In recent years, the rapid development of robotics has intensified research into sensor technologies, particularly for dynamic performance evaluation. Traditional methods for calibrating sensors, such as using weight plates and impact hammers, often rely on step or pulse excitation. These approaches suffer from narrow bandwidth and poor controllability, limiting their applicability in automated systems. To address these issues, I focused on developing a harmonic excitation device based on electromagnetic vibration principles. This device enables frequency and amplitude control through external circuits, offering superior practicality and ease of operation. In this article, I present the design and analysis of a control circuit for dynamic testing of a six-axis force sensor, emphasizing electromagnetic excitation force control. The circuit incorporates a double closed-loop control strategy to mitigate electromagnetic hysteresis and force attenuation at higher frequencies, ensuring consistent performance across the sensor’s operational bandwidth.
The electromagnetic vibrator I designed consists of a dual E-core structure, which forms two closed magnetic circuits. The left circuit includes a fixed iron core, a baffle plate, and a movable armature, while the right circuit mirrors this arrangement. These components are connected via cylindrical bearings, with a transmission rod attached to one bearing that interfaces with the six-axis force sensor test platform. When alternating current is applied to the left and right coils in a split-wave manner, the movable armatures oscillate, driving the transmission rod to generate reciprocating motion. This motion transmits electromagnetic excitation forces to the sensor, facilitating dynamic testing. The vibrator’s ability to produce harmonic excitations over a wide frequency range makes it ideal for evaluating the dynamic characteristics of a six-axis force sensor.
To understand the output characteristics of the electromagnetic vibrator, I derived its mathematical model based on Newton’s second law and electromagnetic theory. The system’s motion can be described by the equation: $$m \ddot{x}(t) + c \dot{x}(t) + k x(t) = F$$ where \( m \) is the equivalent mass, \( c \) is the damping coefficient, \( k \) is the spring stiffness, \( x(t) \) is the displacement, and \( F \) is the electromagnetic force. The electromagnetic force is given by: $$F = \frac{\mu_0 N^2 A}{2} \left( \frac{i(t)}{x(t)} \right)^2$$ where \( \mu_0 \) is the permeability of free space, \( N \) is the number of coil turns, \( A \) is the cross-sectional area of the iron core, and \( i(t) \) is the current. The voltage equation for the electromagnetic circuit is: $$u(t) = R i(t) + \frac{\mu_0 N^2 A}{2} \frac{d}{dt} \left( \frac{i(t)}{x(t)} \right)$$ This nonlinear system was linearized around an equilibrium point, such as \( x_0 = 1 \, \text{mm} \), resulting in the state-space representation: $$\begin{bmatrix} \Delta \dot{x} \\ \Delta \ddot{x} \\ \Delta \dot{i} \end{bmatrix} = \begin{bmatrix} 0 & 1 & 0 \\ -\frac{k}{m} & -\frac{c}{m} & \frac{K_2}{m} \\ 0 & -\frac{K_1}{K_3} & -\frac{R}{K_3} \end{bmatrix} \begin{bmatrix} \Delta x \\ \Delta \dot{x} \\ \Delta i \end{bmatrix} + \begin{bmatrix} 0 \\ 0 \\ \frac{1}{K_3} \end{bmatrix} \Delta u$$ where \( K_1, K_2, K_3 \) are constants derived from the system parameters. The output force is expressed as: $$\Delta F = K_2 \Delta i – K_3 \Delta x$$ This analysis highlights that the electromagnetic force depends on current, displacement, and frequency, necessitating a dedicated control circuit to maintain stability and accuracy.
The control scheme I implemented employs a double closed-loop structure to address issues like phase lag and amplitude decay. The outer loop is a force feedback loop, where the desired force signal is compared with the real-time force measurement. The resulting error is converted to a digital signal, processed by a force controller, and used to generate a current reference value. This reference is then fed into the inner current loop, which compares it with the actual current feedback to compute an error signal. A current controller processes this error to produce the desired current output. The inner loop enhances current response speed, compensating for the inherent inductance of the electromagnetic coils. Key components of the control system include a comparison ring, PI controller, power amplifier, wave-splitting circuit, and current sampling module. The PI controller performs proportional-integral operations to improve dynamic response, while the power amplifier ensures sufficient drive current for the vibrator. Current sampling provides feedback for error correction, refining output waveform precision.
