WO2025202046A1

WO2025202046A1 - Nonlinear model predictive anti-surge control of a centrifugal compressor

Info

Publication number: WO2025202046A1
Application number: PCT/EP2025/057753
Authority: WO
Inventors: Marta FIORUCCI; Giovanni De Magistris; Guido SCHILLACI; Luigi Bono BONACCHI
Original assignee: Nuovo Pignone Technologie SRL
Current assignee: Nuovo Pignone Technologie SRL
Priority date: 2024-03-25
Filing date: 2025-03-21
Publication date: 2025-10-02
Anticipated expiration: 2026-09-25

Abstract

An innovative compressor plant (1000) includes a compressor system (100) and a control unit (200); the compressor system (100) comprises: a compressor (10), an electric motor (20) driving in rotation the compressor (10), an anti-surge valve (30) fluidly coupling an inlet and an outlet of the compressor (10), and a measuring arrangement (40); the control unit (200) is configured to perform nonlinear model predictive control of the anti-surge valve (30) based on measurements carried out by the measuring arrangement (40); the model is based on a plurality of state variables corresponding to physical quantities of the compressor system (100) and is supplemented by a first virtual valve (300) and/or a second virtual valve (400), the opening level of the virtual valves being supplemental state variables of the model.

Description

TITLE

NONLINEAR MODEL PREDICTIVE ANTI-SURGE CONTROL OF A CENTRIFUGAL COMPRESSOR

DESCRIPTION

TECHNICAL FIELD

[0001] The subject matter disclosed herein relates to methods for performing control of an anti-surge valve in a compressor system and compressor plants implementing innovative methods.

BACKGROUND ART

[0002] Model Predictive Control (= MPC) is now-a-days well known and quite popular in different fields of technology; for a detailed disclosure of MPC reference may be made for example to the book by E. F. Camacho and C. Bordons entitled “Model Predictive Control” published by Springer-Verlag in 1999. Historically, MPC has been implemented by using a linear model of the system to be controlled. At present, Nonlinear Model Predictive Control (= NMPC) is gaining more and more attention even if industrial implementation of NMPC is more difficult and more critical. The above mentioned book, that is a bit old, dedicates only one chapter to NMPC. But there are more recent books on this topic, for example the book by L. Gruene and J. Panneck entitled “Nonlinear Model Predictive Control - Theory and Algoritms” published by Springer-Verlag in 2011.

[0003] MPC has already been suggested for anti-surge control of compressors (see e.g. the article by A. Cortinovis et al. entitled “Model Predictive AntiSurge Control of Centrifugal Compressors with Variable-Speed Drives”). Also NMPC has already been suggested for anti-surge control of compressors (see e.g. the article by M. T. Ziabari et al. entitled “Surge Control in Constant Speed Centrifugal Compressors Using Nonlinear Model Predictive Control”).

Moreover NMPC has already has been suggested for evaluation of an antisurge control (see e.g. the article by Silva Dario Eler et al. entitled “Evaluation of an Antisurge Control through Nonlinear Model Predective Controller”).

[0004] NMPC requires a nonlinear model of the system to be controlled that is expected to represent the system more accurately than a linear model in a wider range of condition. In order to achieve high accuracy, and therefore optimal control, the nonlinear model must be very complex. In any case, even if a very complex nonlinear model is used for performing control, it is inevitable that non-measurable disturbances, such as noise or unexpected events, act on the system under control and makes the control non-optimal.

SUMMARY

[0005] Therefore, it would be desirable to provide anti-surge control methods that cope with disturbances in an easy way and that implement or are suitable to implement nonlinear models of the systems to be controlled, in particular compressors, more in particular centrifugal compressors.

[0006] According to a first aspect, the subject matter disclosed herein relates to an innovative method for performing control of an anti-surge valve in a compressor system, the control being predictive and based on a physical nonlinear model of the compressor system, i.e. it is NMPC type. The model is based on a plurality of state variables, but only some of these state variables correspond to physical quantities of said compressor system.

[0007] According to some embodiments of the innovative method, others (preferably one or two) of these state variables correspond to non-measurable disturbances acting on the compressor system. [0008] According to some embodiments of the innovative method, others (preferably one or two) of these state variables correspond to opening levels of virtual valves, i.e. valves that are not included in the compressor system but are added to the model only for the purpose of control calculation, virtually coupled to an inlet or an outlet of the compressor system.

