Nonlinear Control Design Blockset

Noise Inputs

No noise should be included in the Simulink model during optimization. Including noise in the system while optimizing effectively introduces inconsistency into the problem formulation and may cause the optimization to converge more slowly or even fail to converge altogether. Modern control theory techniques often define noise terms in their problem formulation as approximations to plant, actuator, or sensor uncertainty. In other cases, modern control theory effectively uses the noise covariance matrices as tweakable design handles. Using the Nonlinear Control Design Blockset, you can design controllers while directly incorporating uncertainty into plant, actuator, or sensor dynamics by using the Uncertain Variables dialog box. Instead of framing your control design in terms of minimizing various norms of weighted transfer functions, and tuning your response by tweaking the weights, the Nonlinear Control Design Blockset uses the time domain constraint bound paradigm.

Of course, noisy measurements do exist in the real world, and you must take such noise into consideration when you do your design. In the general case, you should simply inspect the system performance with noise added after optimizing. If you must include noise in your system during optimization, follow these suggestions:

• For continuous systems, use the Band Limited White Noise block (found in the Simulink sources library), a fixed time step integration (set the minimum and maximum time step to be equal), and a constant seed for the noise.
• For discrete systems, use the White Noise block (found in the Simulink Sources library) with a constant seed for the noise.

Increasing the noise in a system often forces you to design more conservative control to maintain system stability. If including noise in your system produces unacceptable instability, consider changing your Nonlinear Control Design Blockset constraint bounds to allow less overshoot and longer rise times and settling times. If this results in unacceptable system performance, consider options that decrease sensor noise.

Minimizing Integrated Positive Signals (Control Energy)

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