The model of a permanent magnet DC motor in time domain and frequency domain based on Bond Graph modelling and design of position control using PID controller

Gy Korsoveczki,G Husi

doi:10.1088/1757-899x/1169/1/012004

Abstract

During the research work, the modelling of a permanent magnetic DC (PMDC) motor was realised in time domain and frequency domain via 4 different types of model construction. To achieve this, the Bond Graph model of the motor was determined, and based on them the system equations were defined in time domain firstly and then in frequency domain by using the Laplace transform. According to the system equations in time domain, the state-space model of the motor was also realised and implemented. Based on the system equations in frequency domain, the transfer function of the position control loop was realised. As the further part of the research work, PID control-based position control was designed in both time domain and frequency domain. The controller was tuned according to the Ziegler-Nichols method. Finally, the models were compared from the point of view of behaviour during the tuning process. The models were implemented in LabVIEW environment produced by the National Instruments.

Highlights

Nowadays the technical life is producing high-rate development
The modelling of a permanent magnetic DC (PMDC) motor was realised in time domain and frequency domain via 4 different types of model construction
The Bond Graph model of the motor was determined, and based on them the system equations were defined in time domain firstly and in frequency domain by using the Laplace transform

Summary

Introduction

Nowadays the technical life is producing high-rate development. As the available technological background evolves, the increase in complexity of systems becomes indispensable. It is difficult to establish mathematical relations between domains because the only way is to find a variable that is present in all systems This physical variable is energy, and the language describing its change is Bond Graph modelling, developed by Henry Paynter in 1959. The most important element of the Bond Graph modelling is the causality that defines the directions of effort and flow and allows us to determine the system equations [2], [3]. The space-state model of the motor As a result of the Bond graph modelling the system equations could be realised These differential equations can be written in state-space structure, which is a matrix structure for a better process of a larger number of system equations. The transfer function defines the relation between the system output in frequency domain and the system input in frequency domain [4]

The design of position control using PID controller in different domains

Conclusion