Simulink Model for y = -lOy + f(t) Construct a SimuIink model to solve y = -10y + ƒ(t) y(O) = 1 where ƒ(t) = 2 sin 4t, for 0 ≤ t ≥ 3. • Solution To construct the simulation, do the following steps, 1. You can use the model shown in Figure…

Simulink Model of a Two-Mass-System Develop a Simulink model to plot the unit-step response of the variables XI and X2 with the initial conditions XI (0) = 0.2, XI (0) = 0, X2(0) = 0.5, X2(0) = 0. –Solution First select appropriate values for the matrices in the output equation y = Cz +Bf(t). Since we want…

Model of a Relay-Controlled.Motor The model of an armature-controlled dc motor was discussed in Section 8.6. See Figure 9.4-8. The model is di . L- = -RI – K~w+ v(t) dt dw . 1– = KTI – C(» – Td(t) where the model now includes a torq e Td(t) acting on the motor shaft, due…

Exporting to the MATLAB Workspace We now demonstrate how to export the results of the simulation to the MATLAB work-space, where they can be plotted or analyzed with any of the MATLAB functions . • Solution Modify the Simulink model constructed in Example 9.2-1 as follows. Refer Figure 9.2-3. 1. Delete the arrow connecting the Scope…

Simulink Model of a Rocket-Propelled Sled A rocket-propelled sled on a track is represented in Figure 9.4-2 as a mass m with an applied force f that represents the rocket thrust. The rocket thrust initially is horizontal, but the engine accidentally pivots during firing and rotates with an angular acceleration of 8 = Jr/50 rad/s. Compute the sled’s…

Response with a Dead Zone Create and,run a Simulink simulation of a mass-spring-damper model (9.5-1) using the parameter values m = 1, C = 2, and k = 4. The forcing function is the function 1(1) = sin 1.4e. The system has the dead-zone nonlinearity shownin Figure 9.5-1. • Solution To construct the simulation, do the following…

Model of a Nonlinear Pedulum The pendulum shown in Figure 9.6-1 has the following nonlinear equation of motion, if there is viscous friction in the pivot and if there is an applied moment M(t) about the pivot. Ie +c6 +mgL sin9 = M(t) where I is the mass moment of inertia about the pivot. Create a Simulink…

You develop Simulink models by constructing a diagram that shows the elements of the problem to be solved. Such diagrams are called simulation diagrams or block diagrams. Consider the equation y = 10f (t). Its solution can be represented symbolically as This solution can be represented graphically by the simulation diagram shown in Figure 9.1-1 a. The arrows represent…

Piecewise-Linear Models Unlike linear models, closed-form solutions are not available for most nonlinear differential equations, and we must therefore solve such equations numerically. A nonlinear ordinary differential equation can be recognized by the fact that the dependent variable or its derivatives appears raised to a power or in a transcendental function. For example, the following equations are nonlinear. I y…

One potential disadvantage of a graphical interface such as Simulink is that, to simulate a complex system, the diagram can become rather large and therefore somewhat cumbersome. Simulink, however, provides for the creation of sub system blocks, which playa role analogous to that of subprograms in a programming language. A subsystem block is actually a Simulink program represented by.a single…

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