[0009] According to a second aspect, the subject matter disclosed herein relates to an innovative compressor plant comprising a compressor system and a control unit; the compressor system comprises: a compressor, an electric motor driving in rotation the compressor, an anti-surge valve fluidly coupling an inlet and an outlet of the compressor, and a measuring arrangement; the control unit is configured to control opening/closing of the anti-surge valve based on measurements carried out by the measuring arrangement; furthermore, the control unit is configured to carry out any embodiment of the innovative method as disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS.

[0010] A more complete appreciation of the disclosed embodiments of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

Fig. 1 shows a block diagram of an embodiment an innovative compressor plant, and

Fig. 2 shows a block diagram of an embodiment of an control unit in the innovative compressor plant of Fig. 1.

DETAILED DESCRIPTION OF EMBODIMENTS

[0011] Surge is a highly undesirable and harmful phenomenon that occurs in a centrifugal compressor at certain operating conditions. Such conditions may be shown for example in plane wherein the X-axis corresponds to the so-called “corrected flow” and the Y-axis corresponds to the “actual pressure ratio”; in such plane, the surge conditions correspond to an area delimited by a so-called “surge limit line”. An anti-surge control is a system coupled to a compressor that tries to avoid that the compressor operates in such conditions. To be more precise, the anti-surge control tries to avoid that the operating point of the compressor moves from an area of regular operation to an area of surge operation; the anti-surge control has often also the task to move back the operating point of the compressor from the surge area to the regular area if surge is detected. Typically, the anti-surge control determines repeatedly the operating point of the compressor and calculates the distance of the determined operating point from the “surge limit line”; if such distance exceeds a predetermined threshold it takes some action.

[0012] According to the subject matter disclosed herein, the only action taken by the anti-surge control is to change the opening/closing level of a so-called “anti-surge valve”. As well known, an anti-surge valve is a valve that is configured to fluidly couple in a controlled manner the outlet of the compressor to the inlet of the compressor. According to the simplest possibility, such valve is either completely open (i.e. the opening level corresponds to full flow across the valve) or completely closed (i.e. the opening level corresponds to no flow across the valve).

[0013] In MPC, including NMPC, control is predictive and is based on a physical model of the system; in the case of NMPC, the model is nonlinear; the model is based on a plurality of state variables. According to the prior art, the state variables corresponds to physical quantities in the system. According to the subject matter disclosed herein, there is at least another (preferably other two) state variable that does not correspond to a physical quantity in the system; as it will be better explained in the following, such supplemental state variable does not derive from a more accurate physical model but from the wish to take into account phenomena that are not fully explainable or predictable that may be considered unmeasurable disturbances acting on the compressor system. In any case, according to the subject matter disclosed herein, it may be said that the model of the system is supplemented.

[0014] Considering for example Fig. 1, a compressor system 100 (within e.g. a “compressor plant” 1000), including a compressor 10, is supplemented by a first valve 300 and a second valve 400. These valves 300 and 400 are represented by dashed lines in Fig. 1 as they are not physically present in the system so that they may be called “virtual valve” and considered only for the purpose of anti-surge control. In particular, the first virtual valve 300 is coupled to an inlet 13 of the compressor 10 and the second virtual valve 400 is coupled to an outlet 14 of the compressor 10. According to the embodiment of Fig. 1 (or similar embodiments), thanks to virtual valves 300 and 400 it is possible to take into account quite well most (if not all) of the disturbances acting on the compressor system 100.

[0015] The compressor plant 1000 in Fig. 1 includes at least the compressor system 100 and a control unit 200. Furthermore, there is a measuring arrangement 40 that may be considered part of the compressor system 100 (as it is typically integrated into the system) and that carries out measurements in the compressor system 100; it may include several sensors and/or detectors as well as an electronic unit coupled to these sensors and/or detectors in order to collect and process signals and/or data coming therefrom; according to the embodiment of Fig. 1, the measuring arrangement 40 sends signals and/or data to the control unit 200. Typically, an innovative compressor plant includes other components that are not shown in Fig. 1 for the sake of simplicity of this figure.

