Simulink Examples Index
|Motor Speed Control
|Motor Position Control
|Ball and Beam
Descriptions of the MATLAB tutorial examples are available here.
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.
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 Speed 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.
Motor Position Control
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.
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.
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.
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.
Ball and Beam
MATLAB Basics |
MATLAB Modeling |
Root Locus |
Frequency Response |
State Space |
Digital Control |
Simulink Basics |
Simulink Modeling |