Step 1: Configuring Linearization Points

Open the model.

watertank

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.

Specify the input point.

watertank_io(1)=linio('watertank/PID Controller',1,'input');

Specify the output point with a loop opening.

watertank_io(2)=linio('watertank/Water-Tank System',1,'openoutput');

The linearization points can then be set and viewed in the model.

setlinio('watertank',watertank_io);
watertank

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)

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

States: 
----------
(1.) watertank/PID Controller/Integrator/Continuous/Integrator
      x: 1.69         
(2.) watertank/Water-Tank System/H
      x: 10.1         

Inputs: None 
----------

In this operating point, H is not at the desired value of 10. 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');

Initialize the values of the states of the operating point specification with the ones in the operating point opsim.

opspec = initopspec(opspec,opsim);

The specified operating point can then be searched for (trimmed) using the FINDOP command.

opss = findop('watertank',opspec);

 Operating point search report:
---------------------------------

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

Operating point specifications were successfully met.
States: 
----------
(1.) watertank/PID Controller/Integrator/Continuous/Integrator
      x:          1.26      dx:             0 (0)
(2.) watertank/Water-Tank System/H
      x:            10      dx:      -1.1e-14 (0)

Inputs: None 
----------

Outputs: None 
----------

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 software.

bode(sys);

Close the Simulink model.

bdclose('watertank')