A proportional-integral (PI) controller:
A proportional-derivative (PD) controller:
A function to construct a proportional-integral-derivative (PID) controller:
A PID with specific gain values:
A function to construct a discrete-time PID controller:
A function for a continuous-time lead compensator:
A lead compensator for specific values of gain and pole-zero locations:
A function for a continuous-time lag compensator:
A specific lag compensator:
A digital lag compensator defined in terms of its zero and pole locations:
A general formula for analog low-pass Butterworth filters:
Filters of specific orders:
A third-order Bessel filter:
The general second-order transfer function:
Variations in damping ratio lead to qualitatively different responses:
A linearized inverted pendulum model:
A spring-mass-damper system:
Transfer function between the input voltage and the shaft angular position of a DC motor:
The aileron to roll-rate transfer function of an aircraft:
A temperature-controlled chemical reactor:
An RLC circuit:
A MIMO transfer function describing an aircraft's longitudinal dynamics:
for continuous-time systems and 
for discrete-time systems.
num must be a polynomial matrix and den can be specified as a polynomial matrix or just the common denominator polynomial.
:
:
Options (4)
pole-zero pairs may cancel before being processed by TransferFunctionModel:
:
only prevent pole-zero cancellations:
might result in a system with higher order:
for continuous-time systems:
:
:
EXAMPLES
Basic Examples 
