Optimal Control of Permanent Magnet Motors Using Dynamic

Proceedings of the 2004 IEEE

Conference on Robotics, Automation and Mechatronics Singapore, 1-3 December, 2004

Optimal Control of Permanent Magnet Motors Using Dynamic �rogramming Eldon Gunn2

Jean P. Quirionl,3

I International

2Industrial Engineering,

Rectifier

Automotive, Halifax,

-

Engineering, Dalhousie

University, Halifax, Canada

Firstly, Dynamic Programming is employed in the

permanent magnet synchronous motors (PMSM). Tn particular, a solution that can handle non-zero state tracking is of interest. Secondly, it is shown that the resulting optimal control solution converges to that of linear quadratic regulators (LQR). An LQR is then presented as·an alternative_control method for PMSM, A of the

p erformance

of the LQR with that of

traditional proportional and proportional-integral control1ers is made using time and frequency domain techniques.

with

and permanent magnet motors.

that

decision-making,

optimal

is derived from this DP problem fonnulation in section IV, conclusion is then given in section VI.

II. SINUSOIDAL PMSM MODEL

The well-known differential equations that govern the

Ld

DP

is

characterized

dimensionality" state-space

[1].

and

by

the

so-called

"curse

of

increase,

the

[J]. This "curse" refers to the fact time horizon of a system

computational requirements of DP rapidly explode to a non­ time control of physical systems. However, as shown in this

"curse of dimensionality",

LQR are increasingly used in applications like control of

vehicular driveline vibration

[3],

[2], control of induction motors

e tc . In this paper, the LQR solution deri ved from DP is

employed in the optimal torque control of a sinusoidal

pennanent magnet synchronous motor (PMSM).

PMSM are increasingly becoming the motors of choice in

industrial

increased

and

automotive

efficiency

and

applications

small

size

because

of

their

beneficial to investigate alternative control methods, such as

performance comparison of the derived LQR-based controller

0-7803-8645-0/04/$20.00 © 2004 IEEE

.

I

q

-111'1> d +

VJ

dl

(I) (2)

•

Vd

•

Ld andL are the direct and quadrature inductances. J

•

R s is the stator resistance. m

and Vq are the direct and quadrature voltages.

is the rotational velocity.