Technical Report 2015-013

Constraints in nonlinear L2-stable networked control

Torbjörn Wigren

May 2015

The report derives a robust networked controller design method for systems with saturation where the delay is large and unknown, as in unidirectional flow-control. A classical linear robust criterion is first formulated in terms of the sensitivity- and complementary sensitivity functions. Based on the Popov-criterion a new asymptotic constraint is derived, which specifies the minimum amount of low frequency gain in the sensitivity function, to guarantee non-linear closed loop L2-stability. This result guides the selection of the design criterion, thereby adjusting the linear controller design for better handling of delay and saturation. The controller design method then uses gridding to pre-compute the L2 stability region. Based on the pre-computed stability region, a robust L2-stable controller can be selected. Alternatively, an adaptive controller could recompute L2-stable controllers on-line using the pre-computed stability region. Simulations show that the controller meets the specified stability and performance requirements.

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