For signal acquisition, I designed a modular circuit to handle the outputs from the six-axis force sensor’s strain gauge bridges. Each bridge, configured in a differential full-bridge arrangement, converts mechanical strain into electrical signals. The acquisition module comprises a constant current source, amplification stage, power supply interfaces, conversion interfaces, and output ports. The constant current source, built around an LM317 regulator, supplies a stable 20 mA current to the bridge. The amplification stage uses an INA122 chip to boost the weak bridge signals, with gain adjustable via an external resistor. This modular approach ensures redundancy and stability, critical for accurate dynamic testing of the six-axis force sensor.
The control circuit I developed integrates both the controller and driver sections. The controller, based on analog hardware, utilizes a PID strategy for rapid response. The comparison ring, PI control, and current sampling modules employ UA741 operational amplifiers. The PI control section’s transfer function is: $$G(s) = -K_p – \frac{K_i}{s}$$ where \( K_p = \frac{R_6}{R_4} \) and \( K_i = \frac{1}{R_4 C} \), with \( R_4 \) and \( R_6 \) being adjustable resistors for tuning. The power amplifier uses an MP38CL chip, capable of delivering up to 10 A current with a 20 kHz bandwidth, meeting the demands of the electromagnetic vibrator. The signal conversion circuit includes the constant current source and amplifier, as described earlier. The entire circuit board, housing six identical signal acquisition channels, was fabricated and tested for functionality.
In experimental tests, I evaluated the circuit’s performance by applying sinusoidal signals at frequencies of 100 Hz and 200 Hz with 10 V amplitude from a function generator. The control circuit processed these signals, amplified them, and split the waves for input to the vibrator coils. The resulting excitation forces acted on the six-axis force sensor, and the signal acquisition circuit amplified the bridge outputs for analysis. Data collected via a virtual instrument platform showed strain waveforms concentrated around the excitation frequencies, confirming the circuit’s effectiveness. The output amplitude remained stable across the sensor’s bandwidth, validating the design for harmonic excitation-based dynamic testing of the six-axis force sensor.
To summarize, the control circuit I designed successfully enables precise control of electromagnetic excitation forces for dynamic testing of a six-axis force sensor. The double closed-loop approach minimizes hysteresis and attenuation, while the modular signal acquisition ensures reliable data collection. Experimental results demonstrate consistent performance, making this system suitable for automated sensor calibration. Future work could explore digital control implementations or integration with advanced signal processing techniques to further enhance the dynamic capabilities of six-axis force sensors.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Number of Coil Turns | \( N \) | 500 | – |
| Permeability of Free Space | \( \mu_0 \) | \( 1.25 \times 10^{-8} \) | H/cm |
| Cross-Sectional Area | \( A \) | \( 2.54 \times 10^{-4} \) | m² |
| Coil Resistance | \( R \) | 2.5 | Ω |
| Equivalent Mass | \( m \) | 0.5 | kg |
| Spring Stiffness | \( k \) | \( 3.08 \times 10^5 \) | N/m |
| Damping Coefficient | \( c \) | 3.55 | N·s/rad |
The design and analysis presented here underscore the importance of tailored control circuits for dynamic testing of six-axis force sensors. By leveraging electromagnetic principles and closed-loop control, I achieved a robust system that overcomes limitations of traditional methods. The integration of harmonic excitation enables comprehensive evaluation of sensor performance, paving the way for advancements in robotics and automation. As six-axis force sensors become increasingly critical in applications like robotic manipulation and haptic feedback, such dynamic testing frameworks will play a vital role in ensuring accuracy and reliability.
| Component | Function | Specifications |
|---|---|---|
| UA741 Op-Amp | Comparison, PI Control, Current Sampling | General-purpose operational amplifier |
| MP38CL Power Amplifier | Signal Amplification | 10 A max current, 20 kHz bandwidth |
| LM317 Regulator | Constant Current Source | Adjustable output, 1.25 V reference |
| INA122 Amplifier | Signal Amplification | Gain up to 10000, low power |
| Resistive Bridge | Strain to Signal Conversion | Differential full-bridge configuration |
In conclusion, the electromagnetic excitation control circuit I developed provides a effective solution for dynamic testing of six-axis force sensors. Through careful design and experimentation, I demonstrated its ability to maintain force amplitude consistency and handle harmonic excitations. This work contributes to the broader field of sensor dynamics, offering a practical tool for researchers and engineers working with six-axis force sensors in various robotic and industrial contexts.