By Galal Rabie
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Extra info for Automatic Control for Mechanical Engineers
2. Solve the resulting algebraic equation to find an expression for the variable in terms of Laplace variable s, X(s). 3. Expand the result into partial fractions. 4. Find the inverse Laplace transform, x(t). 4 COMPLEX VARIABLES The following are some of the important relations of complex variables, needed for further analysis. 28) x x2 x3 x 4 xn ... ... 1! 2! 3! 4! n! 5 LAPLACE TRANSFORM TABLES The pairs of Laplace transform are given in tables published in textbooks of mathematics.
F(s) (a) (b) 39 M Galal RABIE, Automatic Control for Mechanical Engineers 8. Derive the transfer function for the given system. G(s) =X1(s)/F(s) 9. A process plant consists of two tanks with cross-sectional areas A1 and A2. The flow rate through the throttle valve is given by: q = ∆h /R, where ∆h is the head difference across the valves in meters and R is the throttle valve resistance. Write the equations describing the system operation and derive the following transfer functions: G1 ( s ) H1 Q , G 2 (s) 2 Q2 Q3 and G 3 (s) 40 H1 Q3 M Galal RABIE, Automatic Control for Mechanical Engineers 10.
24) M Galal RABIE, Automatic Control for Mechanical Engineers The hydraulic servo-actuator is described mathematically by Eqs. 24. The block diagram shown by Fig. 5 K 1 ( s) X s 0. 25) This is a unity gain first order transfer function of time constant T=2/K. 29) v = Applied electric potential difference, V. 7, can be described by the following equations. 31) Assuming zero initial conditions, the application of Laplace transform to Eq. 4 Second Order Element The second order element has a transfer function of the form: G(s) k .
Automatic Control for Mechanical Engineers by Galal Rabie