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# Block Diagram – Solved problems – Catalog 8 – Mass-spring-damper system and electrical system

In this PDF file, the Block Diagram and the Transfer Function are determined by applying block algebra, from the exercises that are part of control systems, signals and systems, analysis of electrical networks, etc. Each problem has a cost of 12.5 euros. The complete workshop costs 27.5 euros. Payment through Paypal is facilitated.

1. Obtain the transfer function G(s)=Y(s)/R(s) of Figure 1, by two methods: using block algebra reduction techniques and using Mason’s formula.

2. Obtain the transfer function G(s)=C(s)/R(s) of Figure 2, by two methods: using block algebra reduction techniques and using Mason’s formula.

3. Obtain the transfer function G(s)=C(s)/R(s) of Figure 3, by using block algebra reduction techniques .

4. Obtain the transfer function G(s)=Y(s)/R(s) of the next Figure, by using block algebra reduction techniques . .

5. Find the equations of the system in Figure 7 and represent it using state variables. From there determine the block diagram of the system. Then, using block diagram algebra, find the transfer function X(s)/U(s). Consider x(t) as the output and u(t) as the input. Check the result using Laplace transform.

6. Find the equations of the system in Figure 8. Find the matrix representation of the system (state variables). Consider x1(t) as the output, and u(t) as the input. Construct the block diagram of the system and use block algebra to determine the transfer function  X1(s)/U(s).

7. Find the equations of the system in Figure 22. Determine the transfer function X1(s)/U(s). Determine the block diagram of the system from the transfer function obtained.

8. Find the equations of the System in Figure 24. Find the state space representation of the system, considering Θ1(t) as the output and T(t) as the input. Find the block diagram of the system and from there, using block algebra, determine the transfer function Θ1(s)/T(s).

9. Find the equations of the system in Figure 25. Determine the transfer function X1(s)/F(s). Obtain the block diagram of the system from the transfer function obtained (Explain step by step). Graph the response of the system to a step function input using Matlab. Consider k1= k2= k3= 1 N/m, b1= b2= b3=1 N-s/m, m1= m2= m3=1 Kg.

Response graph to the unit step of exercise 9.

10. Determine the differential equations that represent the model of the system in Figure 75. Use the node analysis method. Find the transfer function Vo(s)/V(s). Make the representation of the system in block diagram from the transfer function Vo(s)/V(s). Consider R1=1Ω,  R2= R3=1 Ω, L=1 H, C1=C2=1 pF.

11. Obtain the transfer function Vo(s)/V(s) of the electrical system in figure 75, from the block diagram of the system obtained in problem 10, using block algebra. Simulate and analyze in Matlab the response of the system to a unit step input

12. Find the state space representation of the System shown in Figure 39 assuming that Θ4(t) is the output and T(t) is the input. Draw the block diagram of the system and find the transfer function Θ4(t)/T(t). Consider k=2 N-m/rad, b=16 N-m-s/rad, J=4  Kg-m2

13. Find the transfer function ΘL(s)/Ei(s) of the system shown in Figure 56. Find the state space representation of the system, assuming that ΘL(t) is the output and that ei(t) is the input . Represent the System by means of a block diagram. From the block diagram of the system, determine again and by means of block algebra the transfer function ΘL(s)/Ei(s).

14. Find the transfer function ΘL(s)/Θr(s) of the system shown in Figure 59. Design the block diagram of the system.

15. Find the transfer function Q2(s)/Q1(s) of the Liquid Level System shown in Figure 68. Find the state space representation of the System taking q2(t) as the output, and q1(t) as the input. Obtain the block diagram of the system and determine the same transfer function using block algebra.

16. A very simplified model of the dynamics of a rocket is shown in Figure 1. A uniform bar of mass m and length 2L, subjected to the force of gravity G (center of gravity of the bar) and to two external forces applied at its lower end: a vertical V(t) and a horizontal H(t). It is requested: i) Draw the input and output variables diagram. Characterize the equilibrium point determined by x(0)=0, y(0)=0. Ii) Obtain the system of equations linearized around the equilibrium point. iii) Draw the block diagram of the system. iV) Obtain the transfer functions from it

17. Determine the expression for the output C(s) of the system of Figure 90

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Block diagram – Catalog 8- payment for a single exercise

Payment for a single exercise (1 exercise). Block Diagram and the Transfer Function through the application of block algebra, of the exercises that are part of the chair of control systems, signals and systems, analysis of electrical networks. Once the payment is made, please send a copy of the payment receipt to whatsapp +34633129287 to receive the product in this way. (or by email dademuch@gmail.com).

12,50 €

Block diagram – Catalog 8- payment for the entire workshop

Payment for the entire workshop (17 exercises). Block Diagram and the Transfer Function through the application of block algebra, of the exercises that are part of the chair of control systems, signals and systems, analysis of electrical networks. Once the payment is made, please send a copy of the payment receipt to whatsapp +34633129287 to receive the product in this way. (or by email dademuch@gmail.com failing that).

27,50 €

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