| dc.description.abstract | In this thesis adaptive surge control in axial and centrifugal compressor with unknown characteristic was studied.
The compressor to be viewed as the control target, was a part of the compression system which also included the plenum and a throttling device, both located downstream to the compressor.\\
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The literature offers already several research papers dealing with adaptive control of compressors, where the knowledge of the compressor map is not needed in advance.
Summaries of some of the papers has been offered in this thesis.
The author proposed a simplified version of an adaptive controller where the controller gain is being calculated by estimating the compressor characteristic.
The estimation was carried out by using the most basic identification techniques: method of steepest decent and the least-squares.\\
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Both strategies estimated the unknown coefficients of the compressor characteristic by processing input/output data of the latter on-line.
The input signal for the estimation scheme consisted of a flow measurement at the compressor duct while the pressure rise at the compressor would constitute the output signal.
Occasionally, the flow at the compressor duct will be unavailable for measurement.
As a solution, the compression system will was coupled with an observer which predicted the behaviour of the compressor duct flow by considering the model for entire compression system.
The observer originated from \citep{ges_observer} where it has been proven that the flow is being predicted in a exponentially stable manner.
The core of each of the estimation methods was the adaptive law, which will continuously updates the estimates of the unknown coefficients.
The trajectories of the estimates was all said to be bounded functions.
Strictly speaking, they are considered as elements of $\mathcal{L}_\infty$ and $\mathcal{L}_2$ spaces.
This was verified with stability analysis where Lyapunov's direct method was applied.
The stability analysis was previously published in \citep{textbook_adaptiv} and has were included in this report.\\
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Two types of actuators for surge control were considered: closed-coupled valve (CCV) and a piston.
The resulting control law for both actuators was a basic proportional controller which recovered the compression system from surge and bring it towards global asymptotic stability.
The controller operating CCV required feedback from compressor mass flow measurement while the piston was being run by the controller that required feedback from pressure measurements at the compressor discharge and at the plenum.
By assigning the actuator and the controllers, the compressor was brought to global asymptotic stability even if it was operating at the unstable area in the first place.
In the past, the gain for each controller was constructed by the coefficients used to describe the compressor characteristic.
In subject to not knowing the compressor characteristic, the coefficients appearing in the controller would be replaced by their estimates which were generated by the earlier mentioned adaptive laws.
The implementation of the adaptive laws depended on the knowledge of the coordinates of the system equilibrium.
Yet another adaptive law was implemented to estimate the coordinates.
The estimation was needed for equilibrium , since the computation of the latter is restricted to knowing the compressor characteristic.
Linearization of the compression system augmented with the adaptive controller and the equilibrium estimation was used as a tool to demonstrate that under specific conditions the overall systems becomes locally asymptotically stable. | |
