# General Applications

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.

## Featured Examples

### 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.

### 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: Approximate a Sine Wave

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-crossing detection works in Simulink®. Simulink uses zero-crossing detection to accurately simulate an abrupt model change or discontinuity without decreasing the solver time steps. For more information, see Zero-Crossing Detection.

### Spiral Galaxy Formation Simulation Using MATLAB Function Blocks

Use MATLAB Function blocks to simulate and plot galaxy interactions.

### Counters Using Conditionally Executed Subsystems

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.

### Model Stick-Slip Friction and Hard Stops in Mass-Spring-Damper System

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

### State Events

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

Use 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.

### 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.

### Foucault Pendulum Model

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 Simulink 3D Animation

Animate the Foucault Pendulum Model in the Simulink® 3D Animation™ environment. You can modify the pendulum location by changing the `Latitude`

constant values in the model and other parameters in MATLAB® workspace.

### Explore Variable-Step Solvers with Stiff Model

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.

### 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. The model has a single pump and four actuators.

### Two Cylinder Model with Load Constraints

Use Simulink to model a rigid rod supporting a large mass interconnecting two hydraulic actuators. This model eliminates the springs as it applies the piston forces directly to the load.

### 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:

### Collision Avoidance and Trajectory Tracking of a Marine Vessel

Follow a pre-defined trajectory and avoid collisions.

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