I. Introduction With the widespread application of rare-earth permanent magnet brushless DC motors in industrial fields, their superior speed regulation characteristics, long lifespan, high efficiency, and easy maintainability have been widely recognized in the motor industry. Currently, foreign aircraft have begun to use rare-earth permanent magnet (REPM) brushless DC motors (BLDCMs) as actuators in their electric electromechanical actuators (EMAs) to replace traditional ordinary brushed DC motors. However, in China, most aircraft EMAs still use ordinary brushed DC motors. These motors, due to the presence of brushes and commutators, are prone to carbon buildup and electromagnetic interference, resulting in poor maintainability and low reliability, thus significantly hindering the improvement of EMA's overall performance. In the aerospace field, EMAs are key actuators in flight control systems, generally requiring a small electromechanical time constant, i.e., a high system frequency response. This is especially true for manned aircraft with very high reliability requirements. Brushless DC motors, due to the absence of brushes and commutators, have low rotor inertia and fast response. Meanwhile, the brushless motor windings are located on the stator, facilitating heat dissipation and allowing for the fabrication of slot-separated, double-redundant windings, thus improving the reliability of the motor circuit. Therefore, the BLDCM (Brushless Die-Duty Motor Control System), with its high efficiency, reliability, and fast response servo control system, has become a research direction for new electric servo motors. This paper studies a double-redundant BLDCM speed servo control system that can be used for electric servo motor driving. Since servo motor systems generally require small overshoot (<20%), strong resistance to load disturbances, high frequency response, and good real-time performance, this paper, based on the introduction of the double-redundant BLDC system structure, derives the mathematical model of the BLDCM, constructs the dynamic structure block diagram of the speed and current dual closed-loop control system, presents the system simulation structure model under Matlab, and briefly explains the hardware design concept of the system. The experimental and simulation results are consistent, demonstrating the correctness of the system control strategy. This technology can not only be applied to aircraft EMA control but also extended to other industrial servo control fields such as complex robotic arms and conveying devices. II. Composition of the Dual-Redundant Brushless DC Motor Servo System EMA systems generally belong to servo systems, which are further divided into position servo and speed servo systems. The EMA system in this paper is an A/B dual-redundant speed servo control system. Channels A and B operate simultaneously. When channel A fails, the system automatically switches to channel B for normal operation, ensuring sufficient output. This system can accept externally given speed simulation command signals to achieve dual-loop control of speed and current for the dual-redundant rare-earth permanent magnet brushless DC motor. Its overall system structure principle block diagram is shown in Figure 1. III. Dynamic Mathematical Model of the Brushless DC Motor The permanent magnet brushless DC motor is an electromechanical integrated system composed of the brushless DC motor body, rotor position sensor, and drive controller. The position detection in Figure 1 is a rotor position signal unique to BLDCM, used for electronic commutation of motor power. This motor has the excellent mechanical characteristics of ordinary DC motors, and its single-channel speed and current dual-loop control system structure is shown in Figure 2. Generally, the dynamic equation of a brushless DC motor is: where u, ia, e, and Tem are the instantaneous values ​​of voltage (V), current (A), induced electromotive force (V), and electromagnetic torque (N·m) during the dynamic process of the motor, respectively; La is the armature inductance, H; Ra is the armature resistance, Ω; Tem is the load torque, including the output torque on the motor shaft and the constant resistance torque, N·m; TL is the output torque, N·m; Kt is the torque coefficient; RΩ is the resistance coefficient; Ω is the rotor mechanical angular velocity, rad /s; J is the rotor moment of inertia, kg·m2; and n is the instantaneous rotor speed, r/min. Without considering saturation, the magnetic flux Φ of a permanent magnet brushless DC motor can generally be considered constant during normal operation, so Kt is a constant. If all initial conditions are set to zero, and Laplace transforms equations (1) to (4), we can obtain equations (5) to (8) simultaneously. After simplification, we can obtain the motor angular velocity transfer function: where G1 (s) is the voltage-angular velocity transfer function; G2... (s) is the torque-angular velocity transfer function. If the applied voltage U(s) and load torque TL(s) are the inputs and the angular velocity Ω(s) is the output, the dynamic structure diagram of the brushless DC motor can be obtained from equations (5) to (8) as shown in Figure 3. As can be seen from Figure 3, the brushless DC motor itself is a rotor position closed-loop system. The induced electromotive force introduces a negative feedback signal that is proportional to the angular velocity of the motor, which increases the effective damping of the system. The electromagnetic characteristics and electromagnetic parameters (La, Ra) of the motor are related to the rate of rise of the current, which is the basis for the rate of rise of the inner current loop of the double closed-loop control system. The mechanical parameters (Ra, TL) are the main factors that determine the speed loop parameters and stability. From the dynamic mathematical model of the brushless DC motor in Figure 3, it can be seen that the brushless DC motor has two inputs, one is the applied voltage signal U, and the other is the load torque TL. The former is the control input and the latter is the disturbance input. By moving the synthesis point of the disturbance input TL forward and performing an equivalent transformation, the dynamic equivalent structure diagram of the brushless DC motor can be obtained, as shown in Figure 4. Controlling a power switching rectifier always requires a control trigger circuit, so they are often treated as a single link