CtrlGauss Module 1

Transformation and Analysis module for GAUSS

CtrlGauss provides the tools to analyze and design control systems.

"Classical" transfer function and "modern" state-space representations, both continuous and discrete.
Frequency domain design, continuous and discrete, using Nichols, Nyquist, Bode and Root Locus.
Building systems and simulation functions.

SYSTEM MATRIX

CtrlGauss supports three model representations in both continuous and discrete forms:

State-Space
Transfer Function
Pole-Zero-Gain

In CtrlGauss each model is stored in a single system matrix. Because all the information about the system, including whether it is continuous or discrete, is stored in a single matrix, system models in CtrlGauss are easier to handle and keep track of. Also CtrlGauss can do more checking in its functions so you are less likely to produce incorrect results. The following functions are provided to manipulate system matrices:

DISPSYS         display system components
EDITSYS         create or edit a system
IOSEL           select input/output pairs
SYSIO           number of system inputs and outputs
SYSTs           system sampling period
SYSTYPE         type of system, SS, TF or PZ

MODEL CONVERSIONS

Model representations are automatically converted by CtrlGauss to the form required by the function, usually state-space form. The following functions are provided to force explicit conversions:

To convert to and from discrete forms

CtoD            continuous to discrete
DtoC            discrete to continuous

To convert between system representations

SStoSYS         state-space to system matrix
TFtoSYS         transfer function to system matrix
PZtoSYS         pole-zero-gain to system matrix
SYStoSS         system matrix to state-space
SYStoTF         system matrix to transfer function
SYStoPZ         system matrix to pole-zero-gain

CtrlGauss also provides two functions to convert from natural frequencies and damping to and from zeros for both continuous and discrete forms.

WNDtoZ          natural freq. and damping to zeros
ZtoWND          zeros to natural freq. and dampings

MODEL BUILDING

The model building functions allow you to combine model blocks into larger systems. The model building functions are:

UNFBSYS         unity negative feedback
NFBSYS          negative feedback
FBSYS           positive feedback
COMBSYS         combine two systems
PARSYS          parallel two systems
SERSYS          series two systems
SUMSYS          sum the outputs of two systems
SYSBUILD        general interconnection of blocks

SYSBUILD accepts a matrix of block names, finds the blocks and combines them in the manner specified. Special attention is given to pure gain blocks to ensure no extra unnecessary states are included in the final system.

SYSTEM RESPONSES

The following functions are provided by CtrlGauss to generate the root loci, frequency, time, singular value and eigenvalue responses of systems:

SYStoRL         root locus response
SYStoFR         frequency response
SYStoTR         impulse time response
SYStoSTP        step response
SIMSYS          general time response
SYStoSVD        singular value response
SYStoEV         eigenvalue response

These functions provide for automatic selection of gain, frequency and time points so that you can quickly and easily generate a representative response. The results can then be plotted using the enhanced plotting functions provided by CtrlGauss

PLOTTING FUNCTIONS

CtrlGauss provides the following plotting functions:

RTLOCUS         root locus plot
BODE            bode plot
NICHOLS         nichols plot
NYQUIST         nyquist plot
PHFIX           unwrap phase response

By default RTLOCUS, NICHOLS and NYQUIST mark gain/frequency information on the plot. A grid of M- and N-circles or natural frequencies and damping can also be added. These functions can be combined with GAUSS' windowing graphics for professional results.

PHFIX allows you to correct for jumps in the phase plot and also to set the starting phase quadrant of the plot.

NON-LINEAR SYSTEMS

For non-linear systems CtrlGauss can be combined with Forward Software's non-linear simulation module, SimGauss. SimGauss can integrate state vectors as easily as scalars. It provides functions to linearize the system at the current operating point. CtrlGauss can then be used to analyze the system and design a controller. Implementing the controller in SimGauss is as easy as writing.

        d_x     =       Ax + Bu
        y       =       Cx + Du

Stefan Steinhaus, webmaster@steinhaus-net.de