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Main Question Body: Tomato plant can grow by only utilizing the available soil and rain sources. However, with a desired amount of irrigation and fertilization, tomato harvest can be maximized. Question 1: a) Without irrigation and fertilization, a tomato plant reaches maximum $2m$ where $99.9%$ of the growth process occurs in 75 days. At $12.5_{th}$ day, its height is approximately 1.26 $m$. 1) Derive the model, 2) Obtain the analytic solution, 3) Simulate and analyse it. b) With the fertilization, its height becomes $3.5m$ in 60 days. 1) Model the tomato plant, 2) Derive its analytical solution, 3) Simulate and analyse. c) With the fertilization and irrigation, it reaches $5m$ in 60 days. 1) Model the tomato plant, 4) Derive its analytical solution, 5) Simulate and analyse. d) Consider the tomato plant; 1) Classify the system properties, 2) Draw the closed loop block diagram, 3) Reduce the block diagram.
it reaches at 12.5 dass to $1.26m$. it reaches at 75 days to $2m$. $∂t∂x(t) +2x(t)−bu(t)⇒dx(t)=bu(t)u(t)x(t) =2b ⇒SSGlim_{t→∞}x(t)=2b u(t)=ab 5x(5)−x(0)+2x(5)=b4(5)x(s)(s+2)=x(0)+bu(s)x(s)=s+2x(s)_{0} +s+2b ⋅v(s)lim_{t→∞}G(s)(t)x(s)=s+2b ⋅4(s)x(s) s+2⋅(s)lim_{s→∞}s[5(v(s)⇒6 u(s)x(s) =s+ab =G(s)G(s)=s+2b G(t)=2d5+2 e_{−2t}lim_{s→0}G(s)u_{sg}lim_{s→0}G(0)u_{SG} $