CTMS: Simulink Examples Index

Simulink Examples Index

Example	Description	Tutorial
Cruise Control
Motor Speed Control
Motor Position Control
Bus Suspension
Inverted Pendulum
Pitch Control
Ball and Beam

Descriptions of the MATLAB tutorial examples are available here.

Cruise Control

This is a simple example of the modeling and control of a first order system. This model takes inertia and damping into account. Newton's laws are modeled directly in this example, where forces are summed up to provide the acceleration of the vehicle. A simple PI controller is implemented.

Motor Speed Control

A DC motor has second order speed dynamics when mechanical properties such as inertia and damping as well as electrical properties such as inductance and resistance are taken into account. Newton's law and Kirchoff's law are modeled directly by summing forces and summing voltages to provide the motor's acceleration and armature current, respectively. A lag compensator is implemented.

Motor Position Control

The model of the position dynamics of a DC motor is third order, because measuring position is equivalent to integrating speed, which adds an order to the motor speed example. In this example, however, the motor parameters are taken from an actual DC motor used in an undergraduate controls course. This motor has very small inductance, which effectively reduces the example to second order. This uses the same model as the motor speed example with an additional integrator to provide position from the velocity signal. In this example, a discrete-time model extraction and a discrete-time controller are implemented around the continuous plant model.

Bus Suspension

This example looks at the active control of the vertical motion of a bus suspension. It takes into account both the inertia of the bus and the inertia of the suspension/tires, as well as springs and dampers. An actuator is added between the suspension and the bus. Newton's law is modeled directly by summing forces acting on each of the two inertias. A full-state feedback controller is implemented by extracting a set of states directly from the model.

Inverted Pendulum

The inverted pendulum is a classic controls demonstration where a pole is balanced vertically on a motorized cart. It is interesting because without control, the system is unstable. This is a fourth order nonlinear system. This is a particularly difficult system to model in Simulink because of the algebraic constraint. While Newton's laws are still modeled directly, some calculations must be done in advance to derive the form of the algebraic constraint. A PID controller is implemented using Simulink's built-in PID block.

Pitch Control

The pitch angle of an airplane is controlled by adjusting the angle (and therefore the lift force) of the rear elevator. The aerodynamic forces (lift and drag) as well as the airplane's inertia are taken into account. This is a third order, nonlinear system which is linearized about the operating point. The Simulink model is based on the State-Space model developed in the MATLAB tutorials, and the state equations are implemented directly. Because of this, the state vector is available for use in a full-state-feedback controller.

Ball and Beam

This is another classic controls demo. A ball is placed on a straight beam and rolls back and forth as one end of the beam is raised and lowered by a cam. The position of the ball is controlled by changing the angular position of the cam. This is a second order system, since only the inertia of the ball is taken into account, and not that of the cam or the beam. Rather than modeling forces and accelerations, the Lagrangian equations of motion are implemented is Simulink, eliminating the need to express the algebraic constraint explicitly as was done in the inverted pendulum example.

Tutorials