Snapshot of the front panel of the simulator:
Description of the simulated system
In this simulator a general integrator is simulated. You can
freely adjust the input signal u(t) and the gain of the integrator, K.
The relation between the input signal u and the output signal y can be
expressed with the following integral equation:
This integral equation is equivalent with the following
dy(t)/dt = Ku(t)
The transfer function of the integrator is
h(s) = y(s)/u(s) = K/s
The simulator is based on discretizing the integrator with the Runge-Kutta second-order method with
time-step of 0.05 sec.
The aims of the simulator is to give insight into the dynamic behaviour of an
There are many dynamic systems with interating behaviour, e.g.:
- Liquid tanks where the outflow is level is independent of the level,
as if the outflow is produced by a pump. In such a system the pump
control signal can be the input variable and the level is the output
variable of the integrator.
- Thermal systems without heat loss to the environment. The iInput
variable is heat supply (via a heatring element), and the output
variable is the temperature.
- A motor having neglectable (or very quick) dynamics. The input
variable is the motor control signal, and the output variable is the
motor rotational position.
- The integrator-term of a PID-controller. The input variable is the
control error, and the output variable is the integrator term, ui.
Below, U is the amplitude of the input step, and K
is the gain of the integrator.
- The shape of the step response:
Set K = 1. Simulate with an input step amplitude of U = 1.
Characterize the shape of the step response.
- The importance of the gain K:
Simulate with input step amplitude U = 1 for
different values of K, both positive and negative. How does the slope
of the step response depend on K?
- The integrator effect: Simulate
while adjusting the input u(t). Do you see that the integrator actually
("stores") the input?
Updated 23. January 2008.