Applications générales

Uses two models of a bouncing ball to show different approaches to modeling hybrid dynamic systems with Zeno behavior. Zeno behavior is informally characterized by an infinite number of events occurring in a finite time interval for certain hybrid systems. As the ball loses energy, the ball collides with the ground in successively smaller intervals of time.

Use Simulink® to model a hydraulic cylinder. You can apply these concepts to applications where you need to model hydraulic behavior. See two related examples that use the same basic components: four cylinder model and two cylinder model with load constraints.

Use Simulink® to create the thermal model of a house. This system models the outdoor environment, the thermal characteristics of the house, and the house heating system.

Approximate nonlinear relationships of a type S thermocouple.

Design and evaluate a sine wave data table for use in digital waveform synthesis applications in embedded systems and arbitrary waveform generation instruments.

Cet exemple montre comment fonctionnent les passages par zéro dans Simulink®. Dans ce modèle, trois ondes sinusoïdales décalées alimentent un bloc de valeur absolue et un bloc de saturation. À t = 5 exactement, la sortie du bloc Switch passe du bloc de valeur absolue (Abs) au bloc de saturation (Saturation). Le traitement des passages par zéro dans Simulink permet de détecter automatiquement le moment exact où la sortie du bloc Switch change. Le solveur indique l'instant précis où cet événement se produit, que l'on peut constater en examinant la sortie dans la fenêtre Scope.

Use MATLAB Function blocks to simulate and plot galaxy interactions.

Implement counters using Enabled and Triggered subsystems. In this example, the model sldemo_counters controls flow of water into a tank and uses a counter to count the number of times overflow occurs, where overflow occurs when the water level in the tank is 8 meters or more for 30 seconds or more.

One way you can incorporate hard stops and friction changes from stick-slip motion into a mass-spring-damper model.

Handle state events. Run the simulation and see the phase plane plot, where the state x1 is along the X-axis and the state x2 is along the Y-axis.

Use Stateflow® to model a bang-bang temperature control system for a boiler. The boiler dynamics are modeled in Simulink®.

Use a Simulink® to model and animate an inverted pendulum system. An inverted pendulum has its center of mass above its pivot point. To stably maintain this position, the system implements control logic to move the pivot point below the center-of mass as the pendulum starts to fall. The inverted pendulum is a classic dynamics problem used to test control strategies.

Model a double spring-mass-damper system with a periodically varying forcing function. The model uses an S-Function block to animate the mass system during simulation. In the system, the only sensor is attached to the mass on the left, and the actuator is attached to the mass on the left. The example uses state estimation and linear-quadratic regulator (LQR) control.

Model the dynamics of liquid in a tank. The animation provides a graphical display of the tank as it empties and refills, based on tank parameters. When you click START SIM, the tank fills up and empties. When the simulation ends, review the plot showing the liquid height and the states of the two valves.

Two cases where you can use Simulink® to model variable transport delay phenomena.

Model a Foucault pendulum. The Foucault pendulum was the brainchild of the French physicist Leon Foucault. It was intended to prove that Earth rotates around its axis. The oscillation plane of a Foucault pendulum rotates throughout the day as a result of axial rotation of the Earth. The plane of oscillation completes a whole circle in a time interval T, which depends on the geographical latitude.

Solve the differential equations for the Foucault Pendulum problem and displays the pendulum bob movement in the VRML scene. You can modify the Pendulum location by changing the Latitude / Longitude constant values in the model and other parameters (g, Omega, L and initial conditions) in MATLAB® workspace.

The behavior of variable-step solvers in a Foucault pendulum model. Simulink® solvers ode45, ode15s, ode23, and ode23t are used as test cases. Stiff differential equations are used to solve this problem. There is no exact definition of stiffness for equations. Some numerical methods are unstable when used to solve stiff equations and very small step sizes are required to obtain a numerically stable solution to a stiff problem. A stiff problem may have a fast changing component and a slow changing component.

The example shows how to use Simulink® to explore the solver Jacobian sparsity pattern, and the connection between the solver Jacobian sparsity pattern and the dependency between components of a physical system. A Simulink model that models the synchronization of three metronomes placed on a free moving base are used.

Choose the correct zero-crossing location algorithm, based on the system dynamics. For Zeno dynamic systems, or systems with strong chattering, you can select the adaptive zero-crossing detection algorithm through the Configure pane:

Use Simulink® to create a model with four hydraulic cylinders. See two related examples that use the same basic components: single cylinder model and model with two cylinders and load constraints.

Model a rigid rod supporting a large mass interconnecting two hydraulic actuators. The model eliminates the springs as it applies the piston forces directly to the load. These forces balance the gravitational force and result in both linear and rotational displacement.

Model transport delay in a variable speed conveyor belt.

Analyze mechanical power of mass-spring damper system.

Model the second-order Van der Pol (VDP) differential equation in Simulink®. In dynamics, the VDP oscillator is non-conservative and has nonlinear damping. At high amplitudes, the oscillator dissipates energy. At low amplitudes, the oscillator generates energy. The oscillator is given by this second-order differential equation: