Abstract
This paper investigates the application of adaptive slope-seeking strategies to dual-input single output dynamic processes. While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal). Moreover, the consideration of more than one input signal allows minimizing the input energy thanks to the degrees of freedom offered by the additional inputs. The actual process is assumed to be locally approachable by a Hammerstein model, combining a nonlinear static map with a linear dynamic model. The proposed strategy is based on the interplay of three components: (i) a recursive estimation algorithm providing the model parameters and the performance index gradient, (ii) a slope generator using the static map parameter estimates to convert the performance index setpoint into slope setpoints, and (iii) an adaptive controller driving the process to the desired setpoint. The performance of the slope strategy is assessed in simulation in an application example related to lipid productivity optimization in continuous cultures of micro-algae by acting on both the incident light intensity and the dilution rate. It is also validated in experimental studies where biomass production in a continuous photo-bioreactor is targeted.
Highlights
Extremum Seeking Control (ESC) is a Real-Time Optimization (RTO) technique used to drive a measurable process performance index to its optimum following direct input adaptation [1]
The control strategy is built upon the assumption that the process can be described by a block-oriented model, which is made of the interconnection of nonlinear static building blocks and linear time-invariant dynamic building blocks
Microalgae growth in a bioreactor can be described by the Droop model [37], which assumes that extracellular nutrient S is stored in a so-called internal quota Q, before being used for biomass X growth
Summary
Extremum Seeking Control (ESC) is a Real-Time Optimization (RTO) technique used to drive a measurable process performance index to its optimum following direct input adaptation [1]. In [13], an extended Kalman filter is used to estimate the gradient and Hessian of a static quadratic dual-input–single-output (DISO) map to remove thermo-acoustic instabilities in an atmospheric combustor test rig In applications such as PV panels or wind turbine power generation, it is sometimes required to operate at a given sub-optimal operating point so as to adjust the production to the actual load/demand.
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