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    %% Control System Modeling with Model Objects
% Model objects can represent individual components of a control
% architecture, such as the plant, actuators, sensors, or controllers. You
% can connect model objects to build aggregate models of block diagrams
% that represent the combined response of multiple elements.
%%
% For example, the following control system contains a prefilter _F_,
% a plant _G_, and a controller _C_, arranged in a single-loop configuration. 
% The model also includes a representation of sensor dynamics, _S_.
%%
% 
% <<../architecture.png>>
% 
%%
% You can represent each of the components as a model object. You do not
% need to use the same type of model object for each component. For
% example, represent the plant _G_ as a zero-pole-gain (|zpk|) model with a
% double pole at |s| =  -1; _C_ as a PID controller, and _F_ and _S_ as
% transfer functions:

% Copyright 2015 The MathWorks, Inc.

G = zpk([],[-1,-1],1);
C = pid(2,1.3,0.3,0.5);
S = tf(5,[1 4]);
F = tf(1,[1 1]);
%% 
% You can then combine these elements build models that represent your
% control system or the control system as a whole. For example, create the
% open-loop response _SGC_:
open_loop = S*G*C;
%%
% To build a model of the unfiltered closed-loop response, use the 
% |feedback| command:
T = feedback(G*C,S);
%%
% To model the entire closed-loop system response from _r_ to _y_,
% combine _T_ with the filter transfer function:
Try = T*F;
%%
% The results |open_loop|, |T|, and |Try| are also linear model objects.
% You can operate on them with Control System Toolbox(TM) control
% design and analysis commands. For example, plot the step response
% of the entire system:
stepplot(Try)
%%
% When you combine Numeric LTI models, the resulting Numeric LTI model
% represents the aggregate system. The resulting model does not retain the
% original data from the combined components. For example, |T| does not
% separately keep track of the dynamics of the components
% |G|, |C|, and |S| that are combined to create |T|.