[0016] The compressor system 100 comprises (at least) a compressor 10, an electric motor 20 driving in rotation the compressor 10, and an anti-surge valve 30 fluidly coupling an inlet and an outlet of the compressor 10, as well as typically other components. The anti-surge valve 30 is a controlled valve, i.e. its opening level (or equivalently its closing level) is controlled through e.g. an electric signal 31; according to the embodiment of Fig. 1, the signal 31 is output from the control unit 200; more specifically, the control unit 200 is configured to control opening/closing of the anti-surge valve 30 based on measurements carried out by the measuring arrangement 40; how control is performed will be explained later.

[0017] The control unit 200 in Fig. 2 is an embodiment of a Nonlinear Model Predictive Controller (= NMPC) consisting essentially of an observer 210 and a controller 220. Signals and/or data from the measurement arrangement 40 are received and processed by the observer 210. Outputs from the observer 210 are provided to inputs of the controller 220. The controller of the NMPC performs iteratively computations and, based on such computations, outputs a signal (in particular only one signal) or a sequence of data (in particular only one sequence of data) to be provided to the anti-surge valve 30 in order to set its opening or closing level; in the embodiment of Fig. 2, the controller 220 outputs one signal 31 as the control signal of the anti-surge valve 30. The observer 210 is configured to output “current” values of a plurality of state variables of the compressor system 100 used by a model (in particular nonlinear model 221) in the controller 220 to predict the “future”.

[0018] The duration of a calculation iteration of the controller 220 may be called “calculation time step”. At any time step, new outputs are provided by the observer 210 to the controller 220 (using the terminology of MPC, they may be called “past outputs”); this is represented by the upper big arrow pointing to the right in Fig. 2. At any time step, a new output is provided by the controller 220 to the valve 30 (using the terminology of MPC, it may be called a “future input”, i.e. one of the “future inputs”); this is represented by the lower big arrow pointing to the left in Fig. 2. [0019] As shown in Fig. 2, the controller 220 consists essentially of a nonlinear model calculator 221, a comparator 222 and an optimizer 223.

[0020] The nonlinear model calculator 221 iteratively calculates a “predicted output” 224 starting from a so-called “past output” 229A, so-called “past inputs” 229B, and so-called “future inputs” 229C; it embodies a (nonlinear) model of the compressor system 100 including also virtual valves 300 and 400. According to the embodiment of Fig. 2, there is only one output 224 from the nonlinear model calculator 221 corresponding to the (predicted) pressure at the inlet of the compressor 10 and a plurality of inputs 229 A, 229B, 229C to the nonlinear model calculator 221 corresponding to values of the state variables (current values 229B and predicted values 229C) of the compressor system 100 including the opening or closing levels of the virtual valves 300 and 400, and to the current opening or closing level 229 A of the anti-surge valve 30 (which can also be considered a current state variable).

[0021] The comparator 222 iteratively compares the predicted output 224 from the nonlinear model calculator 221 with a reference trajectory 225. According to the embodiment of Fig. 2, there is only one output and only one reference trajectory corresponding to the pressure at the inlet of the compressor 10. According to a typical application of the control unit 200, the objective is to maintain the inlet of the compressor 10 at a constant value; therefore, the trajectory corresponds to an horizontal line and the “reference trajectory” may be called “reference value” or “reference”. The comparator 222 iteratively calculates a difference 226 that may be called “future error” or “predicted error” and that is provided to the optimizer 223.

[0022] The optimizer 223 iteratively calculates so-called “future inputs” 228 starting from the error 226; the “future inputs” 228 corresponds to the predicted values 229C of the state variables of the compressor system 100 including the opening or closing levels of the virtual valves 300 and 400. According to the embodiment of Fig. 1 and Fig. 2, such calculation may be made with the aim of maintaining the inlet of the compressor 10 constant.

[0023] One of the outputs of the optimizer 223 is extracted and provided as the control signal 31 of the of the anti-surge valve 30, i.e. its opening or closing level.

[0024] The optimizer 223 conceptually receives as inputs a cost function 227A and constraints 227B; in other words, its outputs depend on the cost function and the constraints; this will be better explained later on.

