The dimensionless representation minimizes the number of parameters necessary for the system description, and may provide further knowledge of the parameters influence on the dynamical response. Furthermore, the number of dimensionless numbers is a measure of the complexity of the problem at hand. Henceforth, the dimensionless representation may provide a system complexity characterization that is different from mere system order.

Chapter Contents:

• 3.1 Introduction
• 3.2 Transfer function dimensionless representation
• 3.2.1 Transfer function parameters dimensions
• 3.2.2 Transfer function parameters with independent dimensions
• 3.2.3 Transfer function dimensionless numbers
• 3.2.4 Dimensionless transfer function
• 3.3 State space dimensionless representation
• 3.3.1 Interpretation of the state space dimensionless transformation
• 3.4 Comparison between transfer function and state space dimensionless representation
• 3.5 Discrete time models dimensionless representation
• 3.5.1 Discrete time transfer function dimensionless representation
• 3.5.2 Discrete time state space model dimensionless representation
• 3.6 Exercises
• References

Inspec keywords: minimisation; transfer functions

Other keywords: dynamical response; dynamical systems; dimensionless numbers; system complexity characterization; system description; problem complexity; dimensionless representation; system order

Subjects: Control system analysis and synthesis methods; Optimisation techniques