Kitten paw: FOC control 15-mras method of PMSM

1 Preface

   This article briefly introduces the model adaptive method （Model Reference Adaptive System - MRAS） Application in sensorless control of permanent magnet synchronous motor . To be honest, this method is compared with the previous two state observers , That is low More than a little , So its content is also very simple , Let's start with the ugly words , Because this method is rarely used in actual motor control applications , Here we will only introduce the principle and simulation structure , Interested partners can migrate it to the physical hardware and verify it by themselves , But I guess the effect is not very good .

2 MRAS brief introduction

   First intercept those papers MRAS The principle is described as ： The main idea of model reference adaptive method is to take the equation without unknown parameters as the reference model , The equation containing the parameters to be estimated is regarded as an adjustable model , The outputs of the two models have the same physical meaning , Both models work at the same time , The output error is used to form an appropriate adaptive law to adjust the adjustable model parameters , In order to control the object output tracking reference model , As follows ：

   If you look carefully, MRAS Model principle of , Do you feel a little familiar , Post the schematic diagram of the previous state observer ：

   You can find MRAS In fact, it is a simplified version of state observation , It also makes up a mathematical model to simulate the working condition of the real motor , stay MRAS This mathematical model is called the adjustable model , The reference model is the actual motor body , Then the adjustable model is slowly modified by error , The correction process here is called adaptive adjustment , This is it. MRAS How does it work .

   Here is a free discussion session ： Here we might as well discuss MRAS What are the limitations of ？ First of all, the above mentioned MRAS Is a simplified version of the state observer , The simpler the structure is , Then the model itself requires higher precision of model constant parameters and model input , Otherwise, there is no guarantee MRAS The accuracy of the model , This actually means MRAS The anti-interference performance of is not very good , After all, both observation errors and systematic errors will bring uncertainty to this simple model ; In addition, the variable parameters of the adjustable model need to be adjusted by error , Therefore, the adaptive mechanism responsible for adaptive adjustment is extremely important , There must be a reasonable and stable adaptive mechanism to ensure the robustness and timeliness of the adaptive process , No matter what the controller is, it can't take into account all the situations , So this is also extremely difficult . Sum up 2 spot ,MRAS It is extremely difficult to make great achievements in practical motor applications . The above is my personal understanding , Mistakenly spray .

3 Adjustable model and adaptive mechanism

   Here I will not deduce the formula one by one , I recommend you to read a paper 《 Design of speed sensorless control system for permanent magnet synchronous motor based on model reference adaptive , Northeast University - Chang Kai 》, Please download and watch by yourself . The results are posted directly here ：

   among ：

   It can be seen that at last, it is simplified according to the relevant mathematical ideas , Finally, the estimated angular speed of the motor is actually an error PI Adjust the resulting output , This is actually the PLL adjustment I mentioned earlier , So the adaptive mechanism in the adaptive adjustment model is actually a phase locked loop in essence .

4 Simulation setup

   Build according to the above content MRAS The simulation of is also extremely simple ,MARS as follows ：

   The adjustable model part is as follows ：

   The adaptive mechanism is as follows ：

   Run the simulation , Observe the rotor position output by the adaptive model and the actual rotor position output by the motor model as follows ：

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