Active surge control of centrifugal compression systems : Theoretical and experimental results of drive actuation (2007)

This thesis addresses modeling and active surge control of a simple compression system, using only the drive system of the compressor for actuation. Theoretical results are validated by experiments on a test rig that was built as a part of this work. Control laws are derived in two stages. First all system states, such as pressure mass flow and impeller speed, are assumed as available signals. All the resulting control laws require feedback from mass flow. However, transient measurement of this variable is not available. Observers are therefore developed for this purpose.\n\nThe laboratory that was build and from which experimental data are gathered, consists of a compressor, plenum volume, control valve, in between ducting and drive system. The centrifugal compressor stage compresses air from ambient conditions, discharging into a duct connecting compressor and plenum. The plenum discharges over the valve. The drive system consists of a electric motor and drive.\n\nControllers and observers are derived on the basis of the so-called variable speed Greitzer model. This model contains the compressor map, which in many cases involves some uncertainty. Uncertainty can be caused by varying ambient conditions and change of map due to wear and tear. For this reason it was investigated whether it was possible to express the compressor map by measurements. It is shown that this can be done if one has a sufficient length of duct upstream or downstream the compressor.\n\nTwo control strategies are presented. One considers the impeller speed and the other considers applied torque as control variable. As previously mentioned, all control laws require feedback from mass flow, and must be combined with an observer for implementation. Furthermore, torque control laws involve the compressor map. In view of modeling results, this map can be implemented by a model or a measurement in the case of sufficient duct lengths. Experimental validation of control laws indicate that torque control is better than speed control for the setup in question, in terms of it ability to stabilize surge. The reason for this can be explained by the internal loop of the drive system, o¤ering a faster response for torque than for speed control. It is shown by experiments that torque control can extend mass flow range of the machine by more than 15 to 20 percent relative to the point for which surge occurs for the open loop system. These numbers corresponds to two di¤erent impeller speeds, where 20 percent increase was achieved at a lower impeller speed than that of 15 percent. It is also shown experimentally that speed control is able to stabilize a operating point for which surge occurs for the open loop. However, this strategy was not able to considerably increase the operating range\n\nThree type of observes are derived. These are reduced order observers for mass flow, pressure and mass flow observers, and pressure, mass flow and impeller speed observers. Furthermore, the observers vary among themselves in the way one compensates for the compressor map, model or measurement. The main purpose of these observes is to o¤er a estimate of mass flow, so that the derived control laws can be implemented. However, these observers can also o¤er disturbance rejection for pressure and impeller speed measurements. Reduced order observers for mass flow and observers for pressure and mass flow are validated experimentally. It is shown that the mass flow estimates are within an accuracy of 10 percent compared to measured mass flow, and that the pressure estimates offers disturbance rejection. The observers are derived on the basis of the compression system model, not taking the specific control law into account, and can therefore be used for any control law derived on the basis of the Greitzer model.\n\nContributions in work leading to this thesis are considered to be: \n\n- Planning and building of a compression system laboratory for active surge control by means of drive system.\n\n- Extending the Greitzer model by introducing a measurement for the compressor map. Theoretical derivation and experimental validation.\n\n- Extending a previously presented active surge control law, when considering impeller speed as control variable. Theoretical derivation, stability analysis and experimental validation.\n\n- Deriving novel control laws for active surge control when considering impeller drive torque as control variable. Theoretical derivation, stability analysis and experimental validation.\n\n- Deriving novel observers for variable speed Greitzer model. Theoretical derivation, stability analysis and experimental validation.\n\nThe work contained in this thesis has partially been published in six papers:\n\n- Bøhagen B. and J.T. Gravdahl, Control laws for active surge control of centrifugal compressors using drive torque, accepted for publication in Automatica, May 2007\n\n-Bøhagen B. and J.T. Gravdahl, Circle criterion observer for a compression system, to appear in Proceedings of the 2007 American Control Conference, New York, July 2007\n\n- Bøhagen B. and J.T. Gravdahl, Active surge control using drive torque: dynamic control laws, Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, December 2006\n\n- Bøhagen B. and J.T. Gravdahl, Active control of compression systems using drive torque; a backstepping approach, Proceedings of the 44th\n\nIEEE Conference on Decision and Control, Seville, December 2005\n\n- Bøhagen, B., O. Stene and J.T. Gravdahl, A GES mass flow observer for compression systems: Design and experiments, Proceedings of the 2004 American Control Conference, Boston, June 2004\n\n- Bøhagen, B. and J.T. Gravdahl, On active surge control of compressors using a mass flow observer, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, December 2002