Descriptions of the Simulink 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, and simple
controllers are designed.
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. The controller's
objective is to maintain the speed of rotation of the motor shaft with
a particular step response. This
electro-mechanical system example demonstrates slightly more
complicated dynamics than does the cruise control example, requiring
more sophisticated controllers.
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. It differs from
the motor speed example in that there is a free integrator in the open
loop transfer function. Also introduced in this example is the
compensation for a disturbance input. This requires a free integrator
in the controller, creating instability in the system which must be
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. This fourth
order system is particularly difficult to control because of the
existence of two zeros near the imaginary axis. This requires careful
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 which is linearized about vertical equilibrium.
In this example, the angle of the vertical pole is the
controlled variable, and the horizontal force applied by the cart is
the actuator input.
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. This system is also naturally
unstable in that it has a free integrator.
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, although the mass of the beam is taken into
account in the fourth order state-space model. The equations are
linearized by assuming small deflections of the cam and beam. This is
an example of a double integrator, which needs to be stabilized.
Ball and Beam
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