TIDUFE5 July   2025

 

  1.   1
  2.   Description
  3.   Resources
  4.   Features
  5.   Applications
  6.   6
  7. 1System Description
    1. 1.1 Terminology
    2. 1.2 Key System Specifications
  8. 2System Overview
    1. 2.1 Block Diagram
    2. 2.2 Design Considerations
    3. 2.3 Highlighted Products
      1. 2.3.1  TMS320F2800137
      2. 2.3.2  LMG3651R025
      3. 2.3.3  LMG2650
      4. 2.3.4  TMCS1126
      5. 2.3.5  ISO6721
      6. 2.3.6  UCC28881
      7. 2.3.7  UCC27712
      8. 2.3.8  TPS562206
      9. 2.3.9  TLV9062
      10. 2.3.10 TLV74033
  9. 3System Design Theory
    1. 3.1 Totem Pole PFC
      1. 3.1.1 Inductor Ratings
      2. 3.1.2 AC Voltage Sensing
      3. 3.1.3 DC Link Voltage Sensing
      4. 3.1.4 AC Current Sensing
      5. 3.1.5 DC Link Capacitor Rating
    2. 3.2 Three-Phase PMSM Drive
      1. 3.2.1 Field Oriented Control of PM Synchronous Motor
        1. 3.2.1.1 Space Vector Definition and Projection
        2. 3.2.1.2 Clarke Transformation
        3. 3.2.1.3 Park Transformation
        4. 3.2.1.4 Basic Scheme of FOC for AC Motor
        5. 3.2.1.5 Rotor Flux Position
      2. 3.2.2 Sensorless Control of PM Synchronous Motor
        1. 3.2.2.1 Enhanced Sliding Mode Observer With Phase Locked Loop
          1. 3.2.2.1.1 Mathematical Model and FOC Structure of an IPMSM
          2. 3.2.2.1.2 Design of ESMO for the IPMSM
          3. 3.2.2.1.3 Rotor Position and Speed Estimation With PLL
      3. 3.2.3 Hardware Prerequisites for Motor Drive
        1. 3.2.3.1 Current Sensing With Three-Shunt
        2. 3.2.3.2 Motor Voltage Feedback
  10. 4Hardware, Testing Requirements, and Test Results
    1. 4.1 Hardware Requirements
      1. 4.1.1 Hardware Board Overview
      2. 4.1.2 Test Conditions
      3. 4.1.3 Test Equipment Required for Board Validation
    2. 4.2 Test Setup
    3. 4.3 Test Results
      1. 4.3.1 Functional Waveforms
  11. 5Design and Documentation Support
    1. 5.1 Design Files
      1. 5.1.1 Schematics
      2. 5.1.2 Bill of Materials
      3. 5.1.3 Altium Project
      4. 5.1.4 Gerber Files
      5. 5.1.5 PCB Layout Recommendations
    2. 5.2 Tools
    3. 5.3 Documentation Support
    4. 5.4 Support Resources
    5. 5.5 Trademarks
  12. 6About the Author
3.2.2.1.3 Rotor Position and Speed Estimation With PLL

With the arc tangent method, the accuracy of the position and velocity estimations are affected due to the existence of noise and harmonic components. To eliminate this issue, the PLL model can be used for velocity and position estimations in the sensorless control structure of the IPMSM. The PLL structure used with SMO is illustrated in Section 3.2.2.1.2. The back-EMF estimations êα and êβ can be used with a PLL model to estimate the motor angular velocity and position as shown in Figure 3-18.

TIDA-010282 Block Diagram of Phase Locked Loop Position Tracker Figure 3-18 Block Diagram of Phase Locked Loop Position Tracker

Since êα = Ecos(θe), êβ = Esin(θe) and E = ωeλpm, Equation 42 defines the position error.

Equation 42. ε = e ^ β cos ⁡ θ ^ e - e ^ α sin ⁡ θ ^ e = E sin ⁡ θ e cos ⁡ θ ^ e - E cos ⁡ θ e sin ⁡ θ ^ e = E s i n ⁡ ( θ e - θ ^ e )

where

  • E is the magnitude of the EEMF, which is proportional to the motor speed ωe.

When (θe – ̂θe) < π/2, Equation 42 can be simplified as in Equation 43.

Equation 43. ε = E ( θ e - θ ^ e )

Further, the position error after the normalization of the EEMF can be obtained:

Equation 44. ε n = θ e - θ ^ e

According to the analysis, the simplified block diagram of the quadrature phase locked loop position tracker can be obtained as shown in Figure 3-19. The closed-loop transfer functions of the PLL can be expressed as:

Equation 45. θ ^ e θ e = k p s + k i s 2 + k p s + k i = 2 ξ ω n s + ω n 2 s 2 + 2 ξ ω n s + ω n 2

where

  • kp is the proportional gain of the standard PI regulator
  • ki is the integral gain of the standard PI regulator
  • ωn is the natural frequency

The damping ratio, ξ, is given in Equation 46.

Equation 46. k p = 2 ξ ω n ,     k i = ω n 2
TIDA-010282 Simplified Block Diagram of Phase-Locked-Loop Position Tracker Figure 3-19 Simplified Block Diagram of Phase-Locked-Loop Position Tracker