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Task 1: Create the block diagram shown in Fig. 1.2 in Simulink by identifying the appro- priate blocks from the Simulink Library, and enter the required parameters. Step 80 5s+1 Transfer Fon Scope Figure 1.2: Block diagram, exercise 1.

Task 1: Create the block diagram shown in Fig. 1.2 in Simulink by identifying the appro- priate blocks from the Simulink Library, and enter the required parameters. Step 80 5s+1 Transfer Fon Scope Figure 1.2: Block diagram, exercise 1.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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In this exercise, you will model the vehicle speed. We will develop a linear continuous- time model for the speed of a vehicle with mass m [kg], see Fig. 1.1. Denote the velocity of the vehicle v [m/s]. The rate of change of the velocity is the acceleration v (m/sr). Assume that the engine imparts a force u(t). Assume that friction slows the car down and is proportional to the velocity, i.e. friction force equals by where b is a friction coefficient. Finally, assume that the rotational inertia of the wheels and that aerodynamic drag are negligible. bv Figure 1.1: 1st order system of vehicle speed. Using Newton's Law F = ma, we can write the net force: u(t) — bv = mi We re-arrange the equation to m b - v+v= m u(t) b TZ u(t) (1.1) This is a 1st order differential equation, see the general 1st order equation Tx + x = Ku(t) (1.3) where x is the output variable (here: speed, not position), u(t) is the input variable (engine force), 7 is the time constant and K is the steady state gain. Here, 1 (1.2)
Transcribed Image Text:In this exercise, you will model the vehicle speed. We will develop a linear continuous- time model for the speed of a vehicle with mass m [kg], see Fig. 1.1. Denote the velocity of the vehicle v [m/s]. The rate of change of the velocity is the acceleration v (m/sr). Assume that the engine imparts a force u(t). Assume that friction slows the car down and is proportional to the velocity, i.e. friction force equals by where b is a friction coefficient. Finally, assume that the rotational inertia of the wheels and that aerodynamic drag are negligible. bv Figure 1.1: 1st order system of vehicle speed. Using Newton's Law F = ma, we can write the net force: u(t) — bv = mi We re-arrange the equation to m b - v+v= m u(t) b TZ u(t) (1.1) This is a 1st order differential equation, see the general 1st order equation Tx + x = Ku(t) (1.3) where x is the output variable (here: speed, not position), u(t) is the input variable (engine force), 7 is the time constant and K is the steady state gain. Here, 1 (1.2)
A way to represent Eq. (1.3) is to develop a transfer function of the model, as follows: dx d²x dn x dt (1.5) dt dt In our case, the differential equation in Eq. (1.3) can be developed as Tx + x = Ku → 7sx + x = Ku. By re-arranging the transfer function, relating the input u(t) to the output x K TS + 1 We assume, T = 5 and K = 80, then the model becomes x = = sx ; ï = X = Step = s²x; X = -U 80 5s +1 n = Sx -U (1.8) Task 1: Create the block diagram shown in Fig. 1.2 in Simulink by identifying the appro- priate blocks from the Simulink Library, and enter the required parameters. 80 5s+1 Transfer Fon Figure 1.2: Block diagram, exercise 1. (1.6) Scope (1.7) Task 2: Graph the result in the scope for 3 different value combinations of 7 and K. Describe how the shape of the response depends on those two values in your report.
Transcribed Image Text:A way to represent Eq. (1.3) is to develop a transfer function of the model, as follows: dx d²x dn x dt (1.5) dt dt In our case, the differential equation in Eq. (1.3) can be developed as Tx + x = Ku → 7sx + x = Ku. By re-arranging the transfer function, relating the input u(t) to the output x K TS + 1 We assume, T = 5 and K = 80, then the model becomes x = = sx ; ï = X = Step = s²x; X = -U 80 5s +1 n = Sx -U (1.8) Task 1: Create the block diagram shown in Fig. 1.2 in Simulink by identifying the appro- priate blocks from the Simulink Library, and enter the required parameters. 80 5s+1 Transfer Fon Figure 1.2: Block diagram, exercise 1. (1.6) Scope (1.7) Task 2: Graph the result in the scope for 3 different value combinations of 7 and K. Describe how the shape of the response depends on those two values in your report.
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