Problem 2. The Laplace transform of f(t) is expressed as - (K KT) s + (K...

 

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Problem 2. The Laplace transform of f(t) is expressed as - (K₁ K₂T) s + (K₁ − K₂) S(TS + 1)(s + 1) F(s) = a) Use the initial value and final value theorems to obtain the conditions so that f(t) possesses a negative initial slope (derivative) and a positive final value. b) Note that f(t) is regarded as the unit step response of the system described by (K₁ K₂T) S+ (K₁ − K₂) (TS + 1)(s+1) G(s) = - Obtain the time plot for f(t) using MATLAB for the following values of the system parameters, K₁ = 2, K₂ = 1, T = 4. c) Obtain f(t) by the Laplace inverse transformation for the parameter values in part b). Sketch the time response f(t) by hand and confirm it with the MATLAB result. (G(s) represents a reverse reaction process. Notice the presence of a transfer function zero in the right half side of s-plane.) Problem 2. The Laplace transform of f(t) is expressed as - (K₁ K₂T) s + (K₁ − K₂) S(TS + 1)(s + 1) F(s) = a) Use the initial value and final value theorems to obtain the conditions so that f(t) possesses a negative initial slope (derivative) and a positive final value. b) Note that f(t) is regarded as the unit step response of the system described by (K₁ K₂T) S+ (K₁ − K₂) (TS + 1)(s+1) G(s) = - Obtain the time plot for f(t) using MATLAB for the following values of the system parameters, K₁ = 2, K₂ = 1, T = 4. c) Obtain f(t) by the Laplace inverse transformation for the parameter values in part b). Sketch the time response f(t) by hand and confirm it with the MATLAB result. (G(s) represents a reverse reaction process. Notice the presence of a transfer function zero in the right half side of s-plane.)

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