This paper presents a novel model-free sliding mode control (MFSMC) method to improve the speed response of permanent magnet synchronous machine (PMSM) drive system. The ultra-local model (ULM) is first derived based on the input and the output of the PMSM. Then, the novel MFSMC method is presented, and the controller is designed based on ULM and MFSMC. A sliding mode observer (SMO) is constructed to estimate the unknown part of the ULM. The estimated unknown part is feedbacked to MFSMC controller to perform compensation for parameter perturbations and external disturbances. Compared with the sliding mode control (SMC) method, the results of simulation and experiment demonstrate that the presented MFSMC method improves the dynamic response and robustness of the PMSM drive system.

Permanent magnet synchronous motor (PMSM) has been widely used in industrial drives, railway transportation, and electric vehicles (EVs) due to its simple structure, energy-saving, and high efficiency [

The conventional PI control method cannot satisfy higher performance control of the motor [

SMC is widely used for its insensitive to parameter perturbation and is easy to be implemented in engineering. A new SMC with variable speed reaching law was presented to reduce the chattering caused by sign function, and the system performance was improved [

To reduce the dependence of the controller design on the system model, a model-free control (MFC) method [

This paper presents a novel model-free sliding mode control (MFSMC) method based on ULM. It improves the dynamic response and robustness of the PMSM drive system. The main contributions of this paper are summarized as follows:

An MFSMC method that combined SMC with MFC is presented to improve the speed response for the PMSM drive system in case of parameter perturbation. The MFSMC method has the features of both MFC and SMC. More specifically, while the MFC in the system ensures independence on the precise PMSM model, the SMC improves the robustness of the PMSM system to parameter perturbations and external disturbances.

The ultra-local model (ULM) of the speed loop is derived based on the input and the output of the PMSM drive system.

The unknown part of ULM is precisely estimated by the designed SMO and feedbacked to the controller to performed compensation for parameter perturbations and external disturbances.

The rest of this paper is constructed as follows.

PMSM is a multivariable, nonlinear, and strongly coupled system. Neglected the effects of the magnetic saturation, iron losses, and stray losses, the magnetic circuit is considered as linear, and the inductance parameter is considered as constant. Then, the mathematical model of PMSM in the

In the

In the ^{2});

Substituting

Considering parameter uncertainties and unknown disturbances

According to the MFC method [

To improve the speed response and the robustness of the PMSM drive system, this section designs the speed controller by the MFSMC theory.

Based on the ULM

Introducing the term of SMC in MFC speed controller

Substituting

Added and subtracted the speed derivation,

Define the estimated error,

Introducing the state variables

The integral sliding surface is designed as

Derivating of

Chosen

Then the system state will reach the sliding mode manifold in finite time.

This completes the proof.

Substituting control law

Since

Subtracting

The derivative of

Chosen

Then, the error variable

This completes the proof.

Based on the sliding-mode equivalent principle [

To effectively reduce the chattering caused by the sign function of SMO

This section gives the results of simulations and experiments to demonstrate the effectiveness of the presented method.

To verify the advantage of the designed MFSMC speed controller, MATLAB/Simulink is used to simulate the PMSM speed control system. The schematic diagram of the PMSM control system is presented in

Parameter | Unit | Values |

DC voltage | V | 311 |

Stator resistance (_{s} |
Ω | 2.875 |

Number of pole pairs (_{p} |
pairs | 4 |

_{q} |
H | 0.0085 |

_{d} |
H | 0.0085 |

Rotor PM flux (_{r} |
Wb | 0.175 |

Rotational inertia ( |
kg⋅m^{2} |
0.0015 |

Nominal torque | Nm | 10 |

Nominal speed | rpm | 2,000 |

Nominal current | A | 9.5 |

Nominal voltage | V | 160 |

Nominal power | kW | 2 |

The hardware-in-the-loop simulation (HILS) experiments are carried out on an RT-Lab platform [

The above results (

Performance index | SMC | MFSMC |
---|---|---|

Speed error (rad/s) | 0.22 | 0.11 |

Speed response (s) | 0.03 | 0.01 |

Starting time (s) | 0.036 | 0.02 |

Torque ripple (%) | 10 | 5 |

Torque response (s) | 0.012 | 0.006 |

This paper presented a novel MFSMC method to improve the speed response and robustness of the PMSM drive system. The ULM of the speed loop in PMSM is established based on the input and the output of the PMSM drive system. The MFSMC speed controller is designed based on ULM, and the SMO is designed to estimate the unknown part of ULM. The estimated unknown part is feedbacked to the controller to compensate for parameter perturbations and external disturbances. Compared with the SMC method, the results of simulation and experiment prove the presented method has excellent speed control performance and operates well. The MFSMC method has independence on the precise model of PMSM, and has faster response speed and strong robustness than the SMC method.