An Intelligent Speed Controller

Published Date: 02 Nov 2017

Muawia Abdel Kafi Magzoub, Nordin B. Saad, Rosdiazli B. Ibrahim

Department of Electrical and Electronic Engineering

Universiti Teknologi PETRONAS, Bandar Sri Iskandar, 31750

Tronoh, Perak, Malaysia

[email protected]

Abstract—The development of speed control scheme for indirect field-oriented controlled induction motor (IM) drive will be presented in this study. The Conventional-PI controller and Fuzzy-PI controller was studied in closed-loop speed control. Decoupling of the stator current into torque and flux, producing (d-q) currents’ profile of an IM, was involved in the indirect field-oriented control. The components of current (Iqs and Ids,), of an IM, were developed by an intelligence based Fuzzy PI controller. The speed responses, torque and stator currents were observed under the performance of Fuzzy Logic Controller (FLC) and later on compared with the PI-Controller. After above-mentioned exercise, the better dynamic performance was obtained. The simulation was executed, using MATLAB/Simulink, in order to investigate the performance of the controller.

Keywords—PI-Controller, Indirect Field-Oriented Control (IFOC), Fuzzy Logic Controller (FLC).

Introduction

The induction motor is well-known as the workhorse of the industry. The improvement of variable speed induction motor drives has an extending history of more than forty years. The induction motor is also known as the workhorse of the industry. The emergence of variable speed induction motor drives was started around late 1960s, with the rise of the silicon controlled rectifier (SCR). During that era, only the steady state aspects of the induction machine were the basis of the principle of speed control. Recently available sophisticated industrial drives are penetrated after an extensive research and development.. The early period of variable speed induction motor drives can be recorded back to the 1960s, with the emerged of the silicon controlled rectifier (SCR). The v/f control was one of the techniques practiced in the past and that is also commonly used now a days, for the open-loop speed control of drives with low dynamic requirements. In addition to that, the slip frequency control method is another technique, known to produce better dynamics. This method was successfully adopted in all high performance IM drives till the birth of field-oriented control (FOC), as an industry’s standard for AC drives with dynamics close to that of DC motor [1]. Therefore, the vector control or the field-oriented control was one of the most signifcant inventions in AC motor drives, which gave rise to the research and development programs, resulting in the ultimate enhancement of the control performance. On the other hand, an adjustable speed drive provided several process control advantages such as, smoother operation, better acceleration control, different operating speeds for each process recipe, compensation of changing process variables, allowance of slow operation for setup purposes, adjustment to the rate of production, accurate positioning, control on torque or tension and energy saving.

In 1965 Fuzzy Logic was presented as a new type of mathematical set approach by Zadah (put reference number here), which consists of the fuzzy set theory that was proved to be the foundation theory of fuzzy logic. The fuzzy control system is basically based on the fuzzy logic principle that mainly comprises of three phases: fuzzification, inference engine and defuzzification. The first phase converts the inputs into fuzzy sets. While, in the second phase, the inference engine defines the fuzzy rules, which relate the outputs through specific rules using the inputs’ sets. The last phase combines the results of the fuzzy rules, and infers the decision, which is then converted from fuzzy sets to a sharp value [2,3].

There are several research studies beased on control techniques and commercially available tools to provide a controller for VSD, in order to ensure a high degree of reliability and performance. For instance, [4] using a PLC for controlling an inverter to drive an IM but this method was more in the direction of monitoring and protection without any consideration of control analysis aspects. In [5], the system was evaluated when subjected to sudden changes. The changes were in the reference and the optimization of PI coefficients, which was processed using Ziegler-Nichols method and Genetic-Adaptive Neuro-Fuzzy Inference System (ANFIS) model without control analysis. In [6], the PLC based hybrid-fuzzy control for PWM-driven VSD was analyzed with the constant V/f ratio that depended upon s-domain transfer function in a mathematical model of a real plant. However, the optimizations of the controller's performance, against external disturbances, were not taken into consideration.

In this paper, the MATLAB/Simulink software based model of a three-phase induction motor will be derived using mathematical modeling principles. Based on indirect field-oriented control principles, the controller will be designed and later implemented on the model.

Indirect vector control

The induction motor dynamics can be modeled using higher order mathematical equations that fall under one of the VSD control classifications.

Steady state models of induction machines are useful for studying the performance of the machine in the steady state only. This means that all electrical transients are negligible during load changes and stator frequency fluctuations. Such fluctuations are prominent in the applications involving variable speed drives. The variable speed drives are converter-fed from finite sources, unlike the utility sources, due to the limitation of the switch ratings and filter sizes. This results in their incapability to supply large transient power. Consequently, there is an immediate need to evaluate the dynamics of converter-fed variable-speed drives. Firstly, it will significantly assess the sufficiency of the converter switches for a required motor and secondly, the interaction of converter switches will help to determine the digression of current and torque in the converter and motor. The related IM parameters are mentioned in Table I.

Parameters

Figure 1 shows the block diagram of the indirect field- oriented control model for an induction motor.

