Simulink® allows you to model and simulate a wide range of dynamic systems. These example models illustrate a variety of general applications, from simple to complex.
Simulation of Bouncing Ball
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.
Single Hydraulic Cylinder Simulation
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.
Thermal Model of a House
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.
Approximating Nonlinear Relationships: Type S Thermocouple
Approximate nonlinear relationships of a type S thermocouple.
Digital Waveform Generation: Approximating a Sine Wave
Some of the main steps needed to design and evaluate a sine wave data table for use in digital waveform synthesis applications in embedded systems and arbitrary waveform generation instruments.
Accurate Zero-Crossing Detection
How zero crossings work in Simulink®. In this model, three shifted sine waves are fed into an absolute value block and saturation block. At exactly t = 5, the output of the switch block changes from the absolute value to the saturation block. Zero crossings in Simulink will automatically detect exactly when the switch block changes its output, and the solver will step to the exact time that the event happens. This can be seen by examining the output in the scope.
Spiral Galaxy Formation Simulation Using MATLAB Function Blocks
This model was inspired by the classic paper "Galactic Bridges and Tails" (Toomre & Toomre 1972). The original paper explained how disc shaped galaxies could develop spiral arms. Two disc shape galaxies originally are far apart. They then fly by each other and almost collide. Once the galaxies are close enough, mutual gravitational forces cause spiral arms to form.
Counters Using Conditionally Executed Subsystems
The contrast between enabled subsystems and triggered subsystems for the same control signal, through the use of counter circuits. After running the simulation, the scope shows three plots.
Friction Model with Hard Stops
Model friction one way in Simulink®. The two integrators in the model calculate the velocity and position of the system, which is then used in the Friction Model to calculate the friction force.
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.
Bang-Bang Control Using Temporal Logic
Use Stateflow® to model a bang-bang temperature control system for a boiler. The boiler dynamics are modeled in Simulink®.
Inverted Pendulum with Animation
Model an inverted pendulum. The animation is created using MATLAB® Handle Graphics®. The animation block is a masked S-function. For more information, use the context menu to look under the Animation block's mask and open the S-function for editing.
Double Spring Mass System
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.
Tank Fill and Empty with Animation
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.
Simulating Systems with Variable Transport Delay Phenomena
Two cases where you can use Simulink® to model variable transport delay phenomena.
Modeling a Foucault Pendulum
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.
Foucault Pendulum Model with VRML Visualization
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.
Explore Variable-Step Solvers with Stiff Model
The behavior of variable-step solvers in a Foucault pendulum model. Simulink® solvers
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.
Exploring the Solver Jacobian Structure of a Model
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.
Double Bouncing Ball: Use of Adaptive Zero-Crossing Location
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:
Four Hydraulic Cylinder Simulation
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.
Two Cylinder Model with 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.
Modeling Cyber-Physical Systems
Model transport delay in a variable speed conveyor belt.
Power Analysis of Spring Mass Damper System
Analyze mechanical power of mass-spring damper system.
Van der Pol Oscillator
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:
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