Dynamic Modeling and Simulation of a Thermoelectric-Solar Hybrid Energy System Using an Inverse Dynamic Analysis Input Shaper

Table 4

Characteristics of the proposed output function.

Type of output function	Equation of the output function	Output function behavior
Actual output function	𝑋(𝑢)=𝑥(𝑡)𝑋𝐸=1−𝑒^3−𝑢
First derivative of actual output function	𝑋̇(𝑢)=1𝛼𝑋𝐸𝑥̇(𝑡)=−𝑒^3−𝑢𝑑𝑑𝑢−𝑢^3=3𝑢^2𝑒^−𝑢3
Second derivative of actual output function	𝑋̈(𝑢)=1𝛼^2𝑋𝐸𝑥̈(𝑡)=3𝑢^2𝑑𝑒𝑑𝑢^−𝑢3+𝑒^−𝑢3𝑑𝑢𝑑𝑢^2=(6𝑢−9𝑢^4)𝑒^−𝑢3