Indirect Field-Oriented Control model block of a proposed scheme

Mathematical formulae

The dynamic model of the induction motor is derived by using a two-phase motor in direct and quadrature axis. The description of the notations is tabulated in Table II. The state space model of induction motor in a stationary reference frame can be derived with the help of the voltage and flux linkage equations of induction motor in the arbitrary reference frame [7]. The final state-space model of induction motor in a stationary reference frame can be written as shown in equations (1)-(6) below:

Nomenclature

d and q-axis stator current components respectively, expressed in stationary reference frame

d- and q-axis rotor current components respectively, expressed in stationary reference frame

Magnetizing inductance

Self-inductance of the stator and rotor respectively

The resistance of a stator and rotor phase winding respectively

Electromagnetic torque and Load torque reflected on the motor shaft respectively

d and q-axis stator voltage components respectively, expressed in stationary reference frame

Leakage resistance of the stator and rotor respectively

d and q-axis stator flux components respectively, expressed in stationary reference frame

d and q-axis rotor flux components respectively, expressed in stationary reference frame

Mechanical and electrical angular rotor speed respectively

Synchronous speed or dominant frequency

Number of pairs of poles

Operator

The inertia of the rotor

The damping constant which represents dissipation due to winding effect and friction

Design of controller

Conventional PI controller

In general, the conventional PI controller is one of the simplest approaches for speed control in industrial electrical drives and the clear relationship exists between its parameters and the system response specifications. A very common method to determine the Kp and Ki constants, of above-mentioned controller, is the method of Ziegler-Nichols. The conventional PI controller block model is showed in Fig.2.

Conventional PI controller

Fuzzy-PI controller

To determine a fuzzy rule from each input-output data pair, the first step is to find the degree of each data-value in every membership region of its corresponding fuzzy domain. The variable is then assigned to the region with the maximum degree.

When each new rule is generated from the input-output data pairs, a rule degree or truth is assigned to that rule. In the case, where the rule degree is defined as the degree of confidence then it correlates the function, related to voltage and current, with the angle. In the formulated method a degree is assigned, which is the product of the membership function degree of each variable in its respective region.

Fuzzy PI controller

Every training data set produces a corresponding fuzzy rule that is stored in the fuzzy rule base. Therefore, as each input-output data pair is processed, rules are generated. A fuzzy rule or knowledge base is in the form of two-dimensional table, which can be looked up by the fuzzy reasoning mechanism.

By the comparison between reference speed and speed signal feedback, speed error is calculated. Speed error and speed error changing are fuzzy controller inputs. Input variables are normalized with a range of specified membership functions and the normalization factors are named as K1, K2 and K3. Suitable normalization has a direct influence on algorithm optimality and faster response (Fig. 3).

Membership Functions

The Fuzzy Logic Controller initially converts the crisp error and change in error variables into fuzzy variables and then map them into linguistic labels. Membership functions are associated with each label, as shown in the Fig. 3, which consists of two inputs and one output.

C:\Users\user\Desktop\Muawia's Desktop\Figures for UTP Conf\Fuzzy\Error.bmp

C:\Users\user\Desktop\Muawia's Desktop\Figures for UTP Conf\Fuzzy\CE.bmp

C:\Users\user\Desktop\Muawia's Desktop\Figures for UTP Conf\Fuzzy\output.bmp

Membership functions

The fuzzy sets are divided into seven groups. They fuzzy sets are defined as follows:

Z: Zero

PS: Positive small

PM: Positive Medium

PB: Positive Big

NS: Negative small

NM:Negative Medium

NB: Negative Big

PVS: Pos. Very small

NVS: Neg. Very small

NVB: Neg. Very Big

PVB: Pos. very Big

Each of the inputs and the output contain membership functions along with all formerly defined eleven number of linguistics.

Rule Base

The mapping of the fuzzy inputs into the required output is derived with the help of a rule base as shown in Table II below.

Rule matrix for fuzzy PI controller

e

NB

NM

NS

Z

PS

PM

PB

ce

NB

NVB

NVB

NB

NB

NM

NS

Z

NM

NVB

NB

NB

NM

NS

Z

PS

NS

NB

NB

NM

NS

Z

PS

PM

Z

NB

NM

NS

Z

PS

PM

PB

PS

NM

NS

Z

PS

PM

PB

PB

PM

NS

Z

PS

PM

PB

PB

PVB

PB

Z

PS

PM

PB

PB

PVB

PVB

Result Analysis

The simulation results of the PI speed controller and FLC for indirect vector control of induction motor were run for three seconds. While the motor started from standstill at t=0 and reached the rated speed of 313 rpm and the load torque of TL=0, as shown in Figure 5.

fig

figSpeed response

Torque response

The torque response, shown in the figure 6, reflects the ripples that are less for the Fuzzy PI controller as compared to the Conventional PI controller.

Vds and Vqs are generated from Ids and Iqs respectively, which can be seen as DC while Va and Vβ, that were calculated from Vds and Vqs, can be seen as time varying components. This was the reason of designing the controllers in the d-q synchronously reference frame, as illustrated in Figures 7, 8, 9 and 10.

fig

Vds response

fig

Vqs response

fig

Va response

fig

Vβ response

From the above results it is illustrated that the performance of model was up to the expectations when a test was applied with a PI-controller as compared to the Fuzzy PI controller.

Conclusions

In this paper the concept of fuzzy logic has been presented and the SVM-based indirect vector-controlled induction motor drive was simulated using both PI and Fuzzy PI controller. The results of both controllers under the dynamic conditions were compared and analyzed. The simulation results unveiled that the FLC settles quickly and depicts better performance as compared to the PI controller.

Acknowledgment

The authors want to acknowledge the financial support from the Universiti Teknologi PETRONAS through their Graduate Assistantship Scheme.