diagrams (c) and (d) showing the input voltages of phases A and B reveal that, through continuous iteration, the amplitudes of the two-phase motor input voltages stabilize at 224.618V and 179.463V, respectively; the phase difference between the two phase voltages is π / 2. The input square wave voltage stabilizes at 125.6V.
[0079] Figure 5 As shown in Figure (a), the amplitudes of the square wave voltages in phases A and B are approximately 96V; the phase difference is π / 2. The duty cycles are 27.84% and 26.73%, respectively. The measured motor input current and input voltage are as follows: Figure 5 As shown in Figures (b) and (c), the input voltage amplitude of phase A is 160.809V, and the input voltage amplitude of phase B is 156.023V; the phase difference is π / 2. The vibration modes output by the vibration mode sliding mode observer are as follows: Figure 5 As shown in Figure (d), it can be seen that the amplitude of the A-phase vibration mode is stable at 0.6231 μm, and the amplitude of the B-phase vibration mode is stable at 0.6318 μm, with a phase difference of π / 2 between the two phases.
[0080] The experimental load torque was set at 0.25 Nm. According to... Figure 6 As shown in Figure (a), when the duty cycle is 40%, the average torque is 0.2621 Nm; from Figure 6 As shown in Figure (b), the average torque obtained after using iterative learning control is 0.2587 Nm. It can be seen that adding an open-loop PID iterative learning control algorithm can effectively reduce torque ripple and improve control accuracy. The control method proposed in this application can effectively reduce torque ripple.
[0081] Therefore, the open-loop iterative learning control algorithm proposed in this invention can effectively control the TWUSM two-phase vibration mode to accurately follow the given condition, thereby controlling the formation of two-phase modes with equal amplitude and a phase difference of π / 2 to synthesize an ideal traveling wave, further improving the motor drive performance.
[0082] This invention directly targets the two-phase vibration modes for control, thus fundamentally solving the nonlinearity problem of the motor. Compared with the coordinated control approach used in previous research, this invention selects the vibration modes as the direct control target and employs an open-loop and closed-loop PID iterative learning control algorithm, which has higher robustness and faster convergence speed. Therefore, it achieves better control of the two-phase vibration modes, improves the motor's operating efficiency, and reduces torque ripple.
[0083] Any aspects not covered in this invention are applicable to existing technologies.
Claims
1. A two-phase vibration modal control method based on open-loop and closed-loop PID iterative learning, used to control a traveling wave ultrasonic motor to generate equal-amplitude orthogonal vibration modes, and then synthesize an ideal traveling wave; characterized in that, The control method includes the following: The input voltage and current of the traveling wave ultrasonic motor are collected during the current vibration cycle to calculate the two-phase vibration modes of the ultrasonic motor during the current vibration cycle, using y k (t) represents; The calculated two-phase vibration modes are stored in memory. The number of stored sequences must be greater than the number of sequences collected for one vibration cycle according to the sampling frequency. Given a two-phase vibration mode y that satisfies the requirement of equal amplitude and orthogonality of phases A and B. d (t), the difference between the given two-phase vibration mode and the calculated vibration mode is used to calculate the input voltage of the next vibration cycle after passing through the open-loop PID iterative learning control algorithm; The process of the open-loop and closed-loop PID iterative learning control algorithm is as follows: Define the output error e of the kth iteration. k (t) represents the given two-phase vibration mode y d (t) and the calculated two-phase vibration modes y k (t) is subtracted, and the output error e of the (k+1)th iteration is obtained. k+1 (t); Based on the output error e k (t), e k+1 (t) and input voltage u k (t), calculate the input voltage u for the next iteration using formula (3). k+1 (t); Where, k p k i and k d For open-loop PID coefficients, Γ p ,Γ i and Γ d t represents the closed-loop PID coefficients; the open-loop and closed-loop PID coefficients satisfy the convergence condition of iterative learning. The two-phase vibration modes obtained in the (k+1)th iteration are observed using a vibration mode sliding mode observer. When the two-phase vibration mode obtained in the (k+1)th iteration matches the given two-phase vibration mode, the iteration stops to obtain the equal-amplitude orthogonal two-phase vibration mode, and the input voltage at this time is output.
2. The two-phase vibration mode control method according to claim 1, characterized in that, The duty cycle is calculated based on the input voltage obtained from the open-loop PID iterative learning control algorithm to generate a PWM wave output to the full-bridge drive circuit; the square wave voltage u on the secondary side of the full-bridge drive circuit is... o (t) Perform a Fourier expansion: Among them, u on (t) represents the nth harmonic component of the square wave input voltage, u n =2U o [sinnαπ-sinnπ(α-1)] / nπ,U O Let α be the amplitude of the square wave voltage and α be the duty cycle. The square wave signal passes through a matching inductor and a TWUSM static capacitor to form an LC resonant circuit, and the sum of the harmonics of the motor input voltage, u, is obtained as follows: When matching inductor L and static capacitor C are selected to make ω0 close to ω, and considering only the fundamental wave effect, the driving voltage is approximately assumed to be as shown in formula (6): When a full-bridge drive circuit is used to drive the TWUSM, the terminal voltage u output by the open-loop and closed-loop PID iterative learning control algorithm is... k+1 (t) further considers the pulse width, amplitude, and phase of the square wave voltage, u o Keeping it constant, the duty cycle α is calculated according to formula (7): Where U is the terminal voltage amplitude of the open-loop PID iterative learning control algorithm, and Uo is the amplitude of the square wave voltage; The PWM wave output is adjusted according to the obtained duty cycle α and sent to the full-bridge drive circuit to drive the motor.
3. The two-phase vibration mode control method according to claim 1, characterized in that... ,k p =0.1、k d =90、k i =0.001;C p =0.01、C d =220、C i = 0.
01.
4. The two-phase vibration mode control method according to claim 1, characterized in that, The equipment used in the method includes an ARM+FPGA core controller, a Hall current sensor, a high-speed ADC, a full-bridge drive circuit, and a traveling wave ultrasonic motor.
Citation Information
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