[0025] According to typical embodiments, cost function and constraints are incorporated into the optimizer, i.e. it is not provided that they change for a certain application or during operation of the controller, so they are not truly inputs.

[0026] According to some embodiments, some or all of the constraints are embedded into the cost function. In fact, a constraint may be considered an element whose cost is very high when not fulfilled.

[0027] As already anticipated, the innovative method for performing control of an anti-surge valve in a compressor system (for example the compressor system 100 in Fig. 1) is predictive and based on a physical nonlinear model of the compressor system. The model is based on a plurality of state variables corresponding to physical quantities of the compressor system. Furthermore, the model is supplemented at least by a first virtual valve; considering the embodiment of Fig. 1, it may be valve 300 or valve 400. Such virtual valve is virtually coupled to an inlet of the compressor system (as e.g. valve 300 to inlet 13) or to an outlet of the compressor system (as e.g. valve 400 to outlet 14). Such virtual valve has an opening level that is variable. In this way, the opening level of such virtual valve is at least one supplemental state variable of the model. In this way, the operation of the compressor system according to the model can better reflect the operation of the compressor system according to measurements obtained from sensors and detectors of physical quantities.

[0028] According to a simple possibility, the model may be configured so that the (or any) supplemental state variable of the model has only a first value and a second value, the first value corresponding to the virtual valve being completely closed and the second value corresponding to the virtual valve being completely open. Alternatively, it may be provided that the (or any) virtual valve has a set of different opening or closing levels. Still alternatively, the opening or closing level of the (or any) virtual valve may be gradually varied.

[0029] The model may be configured so that the (or any) supplemental state variable of the model changes from a value, for example, the first value to another value, for example the second value, or vice versa abruptly. Considering for example the calculations carried out by the controller 220 as a sequence of “calculation time steps” (or simply “time steps”), the opening and closing level of the (or each) virtual valve may change from a value to another value passing from a time step to the following time step (and be considered constant during any time step).

[0030] As it is clear from Fig. 1, it is advantageous in order to provide an accurate modelling of the compressor system as well as disturbances acting on the system, to provide two virtual valves: a first virtual valve 300 and a second virtual valve 400. In this way, the model is supplemented not only by a first virtual valve but also by a second virtual valve, the first virtual valve being virtually coupled to an inlet of the compressor system, the second virtual valve being virtually coupled to an outlet of the compressor system, the second virtual valve having an opening level that is variable, the opening level of the second virtual valve being a second supplemental state variable of the model.

[0031] According to the advantageous embodiment of Fig. 1 (or to similar embodiments), the compressor system 100 comprises a compressor 10 and surge of the compressor 10 is limited or avoided only by acting on the valve 30; no other elements are changed for this purpose.

[0032] According to a simple possibility, the controller may be configured so that the anti-surge valve has only a first opening level (corresponding to the valve being completely closed) and a second opening level (corresponding to the valve being completely open). Alternatively, it may be provided that the antisurge valve has a set of different opening (or closing) levels. Still alternatively, the opening (or closing level) of the valve may be gradually varied.

[0033] The controller is typically configured so that the anti-surge state changes from an opening (or closing) level to another opening (or closing) level abruptly. Considering for example the calculations carried out by the controller 220 as a sequence of “calculation time steps” (or simply “time steps”), the opening (or closing) level of the anti-surge valve changes passing from a time step to the following time step (and is constant during any time step).

[0034] The preceding paragraphs explain the technical teaching of adding to the (nonlinear) model of a compressor system one or two (or even more, but not too many) state variables related to virtual components, i.e. components that are not physical components of the compressor system. Such teaching may be applied to innovative anti-surge control methods according to the subject matter disclosed herein.

[0035] Innovative anti-surge control methods may be presented from a different perspective. In fact, such methods use nonlinear models based on a plurality of state variables. According to an innovative concept, some of the state variables correspond to non-measurable disturbances.

[0036] In general, an innovative method for performing control of an antisurge valve in a compressor system implements a predictive control and is based on a physical nonlinear model of the compressor system. The model is based on N state variables. N-l or N-2 of the plurality of state variables correspond to physical quantities of said compressor system, for example suction pressure, discharge pressure, flow rate through the anti-surge valve, flow rate through the compressor, suction and discharge temperature, suction and discharge volume, compressor speed. 1 or 2 of the plurality of state variables correspond non- measurable disturbances acting on the compressor system.

