Excerpt

## Abstract

In this paper we describe a technical system for DC motor speed control. The speed of DC motor is controlled using Neural Network Based Model Reference and Predictive controllers with the use of Matlab/Simulink. The analysis of the DC motor is done with and without input side Torque disturbance input and the simulation results obtained by comparing the desired and actual speed of the DC motor using random reference and sinusoidal speed inputs for the DC motor with Model Reference and Predictive controllers. The DC motor with Model Reference controller shows almost the actual speed is the same as the desired speed with a good performance than the DC motor with Predictive controller for the system with and without input side disturbance. Finally the comparative simulation result prove the effectiveness of the DC motor with Model Reference controller.

Keywords: DC motor, Neural Network, Model Reference controller, Predictive controller

### 1.1 Introduction

Short settling time and minimized steady state errors are favored in technical system of speed managed DC motor. DC motors have many applications in lots of fields of industrial, together with robotics, automobiles, servomechanisms etc. The electric motor systems used in lots of industrial applications require higher performance, reliability and variable speed because of their ease of controllability. The speed control of a DC motor is critical in applications where precision and safety are vital. The speed may be managed either by using the control of armature voltage, field voltage or each relying upon the desired overall performance characteristics of the system.The purpose of a motor speed controller is to take a sign representing the desired speed and to drive a motor at that speed.

### 2.1 Mathimatical Model of DC Motor

The system structure of a DC motor is shown in Figure 1, including the armature resistance*Ra*and winding leakage inductance*La*.

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Figure 1 System structure of a DC motor

According to the Kirchhoff’s voltage law, the electrical equation of the DC motor is described as

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Where *ia*(*t*) is the armature current, *vb*(*t*) is the back emf voltage and *vs*(*t*) is the voltage source. The back emf voltage *vb*(*t*) is proportional to the angular velocity (*t*) of the rotor in the motor, expressed as

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Where kb is the back emf constant. In addition, the motor generates a torque*TM*proportional to the armature current, given as

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Where kT is the torque constant.

If the input voltage *Vs*(*t*)=*Vs *is a constant, the resulted armature current *ia*(*t*)=*Ia*, angular velocity (*t*)= and torque *TM*(*t*)=*T *are also constant in the steady state. From (1) to (3), we have

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Under the conservation of power, we know that the input power *IaVs *is equal to the external power *T*and the power consumed in the resistance, i.e.

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Substituting*Vs*in (4) into (6) yields

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From (5) and (7), we know that both and are the same. From (2), we can rewrite (1) and (3) as

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Where. Besides, if the DC motor is used to drive an external torque TL(t) of payload then its mechanical behavior is described as

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Where*JM is*the rotor moment of inertia and*BM*is the frictional coefficient.

Based on (8), (9) and (10), the dynamic equation of the DC motor can be expressed as

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The state space model representation will have the form

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### 3.1 The Proposed Controller Design

The design of model reference and predictive controllers are discussed as follow.

### 3.1 Model-Reference Controller Design

The designing of neural model reference control uses two neural networks:

1. A Neural network controller and

2. A Neural network controller for the plant model

As shown in Figure 2 bellow.

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Figure 2. Block diagram of the model reference controller

There are three sets of controller inputs:

- Delayed reference inputs

- Delayed controller outputs

- Delayed plant outputs

### 3.2 Predictive Controller Design

The design of model predictive controller is used to train a neural network to symbolize the forward dynamics of the plant. The prediction error between the plant output and the neural network output is used as the neural network training signal. The system is represented by the Figure 3:

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Figure 3. Block diagram of the predictive controller

The neural network architecture, training data and training parameters for model reference and predictive controllers are shown in the Table 1 bellow

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## 4. Result and Discussion

Here in this section, the comparisons of the desired and actual speed of the DC motor using random reference and sinusoidal speed inputs for the DC motor with Model Reference and Predictive controllers with and without input side Torque disturbance input. The Simulink model for the DC motor with Model Reference and Predictive controllers using random reference and sinusoidal speed inputs is shown in Figure 4 and Figure 5 respectively.

**[...]**

- Quote paper
- Mustefa Jibril (Author), 2020, DC Motor Speed Control with the Precence of Input Disturbance using Neural Network Based Model Reference and Predictive Controllers, Munich, GRIN Verlag, https://www.grin.com/document/542040

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