Radar antenna servo platforms are the actuating link between the command computer and the antenna aperture. They must set azimuth and elevation angles, hold a fixed pointing direction, and support constant-speed scanning. In integrated radar systems, the platform is also constrained by the antenna envelope, vehicle or shelter dimensions, and mobility requirements. These constraints turn the servo platform into a mass-and-volume problem as much as a control problem: every motor, bearing, encoder, and cable that sits on a moving axis adds inertia and complicates wiring.
A conventional two-axis design uses an azimuth outer yoke and an elevation inner cradle. The elevation motor, elevation encoder, bearings, and cable harness are mounted on the inner axis, and the azimuth drive carries the complete inner assembly. This nested arrangement is mechanically straightforward and can achieve high stiffness, but it is bulky, heavy, and difficult to route through the elevation rotation. For a compact export radar with strict size and weight limits, an alternative layout is needed.
Coaxial layout and the role of spiral bevel gears
The platform described here replaces the nested elevation drive with a coaxial differential arrangement. The azimuth motor, elevation motor, azimuth encoder, elevation encoder, azimuth bearing, and elevation bearing are mounted on a common centerline in the base. Both axes use torque motors in direct drive. The azimuth motor drives an azimuth adapter, while the elevation motor drives an elevation cantilever. The two coaxial members can rotate together or differ in angle and speed.
The elevation cantilever carries a spiral bevel pinion that meshes with a bevel gear fixed to the output turntable. The output turntable axis is perpendicular to the common motor centerline, so the bevel pair provides the right-angle transfer to the elevation axis. When the two coaxial members rotate together, the bevel pair behaves as a locked train and the output turntable rotates in azimuth. When the two members rotate differentially, the pinion rolls around the bevel gear and the output turntable changes elevation. The elevation output is therefore controlled by the relative angle and speed of the two coaxial inputs, not by a motor mounted on the moving elevation cradle.
Gleason-type spiral bevel gears are used because their curved teeth engage gradually, giving smoother transmission and higher contact ratio than straight bevel gears. They are well suited to a compact right-angle stage. The trade-off is that the curved tooth geometry is sensitive to manufacturing accuracy, mounting alignment, and backlash. In this platform, that sensitivity matters because the elevation pair is not a reducing stage.
Kinematic decoupling
Let the elevation bevel pinion have z1 teeth and the output bevel gear have z2 teeth. The gear ratio is
$$
i_G=\frac{z_2}{z_1}=\tan 35^\circ=0.7
$$
Although iG is written as a reduction ratio, its value is below unity, so the elevation pair is speed-increasing: one revolution of the output requires only 0.7 revolution of the motor-side differential. If the elevation motor alone rotates through θ1 while the azimuth motor is stationary, the output elevation angle is
$$
\theta_2=\frac{z_1}{z_2}\theta_1=\frac{\theta_1}{i_G}
$$
If the azimuth motor alone rotates through θ3, the gear constraint would also produce an elevation motion
$$
\theta_4=\frac{z_1}{z_2}\theta_3=\frac{\theta_3}{i_G}
$$
To keep the elevation pointing unchanged during an azimuth rotation, the elevation motor must rotate in the same direction by
$$
\theta_5=\theta_4 i_G=\theta_3
$$
This is the geometric coupling between the two axes. In command form, if θAcmd and θEcmd are the commanded output azimuth and elevation angles, the motor commands become
$$
\theta_{mA}^{\mathrm{cmd}}=\theta_A^{\mathrm{cmd}}
$$
$$
\theta_{mE}^{\mathrm{cmd}}=\theta_A^{\mathrm{cmd}}+i_G\,\theta_E^{\mathrm{cmd}}
$$
The inverse relation shows how strongly the elevation output depends on the difference between the two motor positions:
$$
\theta_A=\theta_{mA},\qquad
\theta_E=\frac{\theta_{mE}-\theta_{mA}}{i_G}
$$
With iG = 0.7, the output elevation motion is 1.43 times the differential input. This is the central accuracy penalty of the layout: motor position errors, encoder errors, and gear backlash in the elevation path are magnified at the output. The azimuth output, by contrast, is directly tied to one motor axis and does not accumulate the second motor error in the same way.
The decoupling is executed inside a single two-axis controller. A DSP and FPGA set handles both axes, and the coupling information is exchanged inside the DSP rather than between two independent drives. This reduces communication latency and improves the real-time consistency of the decoupling. It does not, however, remove mechanical backlash or gear transmission error.
