22-05-2012, 11:54 AM
A Hybrid Adaptive Controller for Permanent Magnet Stepper Motors
Magnet Stepper Motors.pdf (Size: 258.51 KB / Downloads: 69)
INTRODUCTION
There has been considerable advancement in the
development of adaptive control algorithms based on Self
Tuning Regulators (STR) during last decade. The progress in
the field of power electronics, VLSI technologies and
high-speed microprocessors enables these simple and effective
algorithms to meet challenging applications of precision control
of electric drives. However, none of them have been used for
precision positional control of stepper motor especially in
presence of nonlinear dynamics. This paper describes a method
of applying such an adaptive algorithm with a static PID control
law in parallel with each other. The main idea is to develop a
parallel hybrid adaptive controller for positional reference
considering the PMSM nonlinear dynamics. As these
algorithms are simple but effective, its practical application is
highly envisaged.
PMSM DYNAMIC MODEL
The Permanent Magnet Stepper Motor (PMSM) consists of a
slotted stator and a permanent magnet rotor. These types of
motors employ a cylindrical magnet as the rotor and four teeth
or poles in the stator. One side of the rotor is out of alignment by
tooth-wide. Reference [13]-[15] shows a detailed description of
this type of electric machine. Following assumptions have been
considered in developing [14], a general model for two-phase
Permanent Magnet Stepper Motor (PMSM).
SIMULATION RESULTS
For simulation purposes, two different motors are used. The
motors are required to track the shown position trajectory. Two
cases have been investigated with the proposed control scheme.
A typical position reference trajectory θr(t) with trapezoidal
speed reference ωr(t) as shown in fig. 3 is utilized for tracking.
The details of the motor are as shown in appendix. Further, for
the purpose of testing the motor tracking under disturbance
condition, it has been assumed that a constant load torque of 2
Nm and 1 Nm for motor data in Table1 and Table 2 respectively
(which is unknown to the controller) is applied at t = 0.15 s.
These equations have been simulated with the simulation
constants K 1 –5 as mentioned in [1]. They are, k1 = 80000, k2 =
65*k1, k3 = 500, k4 = L/T, k5 = R/T, T = 0.0005 where T is the
equivalent time constant of the current loops.
CONCLUSION
An online hybrid adaptive control technique based on minimum
variance control law is developed to track positional error
effectively for changing parameter values. An online recursive
least square identification method is used to identify the error
based on pervious output. The main focus is to develop a simple
but effective adaptive control technique, which can effectively
reduce the positional error. Simulation results show that these
simple but effective techniques have considerable effect when
compared to the PID control law for normal as well as varying
parameters. The positional error has reduced to zero in both the
cases, where two different motor data sets have been selected.
Moreover there is a tendency in both the cases that the error
reduces to zero quickly after the disturbance or change in
parameters. Further, it is observed that error values are less and
doesn’t increase even though there is a change in the parameter
values.