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Gain Scheduling Control of Permanent Magnet Brushless dc Motor
Gain Scheduling Control of Permanent Magnet Brushless dc Motor
Bhim Singh, Fellow
A H N Reddy, Non-member
S S Murthy, Fellow
This paper presents a gain-scheduling control scheme for a proportional integral controller (PI) for speed control
of permanent magnet brushless dc (PMBLDC) motor drive. It is well known that, a conventional PI controller is
most widely used in industry due to its simple control structure. While PI controller is widely used in industrial
applications, they exhibit poor performance when applied to systems containing unknown non-lineariy such as dead
zones, saturation and hysteresis. In this proposed scheme, the PI gains are allowed to vary within a pre- determined
range and therefore eliminates the problems faced by the conventional PI controller. The performance of the
proposed scheme is simulated and compared with a minimal control hardware structure using the Intel 80196 kc
single-chip microcontroller. The experimental results show improvement in transient as well as steady state response
of the brushless dc drive over conventional fixed gain PI controller. The model of the system consists of the proposed
speed controller, reference current generator, PWM current controller, inverter and motor. Experimental results
of the scheme are compared under starting, speed reversal conditions for both PI and the proposed gain scheduled
PI controllers.
Keywords : Control; PMBLDC motor; Gain scheduling; PWM controller; Microcontroller
INTRODUCTION
Permanent magnet brushless motors have found wide applica-
tions due to their high power density and ease of control. These
features have resulted in the increased demand of brushless dc
motor in high performance servo and robotic applications. Per-
manent magnet motors are generally classified as permanent
magnet brushless dc motor with trapezoidal back emf and perma-
nent magnet synchronous motors with sinusoidal back emf.
PMBLDC is chosen over PMSM due to higher power density.
Moreover, PMBL machine with trapezoidal back emf have sim-
plicity in control. These machines suffer inherently from torque
ripples
1
. The brushless dc motor employs a dc power supply
switched to the stator phase windings of the motor by power
devices. The switching sequence being determined from the rotor
position. Advances in high-energy permanent magnet materials
and power electronics have widely enhanced the applications of
PMBLDC machines in variable speed drive similar to ac ma-
chines
2
.
The brushless dc motor has been widely known for its high
efficiency and low maintenance requirement as compared to dc
motor. Attempts have been made to present the dynamic model-
ling and analysis of PMBLDC motor using different control
laws
3, 4
. There has been tremendous research for providing suit-
able speed controller for PMBLDC machines. It is well known
that a conventional PI controller is most widely used in industry
due to its simple control structure, ease of design and low cost.
However, the PI type controller only cannot give a good control
performance. Moreover, it suffers from disadvantages of slower
response, larger overshoots, and oscillation. As the PMBLDC
machine has nonlinear model, the linear PI control is not a good
option. This boosted the use of nonlinear control schemes for
PMBLDC motor such as model reference adaptive systems
5
,
variable structure control. Several adaptive control algorithms
have been theoretically developed and proposed in last few years,
but very few of these have been practically employed in the
control of electric drives due to their complexity and poor per-
formance. Moreover, it requires tuning of parameters accurately.
Since in electric drives the control loop actions must be performed
within less than few milliseconds, practical implementation of
adaptive algorithms is feasible with the aid of costly DSPs in order
to manipulate just in time the control signals. Another type of
controller based on fuzzy logic is being incresingly applied to
many systems with non-linearity and uncertainty. But in spite of
several well-known advantages, the design of fuzzy logic control-
lers is still practically performed with trial and error method. This
fact has prevented a wide diffusion of system controllers based
on fuzzy set theory. The problem of developing a simple tuning
procedure properly working on in wide range of operating condi-
tions is still open.
