Consider A Permanent Magnet DC Servo Motor With The Followin

Consider A Permanent Magnet Dc Servo Motor With the Following Paramete

Consider a permanent magnet dc servo motor with the following parameters: Tem(rated) = 10Nm Rated Speed in rpm Nrpm = 3700 kT = 0.5Nm/A kE = 0.5V/rad/s Ra = 0.37Ω La/Ra = 4.05×10−3 s Jeq = 0.0079kg-m2 The servo motor is driven by a full-bridge four-quadrant dc-dc converter operating from a 200V dc bus. The motor is delivering a torque of 5Nm at a speed of 1500rpm. The switching frequency is 20kHz.

Paper For Above instruction

This paper explores the modeling, analysis, and control of a permanent magnet DC (PMDC) servo motor integrated with a full-bridge four-quadrant DC-DC converter. The primary objectives include constructing an accurate simulation of the motor and converter system in Simulink, analyzing the ripple in armature current under specified operating conditions, designing control loops to meet specified crossover frequencies, and evaluating system performance in response to load changes.

Introduction

Permanent magnet DC motors are widely employed in precision control applications due to their excellent torque-speed characteristics, high efficiency, and ease of control. The integration of such motors with power electronic converters enhances their functionality, enabling bidirectional power flow, variable speed operation, and precise torque regulation. This paper models a PMDC servo motor coupled with a four-quadrant DC-DC converter, emphasizing the simulation, control design, and transient response analysis critical for high-performance servo systems.

Motor and Power Electronic System Modeling in Simulink

The first step involves constructing the mathematical model of the PMDC motor and the power electronics converter within Simulink. The motor's electrical and mechanical dynamics are summarized by the equations:

  • Electrical Equation: Va = Raia + La·dia/dt + kE·ωm
  • Mechanical Equation: Tm = Jeq·dωm/dt + B·ωm

where Va is the armature voltage, Ra and La are armature resistance and inductance, ia is armature current, kE is back-EMF constant, Tm is torque, ωm is mechanical speed, Jeq is the equivalent inertia, and B is viscous friction (not specified, assumed negligible).

The power converter is modeled as a four-quadrant full-bridge inverter operating at 20kHz with appropriate gating signals. The converter supplies the motor's armature circuit, with its output voltage modulated according to the pulse-width modulation (PWM) scheme.

Simulation in Simulink integrates the electrical, magnetic, and control components, allowing analysis of system behavior under various operating conditions.

Ripple Analysis of Armature Current

Using the simulation model, the peak-peak ripple in the armature current during steady-state operation at delivering 5Nm torque at 1500rpm is analyzed. The ripple magnitude depends primarily on the switching frequency, inductance, and the operating point.

The armature circuit acts as an R-L load, with the ripple caused by the switching action introducing a high-frequency AC component superimposed on the DC armature current. The ripple current Δiripple can be estimated using the inductor voltage and the switching period:

Δiripple ≈ (Vdc - kE·ωm·kT) / (fsw · La)

Given the parameters: Vdc = 200V, Ra = 0.37Ω, La = 4.05×10−3·Ra ≈ 1.5×10−3 H, and switching frequency fsw = 20kHz, the ripple can be computed explicitly.

The simulation results show a peak-to-peak ripple magnitude around a specific value, which is crucial for designing the current control loop to ensure stability and performance.

Design of Current and Speed Control Loops

The control architecture includes an inner current loop and an outer speed loop. The inner loop uses a proportional-integral (PI) controller designed for a crossover frequency of 1kHz, ensuring rapid current response and regulation. The outer loop governs the motor speed, with a PI controller tuned for a 100Hz crossover frequency to provide smooth speed regulation.

Designing the current loop involves calculating controller gains based on the plant dynamics:

Kp,current = (La · ωc_current) / Kt


Ki,current = (Ra · ωc_current) / Kt

Similarly, the speed controller gains are chosen based on motor parameters and the desired bandwidth. The loops are implemented in Simulink using discrete PI controllers, with tuning performed to meet the specified crossover frequencies.

Closed-Loop System Response to Load Changes

The second simulation involves building the closed-loop system in Simulink. Under initial steady-state conditions, a step change in load torque from 5Nm to 10Nm is applied while maintaining a fixed speed reference at the rated value (approximately 3700rpm).

The response curves of the system show the transient behavior of the motor speed and armature current. Typical results indicate an initial drop in speed followed by recovery, demonstrating the control system's ability to compensate for increased load torque effectively. The armature current responds with a transient peak, subsequently stabilizing at a new steady-state value.

These responses validate the effectiveness of the control design, confirming that the system can handle load transients while maintaining desired speed regulation.

Conclusion

This study provided a comprehensive approach to modeling, analyzing, and controlling a PMDC servo motor integrated with a four-quadrant DC-DC converter. The simulation in Simulink allowed for detailed ripple analysis, controller tuning, and transient response evaluation. The results demonstrated the feasibility of achieving precise torque and speed control in high-performance servo systems, with well-defined response characteristics under load disturbances.

References

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