Consider a first-order system P(s) = +1, where y is output of the system and u is input to the system. We call the system P to be controlled the plant. Y P(s) Plant 1.1. Plant Analysis. In this section, let us analyze the properties of the given plant. 1.1.1. The Ordinary Differential Equation Equating y and u. Let Y(s) denote the Laplace transform of the output y and U(s) denote the Laplace transform of the input u. Then we have P(s) = Y(s) U(s) 1 8+1 SY(s) + Y(s) == U(s) 1) What is the differential equation representation of the plant? Hint: Derive by taking the inverse Laplace transform of (1). 1.1.2. Plant Poles and Zeros. 1) What is the characteristic equation of P(s)? 2) What is the plant pole? (1)