It is well known that, PI controller can be simple to implement in
practice. To satisfy the demand for easy to use servo system
auto-tuning technology have been applied from a practical point
of view. Many kinds of auto-tuning technology have been pro-
posed so far
7, 8
. In case of fuzzy reasoning type of auto-tuning
method, it still remains a serious problem that fuzzy rules should
be set by designer. Some researchers proposed gain scheduled
scheme for PI controller, as it is simple to implement and provides
good performance
8
. In the present investigation, PI gains are
tuned such that the drive system exhibits satisfactory transient and
steady state response under varying operating conditions, such as
starting and reversal. Though it is possible to provide linear PI
controller for different conditions, it is difficult to achieve manu-
ally. Hence, an automated design requiring minimum of hu-
man intervention for tuning is required. Here, a gain scheduling
of PI controller is implemented on a single chip microcontroller
Bhim Singh, A H N Reddy and S S Murthy are with the Department of
Electrical Engineering, IIT Delhi, India 110 016.
This paper (redrafted) was received on January 2, 2003. Written discussion on
this paper will be received until November 30, 2003.
52
IE(I) Journal-EL (Intel 80196 kc) for the speed control of the drive system. To make
the drive system more reliable all the control loops like speed and
current control loops are programmed digitally.
The key feature of the proposed gain scheduling scheme of
adaptive control is the reduced amount of computation. An easy
and low cost practical implementation of the procedure is possible
without employing expensive dedicated computing systems. This
scheme is very easy to implement in practice since an existing PI
controller is tuned automatically. In this scheme, the gains are
allowed to vary over a predetermined range for varying operating
conditions. It is well known that the proportional term
(K
P
) is
responsible for improving overshoots, rise time response and the
integral
(K
I
) term reduces steady state error. When the speed error
is large, a large value of proportional gain is necessary for better
control effort and similarly when the speed error is small a large
value of integral gain is necessary to overcome steay state error.
In this paper, the basic building blocks and operational beha-
viour of PMBLDC motor drive are described first. Then the drive
system is analyzed in terms of speed controller, current controller
and inverter. Next, the scheme is simulated under real time
conditions and compared with PI controller. At last the implemen-
tation of the present scheme is presented and the drive perform-
ance is compared with the conventional PI controller.
Experimental results show improvements in transient as well as
steady state performance over the conventional PI controller.
OPERATIONAL BEHAVIOUR AND CLOSED LOOP
CONTROL OF PMBLDC MOTOR DRIVE
A permanent magnet brushless dc (PMBLDC) motor drive is a
combination of ac machine, rotor position sensor and inverter that
results in a system producing a linear speed-torque characteristic
similar to the conventional dc motor and due to this motor is
named as brushless dc motor. It has 3-phase windings on the stator
similar to 3-phase squirrel cage induction motor and magnets are
placed on the rotor to provide air gap flux resulting in brushless
rotor construction. It has trapezoidal induced emf in stator phase
windings when it is operated at definite speed. The quasi-square
wave ac current is fed to stator phase winding through electronic
commutator (using current controlled voltage source inverter and
rotor position sensor), which results in constant torque developed
by the motor. At any instant of time, two out of 3-phase stator
winding of the motor carry currents having proper synchroni-
zation with rotor magnets position and develop electromagnetic
torque. The output torque is dependent upon the amplitude of
stator current and the flux produced by PM rotor. The use of high
energy density permanent magnet material has resulted in reduced
motor weight, increased efficiency, high torque, and low rotor
inertia with associated fast response.
Figure 1 describes the basic building blocks of the PMBLDC
motor drive. The drive consists of gain scheduled PI controller,
reference current generator, PWM current controller, position
sensor, motor and MOSFET based inverter. The speed of the
motor is compared with the reference value and the error in speed
is processed in gain scheduled PI controller. The output of gain
scheduled PI controller is considered as the reference torque. A
limit is put on the speed controller output depending on maxi-
mum winding currents. The reference current generator block
generates the three phase reference currents
(i
a , i
b , i
c

) using the
limited peak current magnitude decided by the controller and the
position sensor. The reference currents have the