4.5. EXERCISES AND PROJECTS 163
where dydt(t) is the rocket velocity at timet(the plant output),y(t)is
the altitude of the rocket above sea level, andc(t)is the plant input
that controls the nozzle opening which in turn controls the velocity of the
exhaust gas. The exhaust gas velocity determines the thrust of the rocket.
The following parameters are given:
ïInitial mass of the rocket and fuelM=20,000 + 5000 = 25,000 kg
ïFuel consumption ratem=10kg/s(assumed to be constant)
ïCross-sectional area of rocketA=1m^2
ïGravitational constantg=9.81456 m/s^2
ïRadius of earthR=6. 37 ◊ 106 m
ïDensity of airρa=1.21 kg/m^3
ïDrag coefficient of the rocketCd=0. 3
Caution: The rocket cannotflyindefinitely!
The rocket should impact at a distance of 500 kilometers from the point
of blastoff. The maximum altitude it can reach is 15 kilometers above sea
level and the minimum altitude is 10 kilometers.
(a) For a selected altitude, compute the trajectory that the rocket should
follow.
(b) Develop both Mamdani type and Sugeno type fuzzy controllers that
control the rocket along the desired trajectory.
(c) Simulate the dynamics of motion usingMatlabor any appropriate
simulation tool.
(d) Compare the performance of Mamdani and Sugeno controllers.
(e) Obtain a linearized model of the system and show that the system is
inherently unstable.
(f) Develop an output state-variable feedback controller and simulate its
performance.
Prepare a detailed report discussing the results. Comment on the stability
performance of the system due to possible disturbances.
9.Project(This project obtains fuzzy rules from input-output data and
implements a Mamdani fuzzy inference system using these rules.)
Approximate the functionf(x 1 ,x 2 )=^12 x^21 +^12 x^22 with a Mamdani fuzzy
inference system (FIS) using triangular antecedent membership functions
and triangular consequent membership functions.
