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    %% Creating Uncertain Parameters
% An uncertain parameter has a name (used to identify it within an
% uncertain system with many uncertain parameters) and a nominal value.
% Being uncertain, it also has variability, described in one of the
% following ways:
%%
% 
% * An additive deviation from the nominal
% * A range about the nominal
% * A percentage deviation from the nominal
% 
%%
% Create a real parameter, with name '|bw|', nominal
% value 5, and a percentage uncertainty of 10%.

% Copyright 2015 The MathWorks, Inc.

bw = ureal('bw',5,'Percentage',10)
%% 
% This command creates a |ureal| object that stores a number of parameters
% in its properties.  View the properties of |bw|.
get(bw)
%%
% Note that the range of variation (|Range| property)
% and the additive deviation from nominal (the |PlusMinus| property)
% are consistent with the |Percentage| property value.
% 
% You can create state-space and transfer function models with uncertain
% real coefficients using |ureal| objects. The result is an
% uncertain state-space (|uss|) object. As an example, use the uncertain real parameter
% |bw| to model a first-order system whose bandwidth is between 4.5 and 5.5
% rad/s.
H = tf(1,[1/bw 1])
%% 
% Note that the result |H| is an uncertain system,
% called a |uss| model. The nominal
% value of |H| is a state-space (|ss|) model. Verify that
% the pole is at -5, as expected from the uncertain parameter's nominal value of 5.
pole(H.NominalValue)
%%
% Next, use |bodeplot| and |stepplot| to examine
% the behavior of |H|. These commands plot the responses
% of the nominal system and a number of random samples of the uncertain system.
bodeplot(H,{1e-1 1e2});
%%  
stepplot(H)
%%
% While there are variations in the bandwidth and time constant of |H|, the
% high-frequency rolls off at 20 dB/decade regardless of the value of |bw|.
% You can capture the more complicated uncertain behavior that typically
% occurs at high frequencies using the |ultidyn| uncertain element.