Problem 1: The linearized equations describing the vertical motion of a hot-air balloon are given by: tau _(1)T^(?)=-T+u tau _(2)z^()+z^(?)=aT+w where T represents the hot-air temperature, z represents the altitude of the balloon, u repre- sents the burner heating rate, and w is the wind speed. In what follows we will assume that w=0 and to si solutionspile.com

Question

Problem 1: The linearized equations describing the vertical motion of a hot-air balloon are given by:

\tau _(1)T^(?)=-T+u
\tau _(2)z^(¨)+z^(?)=aT+w

where

T

represents the hot-air temperature,

z

represents the altitude of the balloon,

u

repre- sents the burner heating rate, and

w

is the wind speed. In what follows we will assume that

w=0

and to simplify the computations the parameters

\tau _(1),\tau _(2)

, and

a

will assume the following unrealistic values:

\tau _(1)=0.02,\tau _(2)=0.5,a=10

Compute the transfer function from the input

u

to the balloon's altitude. Design a controller for a unity-feedback loop so that the step response has no overshoot and the rise time is no greater than 0.9 seconds. solve for me

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