MATLAB

Assignment 9:

Disturbance signals represent unwanted inputs which affect the control-system's output, and result in an

increase of the system error. It is the job of the control-system engineer to properly design the control

system to partially eliminate the affects of disturbances on the output and system error.

Overview for disturbance input problem: The construction of the tunnel under the English Channel from France to the Great Britain began in December

1987. The first connection of the boring tunnels from each country was achieved in November 1990. The tunnel

is 23.5 miles long and bored 200 feet below sea level. Costing $14 billion, it was completed in 1992 making it

possible for a train to travel from London to Paris in three hours.

The machine operated from both ends of the channel, bored towards the middle. To link up accurately in the

middle of the channel, a laser guidance system kept the machines precisely aligned. A model of the boring

machine control is shown in the figure, where Y(s) is the actual angle of direction of travel of the boring

machine and R(s) is the desired angle. The effect of load on the machine is represented by the disturbance,

Td(s).

Figure: A block diagram model of a boring machine control system

Transfer function from R(s) to Y(s)

Assume Td(s) = 0 then the block diagram will be

Due to unit step – r(s) for K=20

% Response to a Unit Step Input R(s)=1/s for K=10

numg=[1];deng=[1 1 0];plant=tf(numg,deng);

K =10;

num=[11 K]; den=[0 1];

contr=tf(num,den);

sys_s=series(contr,plant)

sys=feedback(sys_s,[1]);

stepinfo(sys)

Repeat this for K=20, 50 and 100.

Gc(s) Controller

K + 11s

G(s) Plant

1

s(s + 1)

-

+ R(s) Desired Angle

Y(s)

Angle +

+ Td(s)

Gc(s) Controller

K + 11s

G(s) Plant

1

s(s + 1)

-

+ R(s) Desired Angle

Y(s)

Angle

Transfer function from Td(s) to Y(s)

Assume R(s) = 0 then the block diagram will be

Due to unit disturbance – Td(s) for K=20

% Response to a Unit Step Input R(s)=1/s for K=10

numg=[1];deng=[1 1 0];plant=tf(numg,deng);

K =10;

num=[11 K]; den=[0 1];

contr=tf(num,den);

sys=feedback(plant,contr);

stepinfo(sys)

Repeat this for K=20, 50 and 100.

Exercise 3: a) For each case find the percentage overshoot(%O.S.), rise time, settling time, steady state of y(t)

Unit Step Input Unit Step Disturbance

Overshoot Rise Time Setting

time

Steady

state Overshoot Rise Time

Setting

time

Steady

state

K=10

K=20

K=50

K=100

b) Compare the results of the two cases and investigate the effect of changing the controller gain on the influence of the disturbance on the system output

G(s) Plant

1

s(s + 1)

-

+ Td(s) Y(s) Angle

Gc(s) Controller

K + 11s