in system analysis. The input to this link is the control voltage Uct of the trigger circuit, and the output is the applied voltage U of the brushless DC motor. Their amplification factor KS can be considered a constant. Since the power switching device exhibits hysteresis, the triggering and rectifier can be considered an amplification link with pure hysteresis, and its transfer function can be approximated as a first-order inertial link. The calculation and detection of speed and current can be considered instantaneous, so their amplification factors are also their transfer functions, expressed by equations (11) and (12). Knowing the transfer functions of each link, we can combine them according to the relationships shown in Figure 5 to obtain the dynamic structure block diagram of the brushless DC motor dual-loop control system. Figure 5 shows that this speed-current dual-loop control system is a cascade control. To achieve parameter matching, a limiter must be set after the regulator. In Figure 5, WASR(S) and WACR(S) represent the speed PI regulator and the current PID regulator, respectively. IV. System Simulation To verify the feasibility of the overall system design and the adopted control strategy, a system simulation was performed on the entire control system. Based on the dynamic structure block diagram of the brushless DC motor dual-closed-loop control system in Figure 5 and the control principle block diagram in Figure 2, the system simulation structure model in Matlab is shown in Figure 6. The parameters La, Kt, J, Ra, and RΩ of the actuator motor can be calculated and used to implement PI control for the speed regulator and PID control for the current regulator. The two-stage regulators then achieve cascade control. The parameters Kps, KIs, TS, Kpi, KIi, KDi, and Ti of the two-stage regulators are simulated and tuned using computer simulation. Due to the different parameters of the two stages in the cascade PID regulator, the basic method of system simulation is: first, perform inner loop simulation separately, and then simulate the inner loop as a component of the outer loop. During the simulation, the parameter tuning of the current loop PID control algorithm and the speed loop PI control algorithm are determined using the PID normalized parameter tuning method. First, the four parameters Kpi, KIi, and Kpi of the current loop PID control algorithm are determined using the RID normalized parameter tuning method. KDi and Ti are used, and the current loop is considered as a component of the speed loop. The three parameters of the speed loop PI control algorithm, Kps, KIS, and TS, are then determined using the PID normalized parameter tuning method. During system simulation, only a single channel of the dual-redundant rare-earth permanent magnet brushless DC actuator is simulated. The single-channel motor technical parameters are: rated voltage 48V, rated speed 10000r/min, back EMF coefficient Ke = 0.0229V/r·min⁻¹, number of pole pairs 2, rated torque 0.6 N·m, rotor moment of inertia J = 1.2 × 10⁻⁴ kg·m², armature winding resistance per phase 2.6Ω, and phase winding inductance L = 3.62mH. During simulation, the motor starts under no-load, and a rated load of 0.6 N·m is applied after 0.4 s. Figure 7 shows the simulated motor speed curve. As can be seen from Figure 7, the system has almost no overshoot, strong resistance to load disturbances, good real-time performance and fast response, and good robustness, which can meet the performance requirements of the electric servo speed servo system. V. System Implementation and Testing (I) Hardware Implementation of the System This EMA dual-redundant system adopts dual closed-loop control of speed and current. The speed loop is the outer loop, which adopts PI control, and the current loop adopts PID control. After the dual-redundant system is powered on, channels A and B work simultaneously. When channel A experiences faults such as "overcurrent", "power supply failure", "motor phase loss", or "rotor position sensor loss", the system automatically switches to channel B and works normally. The system employs a dedicated SG1525 PWM generator and utilizes a GAL20V8B programmable device for electronic commutation logic synthesis. A 6-unit IR2130 chip is used to implement the integrated drive of a three-phase bridge inverter composed of MOSFET power transistors. The speed and current loop regulators use an LM124 amplifier for cascade control and signal limiting conditioning. The amplitude of the given analog signal (-10 to +10V) represents the speed of the BLD-CM motor, and its limiting value is matched to the given signal. The first value of the given analog signal represents the forward/reverse direction of the motor. The current feedback value is obtained by detecting the voltage drop across the sampling resistor connected in series in the DC bus circuit. The speed feedback is obtained by synthesizing the signals from the three-phase rotor position sensors and processing them through an f/v converter LM2907. The LM2907 offers high linearity, good repeatability, and a wide bandwidth. (II) System Performance Testing Under a 48V input voltage, the mechanical characteristics of the motor were measured when the dual-redundant system's A and B channels rotated forward (clockwise) or reverse (counter-clockwise) and simultaneously (clockwise or reversed), respectively. Figure 8 shows the measured mechanical characteristics of the motor. The actual waveform of the brushless DC motor controller, measured using a digital memory oscilloscope, is shown in Figure 9. Curve 1 represents the motor phase voltage waveform, and curve 2 represents the PWM chopper control waveform of the power switch. VI. Conclusion Simulation and system testing of the established speed servo system mathematical model show that: 1. Under the same load torque, the dual-redundant motor has slightly higher speed and current than the single-channel motor. Since the motor's no-load speed is above 12000 r/min, with the closed-loop control, it is easy to stabilize at the rated speed of 10000 r/min by adjusting the PWM duty cycle; 2. The simulation results of the system mathematical model derived in this paper are consistent with the actual test results, indicating that its approximation is acceptable in engineering. 3. With the addition of a rudder surface position sensor, this speed servo system can easily form a three-closed-loop servo system of position, speed, and current.