Linearization Command Line Introduction

The command line tools available in Simulink Control Design allow for the programmatic specification of the input and output points for the linearization of a model. Additionally, there are new command line tools to extract and specify operating points for a linearization. This demo introduces some of these commands by linearizing a water-tank feedback control system. An open loop linearized model of the watertank will be extracted at an operating point where the tank level is at H = 10. The following 3 steps linearize and analyze the water-tank model.

Step 1: Configuring Linearization Points

The linearization points specify the inputs and outputs of a linearized model. To extract the open loop linearized model, add an input point at the output of the Controller block and an output point, with a loop opening, at the output of the Water-Tank System block.

% Open the model

watertank
% Specify the input point
watertank_io(1)=linio('watertank/Controller',1,'in');
% Specify the output point with a loop opening
watertank_io(2)=linio('watertank/Water-Tank System',1,'out','on');

You can then set and view the linearization points in the model.

setlinio('watertank',watertank_io);

Step 2: Computing and Specifying Operating Points

This next step involves finding an operating point of the Simulink model 'watertank' so that the level of the tank is at H = 10. One approach is to simulate the model then extract the operating point when the simulation is near the desired value. The command FINDOP will simulate a model and extract the operating points at times defined in the function call.

opsim = findop('watertank',10)
findop: Adding a snapshot block to the model watertank and beginning simulation.
findop: Snapshot block removed and returning snapshot.


 Operating Point for the Model watertank.
 (Time-Varying Components Evaluated at time t=10)

States: 
----------
(1.) watertank/Controller/Integrator
      x: 0.872        
(2.) watertank/Water-Tank System/H
      x: 9.7          
 
Inputs: None

In this operating point, H is not at the desired value of 10, it is at a value of 9.7. However, you can use this operating point to initialize a search for the desired operating point where H = 10. An operating point specification object allows you to specify the desired value of H = 10.

% Create an operating point specification object
opspec = operspec('watertank');
% Create an output specification on the first output of the water tank block
opspec = addoutputspec(opspec,'watertank/Water-Tank System',1);
% Set the specification of H = 10 for the output
opspec.Outputs.Known = 1;
opspec.Outputs.y = 10;
% Initialize the values of the states of the operating point specification
% with the ones in the operating point opsim
opspec = initopspec(opspec,opsim);
% Search for the specified operating point using the FINDOP
% function
opss = findop('watertank',opspec);
 Operating Point Search Report:
---------------------------------

 Operating Point Search Report for the Model watertank.
 (Time-Varying Components Evaluated at time t=0)

Operating condition specifications were successully met.

States: 
----------
(1.) watertank/Controller/Integrator
      x:          1.26      dx:             0 (0)
(2.) watertank/Water-Tank System/H
      x:            10      dx:             0 (0)
 
Inputs: None
 
Outputs: 
-----------
(1.) watertank/Water-Tank System
      y:            10    (10)
 

Step 3: Linearizing and Analyzing the Model

You are now ready to linearize the plant model by using the LINEARIZE function.

sys = linearize('watertank',opss,watertank_io);

The resulting model is a state space object that you can analyze using any of the tools in the Control System Toolbox.

bode(sys);