Introduction to Uncertain Elements

Uncertain elements (also called uncertain Control Design Blocks) are the building blocks used to form uncertain matrix objects and uncertain system objects. There are six types of uncertain blocks, summarized in the following table.

Function	Description
ureal	Uncertain real parameter
ultidyn	Uncertain, linear, time-invariant dynamics
umargin	Uncertain gain and phase
ucomplex	Uncertain complex parameter
ucomplexm	Uncertain complex matrix
udyn	Unmodeled dynamics

To build models uncertain systems, you combine these control design blocks with fixed dynamic elements to create uncertain state-space (uss) models.

All of the elements have properties, which are accessed through get and set methods. This get and set interface mimics the Control System Toolbox™ and MATLAB^® Handle Graphics^® behavior. For instance, get(a,'PropertyName') is the same as a.PropertyName, and set(b,'PropertyName',Value) is the same as b.PropertyName = value. Functionality also includes tab-completion and case-insensitive, partial name property matching.

For ureal, ucomplex and ucomplexm elements, the syntax is

p1 = ureal(name,NominalValue,Prop1,val1,Prop2,val2,...); 
p2 = ucomplex(name,NominalValue,Prop1,val1,Prop2,val2,...); 
p3 = ucomplexm(name,NominalValue,Prop1,val1,Prop2,val2,...); 

For ultidyn and udyn, the NominalValue is fixed, so the syntax is

p4 = ultidyn(name,ioSize,Prop1,val1,Prop2,val2,...); 
p5 = udyn(name,ioSize,Prop1,val1,Prop2,val2,...); 

For umargin blocks, you provide the range of gain variation you want to model. umargin interprets this range as a disk-based gain margin. To get a disk-based gain margin from a target gain and phase variation, use getDGM.

DGM = getDGM(GM,PM,'balanced);
p6 = umargin(name,DGM,Prop1,val1,...);

For ureal, ultidyn, umargin, ucomplex and ucomplexm elements, the command usample will generate a random instance (i.e., not uncertain) of the element, within its modeled range. For example,

usample(p1) 

creates a random instance of the uncertain real parameter p1. With an integer argument, whole arrays of instances can be created. For instance

usample(p4,100) 

generates an array of 100 instances of the ultidyn object p4. See Generate Samples of Uncertain Systems to learn more about usample.