Acceleration and torque sizing
The angular acceleration requirement comes from two sources: the acceleration needed to meet the system reaction time and the acceleration needed to support the velocity-loop bandwidth. No explicit maximum acceleration was imposed by the system specification. Using an engineering velocity-loop small-signal bandwidth of fbw = 40 Hz at an amplitude of Am = 0.5°/s, the required acceleration is
$$
\varepsilon_{bw}=A_m\,2\pi f_{bw}
=0.5\times 2\pi\times 40
=125.66^\circ/\mathrm{s}^2
$$
A design acceleration of 150°/s² was adopted to cover both the bandwidth and response-time requirements. The load inertia was obtained from a 3D model using the reflected form J = JM + JL/iG2. Bearing friction was calculated from
$$
M_f=\mu P\frac{d}{2}
$$
where μ = 0.0015 is the maximum rolling-friction coefficient used for the deep-groove ball bearings, P is the bearing load under 2g overload, and d is the nominal bearing bore. The azimuth bearing used d = 0.05 m; the elevation bearing used d = 0.1 m. The resulting torque budget is summarized in Table 1.
| Axis | J (kg·m²) | ε (°/s²) | Macc (N·m) | Mf (N·m) | Mm (N·m) |
|---|---|---|---|---|---|
| Azimuth | 0.07 | 150 | 0.183 | 0.00183 | 0.370 |
| Elevation | 0.03 | 150 | 0.0785 | 0.00294 | 0.216 |
The design load torque was 0.185 N·m for the azimuth axis and 0.1079 N·m for the elevation axis. Applying the 2.0 engineering factor gave motor torque requirements of 0.370 N·m and 0.216 N·m, respectively. The elevation axis requires less torque, but its accuracy is more sensitive to the gear train because the output is derived from the differential of two motor axes.
Drive and control implementation
The platform uses a three-loop structure: a current loop, a velocity loop, and a position loop. The velocity and position loops use PID controllers; the current loop uses PI regulators. Speed and acceleration feedforward reduce dynamic lag and improve tracking accuracy during scanning and large-angle moves.
The current loop is the most demanding part of the AC drive because it involves coordinate transformation and field orientation. The controller uses field-oriented control in the synchronous d–q frame, with PI regulators that include active damping, back-EMF and cross-coupling decoupling feedforward, and vector anti-windup. The inverter uses seven-segment SVPWM, dual-resistor delay-free current sampling with current prediction, and resolver feedback for motor commutation. Because the motors operate mainly at low speed and the SVPWM remains in its linear range, field weakening is not used.
The current regulator tuning follows the locked-rotor model. With Kp = Laωc and Ki = Raωc, the closed-loop current response is
$$
\frac{i_a}{i_a^*}=\frac{\omega_c}{s+\omega_c}
=\frac{1}{T_c s+1}
$$
where La and Ra are the armature inductance and resistance, ωc is the current-loop bandwidth, and Tc = 1/ωc. This tuning gives a first-order response without overshoot or steady-state error in the simplified model. The current-loop bandwidth was set to 500 Hz. Typical AC servo current loops range from 500 Hz to 2 kHz, with small high-bandwidth drives reaching 3–5 kHz; 500 Hz is consistent with the motor time constant and the low-speed operating regime of this platform.
The anti-windup strategy uses a vector limit rather than independent d and q limits because the two axes are coupled. The PWM output space vector is limited to a circle of radius Vdc/3, with a phase-error-minimizing limit strategy. This keeps the inverter within its linear modulation range while avoiding integrator windup during large commands or disturbances.
The tightly coupled two-axis drive is a single unit with a 18–36 V input, 6 A rated current, 12 A peak current, and support for two motors. It provides RS422/485, CAN, and PWM communication and accepts resolver, SSI, BiSS-C, and Hall feedback. The unit weighs 0.25 kg and measures 120 × 80 × 16 mm. Its small size is important because the drive is part of the platform’s constrained envelope, not an external rack-mounted subsystem.
The axis encoders use an SSI interface with a 2 Mbps data rate and a 10 kHz update period. The 24-bit frame carries 22 bits of position data, one parity bit, and one alarm bit. A full-order PLL observer filters the encoder position and estimates position, speed, and acceleration for the control loops. This allows a medium-resolution, medium-accuracy absolute encoder to provide cleaner feedback than its raw quantization alone would suggest.
The control software performs host communication, command decoupling, encoder acquisition and zero correction, PLL observation, position/velocity loop calculation, current-loop control, SVPWM modulation, and fault protection. The fault logic covers communication failure, encoder failure, position/velocity/current out-of-tolerance conditions, overcurrent, open circuit, overvoltage, undervoltage, and overtemperature. The host sends motion commands over RS422 and receives speed, position, and status information in real time.
