Nonlinear Control Design Blockset

Running the Optimization

After adjusting the constraints and defining tunable variables, start the optimization by clicking the Start button on the Nonlinear Control Design Blockset control panel or by selecting Start from the Optimization menu. For the problem posed above, a PC running Windows NT 4.0 outputs the following.

Because of different numerical precision, the results of the optimization may differ slightly across different platforms. The constraint figures on the next page show the initial and final response plots for the cart position and pendulum angle error signals.

You may want to investigate how incorporating noise into the observed data affects the optimization. To do this simply:

• Reinitialize the tunable variables to their initial values.

• m = 0.21;
  l = 0.61/2;
  

• Add random noise to the observed data vectors.

• yHat = yHat + 0.001*rand(size(yHat));
  ThetaHat = Thetahat + 0.001*rand(size(ThetaHat));
  

• Restart the optimization.

The optimization still converges to the known solution, but it takes more iterations to do so.

Due to the design of the experiment, you know that the solution mass and length are larger than the initial mass and length (re: a clay ball is stuck to the end of the pendulum). Thus, you can constrain the lower bounds of the tunable parameters using the Tunable Parameters dialog box. In general, add such constraints whenever possible since the added information allows the optimization to make better decisions about how to search the parameter space.

Adjusting Constraints

Solving the Optimization Problem