< prev

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8

Page 4 of 8
next >

Majalah Ilmiah UNIKOM

Vol.9, No. 2

210

H a l a m a n

DESIGNING THE CONTROL SYSTEM

In this section a linear Proportional-

Integral-Derivative (PID) controller is

designed to regulate the elevation and

travel angles of the 3-DOF Helicopter to

desired positions. The PID control gains

are computed using the Linear-Quadratic

Regular algorithm.

Using the weighting matrices

and

and the state-space matrices (A,B) found

previously, the control gain

is calculated by minimizing the cost

function

with the Matlab LQR command. Examining

the feedback gains obtained from LQR

design, we note the following feature : the

second row gains have the exact same

magnitudes as the first row.

Further examination reveals that the sum

of the rows results in :

which can be re-written as

which is the Proportional+Integral+

Derivative (PID) controller about the

elevation axis.

Examining the difference between the

gains, the feedback loop can be

decomposed into two loops : one for pitch

and one for travel.

The above equation can be re-written as.

which is a PD loop to command the pitch

to track the desired pitch. The desired

pitch is defined as.

which is another PID loop that controls the

travel position. We now have the following

control equations.

Muhammad Aria

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)