Static accuracy budget and test method
The static error budget considered three terms: absolute encoder accuracy Δ1 ≤ 40″, resolution error Δ2 = 1.236″ (one-half quantization unit), and machining/assembly error Δ3 = 5″, including misalignment between the encoder axis and the platform axis. The RMS angular error is
$$
\Delta_{\mathrm{m-abs}}
=\sqrt{\Delta_1^2+\Delta_2^2+\Delta_3^2}
=\sqrt{40^2+1.236^2+5^2}
=40.33”
$$
The estimated position repeatability was
$$
\Delta_{\mathrm{p-rpt}}\le 4\Delta_{\mathrm{m-rpt}}
=4\times 1.236”
=4.944”
$$
For a direct-drive torque-motor system with high stiffness and high-bandwidth feedback, the absolute position accuracy was estimated to approach the encoder-dominated value of about 40.33″, or 0.0112°. That estimate is a sensor-and-assembly budget, not a complete electromechanical error model. It does not include bevel-gear backlash, differential error accumulation, or load-induced deflection.
Positioning accuracy was measured with a laser precision angle measurement platform. A photoelectric ball was mounted on the load, and its spatial position was captured while the platform was commanded to different angles. For azimuth measurement, the elevation axis was locked and the azimuth axis was commanded from −50° to 50° in 5° steps. Although the azimuth axis itself has a −90° to 90° range, the ball mounting limited valid measurement to −50° to 50°. For elevation measurement, the azimuth axis was locked and the elevation axis was commanded over its full −90° to 90° range in 5° steps. The measured angle was compared with the commanded angle, and the error was defined as measured minus commanded.
Measured positioning performance
Table 2 lists selected points from the 5°-spaced measurements. The azimuth axis stayed within ±0.09° over the tested range, with the largest absolute error of 0.09° at −30°. The elevation axis reached a maximum absolute error of 0.16° at −75° and also exceeded 0.1° at +90°, where the error was 0.15°. Since 0.1° corresponds to 360″, the elevation axis did not fully meet the 0.1° target at all measured points.
| Commanded angle (°) | Azimuth error (°) | Elevation error (°) |
|---|---|---|
| −90 | — | −0.13 |
| −75 | — | −0.16 |
| −60 | — | −0.07 |
| −50 | −0.08 | +0.07 |
| −40 | +0.07 | +0.09 |
| −30 | −0.09 | +0.04 |
| −20 | 0.00 | −0.11 |
| −10 | −0.06 | −0.06 |
| 0 | +0.01 | +0.03 |
| 10 | +0.04 | −0.07 |
| 20 | +0.02 | +0.10 |
| 30 | −0.08 | +0.13 |
| 40 | +0.06 | −0.07 |
| 50 | +0.02 | −0.06 |
| 60 | — | +0.10 |
| 75 | — | +0.12 |
| 90 | — | +0.15 |
The measured errors are substantially larger than the 40.33″ static budget. The azimuth error of 0.09° is about eight times the budget, and the elevation error of 0.16° is about fourteen times the budget. This gap is consistent with mechanical error sources that the static budget does not capture. The elevation axis is the limiting axis for three reasons. First, the bevel pair introduces backlash and transmission error, and the speed-increasing ratio magnifies those errors at the output. Second, the elevation output is the difference between two motor positions divided by 0.7, so azimuth-motor error and elevation-motor error both accumulate in the output elevation. Third, the lightweight structure and the photoelectric ball mounted at the outer edge of the elevation axis produce an eccentric moment that can deflect the assembly and perturb the pointing result.
The platform therefore demonstrates the intended coaxial differential concept: the two drive axes are moved to the base, the elevation output is generated by differential motion through spiral bevel gears, and the geometric decoupling is implemented in a single two-axis controller. The layout simplifies cable routing and reduces the moving mass associated with a conventional nested elevation drive. Functional testing indicates basic pointing capability and speed smoothness, and the azimuth axis meets the 0.1° target over the measured range. The elevation axis remains the accuracy bottleneck, with a maximum error of 0.16° and a 0.1° target that is not fully met at all points.
The main engineering lesson is that the coaxial differential architecture trades mechanical simplicity for error sensitivity. It is attractive when envelope and mass dominate, but its accuracy depends strongly on bevel-gear manufacturing quality, backlash control, structural stiffness, and compensation of the differential error path. The static encoder budget alone is not sufficient to predict system accuracy. For this platform, further improvement would require tighter gear machining and mounting, backlash compensation or preload, better structural balance, and control strategies that account for the differential error accumulation rather than only geometric decoupling.