real solutions to real problems using real tools
home page about products contact

QFT Frequency Domain Control Design Toolbox - Applications

For feedback design, QFT methodology fits a wide range of applications:

Plant Uncertainty
The controller should meet specifications despite variations in the parameters of the plant model. For example, in a car's CD player, the first mode's natural frequency may vary by 15% due to temperature changes. QFT will work directly with such uncertainties and does not require any particular representation.

Experimentally Derived Plant Models
Many systems have complex dynamics, which can be very difficult to model analytically. For example, the dynamics of the radial loop in a compact disk or a disk drive mechanism contain a large number of mechanical resonances. Even a detailed finite-element analysis cannot generate a reasonable model for control design with such tight specifications. A common approach to this problem is to run several physical experiments and then to either identify a transfer function for each input/output time series, or perform QFT design using the frequency response measurements. If the identification process is repeated under different operating conditions, the resulting set of transfer functions may not necessarily have the same order of numerators and denominators. QFT works with such systems.

Linear Plants from Nonlinear Dynamics
Often, nonlinear plant dynamics are approximated using linearization. For example, a missile operating over a large flight envelope is typically represented by a set of rational transfer functions derived at several altitude/Mach number operating points. QFT works with such sets, and allows you to design a single controller for the whole set of transfer functions.

Multiple Performance Specifications
This type of design problem consists of several closed-loop performance specifications, where the objective is to synthesize a controller to meet all specifications simultaneously (a robust performance problem). The QFT bounds reveal the precise nature of the tradeoffs between the specification. Also, specifications are often incomplete, e.g., in a noise control system, noise reduction should be at least 24dB in the range 1 00–500 Hz. QFT works with such incomplete forms and does not require specifications to be defined at each frequency from zero to infinity.

Hardware Constraints
The complexity and bandwidth of real-world controllers are constrained by hardware. QFT allows you to determine quickly if a simple controller, such as a proportional or PI, can provide satisfactory performance despite hardware constraints.