Linearize Engine Speed Model

This example shows how to linearize an engine speed model for multiple output conditions.

Engine Speed Model

Open the model.

mdl = 'scdspeed';
open_system(mdl)

For this example, you find linear models from the spark advance and throttle angle inputs to the output engine speed. You do so for three speed conditions: 2000, 3000, and 4000 rpm.

Find Operating Points

Create an array of three operating point specifications.

opspec = operspec(mdl,[3 1]);

Since the Simulink® model does not have any root-level inports, opspec does not contain any output specifications. You can add output specifications for a given signal in your model using the addoutputspec function.

Add an output specification to the output of the rad/s to rpm block.

opspec = addoutputspec(opspec,'scdspeed/rad//s to rpm',1);

For each specification, indicate that the output value is known and specify the output value. Set the known speed values to 2000, 3000, and 4000 rpm.

opspec(1).Outputs.Known = 1;
opspec(1).Outputs.y = 2000;
opspec(2).Outputs.Known = 1;
opspec(2).Outputs.y = 3000;
opspec(3).Outputs.Known = 1;
opspec(3).Outputs.y = 4000;

View the specifications object for the third operating condition.

opspec(3)

ans = 


 Operating point specification for the Model scdspeed.
 (Time-Varying Components Evaluated at time t=0)

States: 
----------
     x         Known    SteadyState     Min         Max        dxMin       dxMax   
___________ ___________ ___________ ___________ ___________ ___________ ___________
                                                                                   
(1.) scdspeed/Throttle & Manifold/Intake Manifold/p0 = 0.543 bar
   0.543       false       true        -Inf         Inf        -Inf         Inf    
(2.) scdspeed/Vehicle Dynamics/w = T//J w0 = 209 rad//s
  209.48       false       true        -Inf         Inf        -Inf         Inf    

Inputs: 
----------
  u   Known  Min   Max 
_____ _____ _____ _____
                       
(1.) scdspeed/Throttle  perturbation
  0   false -Inf   Inf 

Outputs: 
----------
  y   Known  Min   Max 
_____ _____ _____ _____
                       
(1.) scdspeed/rad//s to rpm
4000  true  -Inf   Inf 

Search for operating points that meet these specifications using the findop function.

opt = findopOptions('DisplayReport','off');
op = findop(mdl,opspec,opt);

View the resulting operating point for the third operating condition.

op(3)

ans = 


 Operating point for the Model scdspeed.
 (Time-Varying Components Evaluated at time t=0)

States: 
----------
   x   
_______
       
(1.) scdspeed/Throttle & Manifold/Intake Manifold/p0 = 0.543 bar
0.4731 
(2.) scdspeed/Vehicle Dynamics/w = T//J w0 = 209 rad//s
418.879

Inputs: 
----------
  u   
______
      
(1.) scdspeed/Throttle  perturbation
5.8292

Linearize Model

To linearize the model, first specify the linearization input points at the outputs of the throttle and Spark Advance blocks.

io(1) = linio('scdspeed/throttle (degrees)',1,'input');
io(2) = linio('scdspeed/Spark Advance',1,'input');

Next, specify the linearization output point at the output of the rad/s to rpm block.

io(3) = linio('scdspeed/rad//s to rpm',1,'output');

Linearize the model for each of the operating conditions.

sys = linearize(mdl,op,io);

Plot the Bode magnitude response for the resulting linear models.

bodemag(sys)

Close the model.

bdclose(mdl)