Performance Investigation of AC Servomotor Position Control using Fuzzy Logic and Observer Based Controllers Performance Investigation of AC Servomotor Position Control using Fuzzy Logic and Observer Based Controllers.

: An AC servomotor which is mostly a two-phase induction motor with two stator field coils placed 90 electrical degrees apart used for controlling position, speed and acceleration in manufacturing industries. In this paper, a two-phase induction motor has been designed with a fuzzy logic and observer based controllers to improve the performance of the system. Comparison of the AC servomotor with the proposed controllers for tracking a step and a square desired position signal input has been done using Matlab/Simulink toolbox and a promising result obtained.


1.
Introduction AC servomotor is a rotary actuator or linear actuator that lets in for specific manage of angular or linear position, velocity and acceleration. It consists of a suitable motor coupled to a sensor for role feedback. It also requires a fairly sophisticated controller, often a devoted module designed mainly to be used with servomotors. AC servomotors aren't a specific elegance of motor, despite the fact that the term servomotor is often used to consult a motor suitable for use in a closed-loop control system. AC servomotor is a closed-loop servomechanism that makes use of position feedback to control its movement and very last role. The input to its manipulate is a signal (either analogue or digital) representing the position commanded for the output shaft.

Mathematical Model of the AC Servomotor
An AC servomotor is basically a two-phase induction motor that has two stator field coils placed 90 electrical degrees apart, as shown in Figure 1.

Figure 1 AC servomotor
In a two-phase motor the ac voltage E1 and E2 are equal in magnitude and separated by a phase angle of 90 degrees. A two-phase induction motor runs at a speed slightly below the synchronous speed and is essentially a constant-speed motor. The synchronous speed ns is determined by the number of poles P produced by the stator windings and the frequency f of the voltage applied to the stator windings.
When the unit is used as a servomotor, the speed must be proportional to an input voltage. The twophase motor can be used as a servomotor by applying an ac voltage E1 of fixed amplitude to one of the motor windings. When the other voltage E2 is varied, the torque and speed are a function of this voltage. Figure 2 shows a set of torque-speed curves for various control voltages. T E  about the origin and keeping only the linear terms: If the torque-speed motor curves are approximated by parallel straight lines, the partial derivative coefficients of Equation (1) are constants that can be evaluated from the graph. Let For a load consisting of a moment of inertia and damping, the load torque required is Since the generated and load torques must be equal, Equation (1) In order for the system to be stable the Observation of the motor characteristics shows that 2 T K     is negative; therefore, the stability requirement is satisfied. The transfer function of the AC servo motor becomes Table 1 shows the parameters of the AC servo motor.

Proposed Controllers Design
In this section, the design of the proposed controllers will be discussed.

Fuzzy Logic Control Fuzzy Logic Control (FLC) or Fuzzy Linguistic
Control is a knowledge primarily based control strategy that can be used  While both a sufficient correct and but no longer unreasonably complicated model of the plant is unavailable, or  When a (single) specific degree of overall performance isn't significant or realistic. gives nonlinear transformations with none built-in dynamics. The block diagram of the AC servomotor with fuzzy logic controller is shown in Figure 3.

3.11
Input and Output of fuzzy controller The error and change of error input and the output of the fuzzy logic controller is shown in Figure  4, Figure 5 and Figure 6 respectively.

Observer-Based Controller Design
The deal with the general case where only a subset of the states, or linear combinations of them, are obtained from measurements and are available to our controller. Such a guideline is referred to as the output feedback problem.
The output is of the form   6 y Cx Du   We shall examine a class of output feedback controllers constructed in two stages: 1. Contracting an observer | a system dynamic that is driven by the inputs and the outputs of the system, and yield a deliberation of its state variables; 2. Using the estimated state instead of the actual state in a estate response scheme.
The block diagram of the AC servomotor with the observer-based controller is shown in Figure 7 bellow. The controller Gc (s) can be further derived in the following form: The controller Gc (s) in Equation (8) is called the observer-based controller, since the structural idiot of the observer is implicitly reflected within the controller.
Where the state space model of the plant, G, the state feedback gains vector K, and the observer gain vector H are then returned, respectively.
We select the weighting matrix Q and R as

Result and Discussion 4.1 Comparison of the AC Servomotor with Fuzzy Logic and Observer Based Controllers for Tracking Step Position Signal
The Simulink model of the AC servomotor with fuzzy logic and observer based controllers for tracking desired step position input signal is shown in Figure 8 below. The comparison simulation result is shown in Figure 9 below. Figure 9.
Step response simulation result The data of the rise time, percentage overshoot, settling time and peak value is shown in Table 2.  Table 2 shows that the AC servomotor with fuzzy logic controller improves the settling time and the percentage overshoot better than the AC servomotor with observer based controller.

Comparison of the AC Servomotor with Fuzzy Logic and Observer Based Controllers for Tracking Square Position Signal
The Simulink model of the AC servomotor with fuzzy logic and observer based controllers for tracking desired square position input signal is shown in Figure  10 below. The comparison simulation result is shown in Figure 11 below. The simulation result of Figure 11 shows that the AC servomotor with fuzzy logic controller improves the settling time with 0.7 second and with zero percentage overshoot.

5.
Conclusion In this paper, modeling, designing and simulating of an AC servomotor with fuzzy logic and observer based controllers have been done with the help of Matlab/Simulink Toolbox successfully. A two-phase induction motor that has two stator field coils placed 90 electrical degrees apart is used as a servomotor by applying an ac voltage E1 of fixed amplitude to one of the motor windings and the other voltage E2 is varied. Comparison of the AC servomotor with the proposed controllers for tracking a step and a square desired position signal input has been done. The simulation result for tracking the desired step input position signal proves that the AC servomotor with fuzzy logic controller improves the settling time and the percentage overshoot while the simulation result for tracking the desired step input position signal proves that the AC servomotor with fuzzy logic controller improves the settling time with 0.7 second and with zero percentage overshoot.