[0037] Such model may be configured so that a first non-measurable disturbance is modelled as an opening level of a first (virtual) valve coupled to an inlet of the compressor system, and/or, that a second non-measurable disturbance is modelled as an opening level of a second (virtual) valve coupled to an outlet of the compressor system

[0038] The first non-measurable disturbance and/or the second non- measurable disturbance may be modelled as constant in time within a calculation time step, i.e. as changing only passing from a time step to the following time step.

[0039] Also within this different perspective, surge of the compressor is preferably limited or avoided only by acting on the anti-surge valve, i.e. by changing its opening or closing level.

[0040] Embodiments of the innovative methods may be incorporated in and/or carried out by compressor plants that, therefore, may be considered innovative compressor plants.

[0041] In general, an innovative compressor plant comprises a compressor system (such as the system 100 in Fig. 1) and a control unit (such as the unit 200 in Fig. 1 and Fig. 2); the compressor system comprises: a compressor, an electric motor driving in rotation the compressor, an anti-surge valve fluidly coupling an inlet and an outlet of the compressor, a measuring arrangement; the control unit is configured to control opening/closing of the anti-surge valve based on measurements carried out by the measuring arrangement; the control unit is configured to carry out an innovative anti-surge control method.

[0042] Advantageously, the control unit (such as the unit 200 in Fig. 1 and Fig. 2) comprises: an observer (such as the observer 210 in Fig. 2) having inputs coupled to the measuring arrangement and having outputs, and a controller (such as the controller 220 in Fig. 2) having inputs coupled to the outputs of the observer and an output coupled to the anti-surge valve; the observer is configured to generate and output values of state variables of a physical model of the compressor system starting from measurements from the measuring arrangement; the controller incorporates a physical nonlinear model of the compressor system and is configured to generate an output signal (in particular the control signal 31 of the anti-surge valve 30 in Fig. 1 and Fig. 2) starting from at least the values of the state variables from the observer.

[0043] The observer (for example observer 210) of the control unit of an innovative compressor plant is advantageously an Extended Kalman filter. Such filter is known as such so it is unnecessary to provide a detailed description herein.

[0044] As shown for example in Fig. 2 and as already described, the controller advantageously comprises a nonlinear model calculator, a comparator and an optimizer.

[0045] As shown for example in Fig. 2 and as already described, the optimizer conceptually receives as inputs a cost function and constraints; in other words, its outputs depend on the cost function and the constraints; this will be better explained later on.

[0046] The cost function must be minimized by the optimizer. According to some advantageous embodiments, the cost function includes up to four addends (preferably four addends), each of them being a function. A first addend is aimed at minimizing the opening time of the anti-surge valve; in other words, it is preferable to avoid that the anti-surge valve is open, i.e. the flow from the outlet of the compressor is fed back to the inlet of the compressor, when not (strictly) necessary. A second addend is aimed at minimizing the difference between the compression suction pressure and the reference; in other words, it is desired to track the compressor suction pressure reference. A third addend is aimed at minimizing constraints violation (e.g. avoiding surge, avoiding excessive discharge pressure, etc.). A fourth addend is aimed at avoiding that the opening or closing level of the anti-surge valve is changed too quickly.

[0047] The main constraint is to avoid surge, or, more specifically, to avoid that the compressor enters into the surge region, or, even more specifically, to avoid that the operating point of the compressor goes beyond the Surge Limit Line. Depending on the specific embodiment, there may be constraint relating to e.g. maximum/minimum pressure or maximum/minimum temperature or maximum/minimum flow.

[0048] It is to be noted that the fourth addend, relating to the op ening/c losing speed of a valve, is part of the cost function to be optimized. However, alternatively, the opening/closing speed of a valve may be dealt with as a constraint. Considering, in general, any parameter, a constraint is rigid while a cost function provides more flexibility to the value of the parameter.

Claims

1. A method for performing control of an anti-surge valve fluidly coupling an inlet and an outlet in a compressor system, the control being predictive and based on a model, the model being a physical nonlinear model of said compressor system, characterized by the fact that the model is based on a plurality of state variables corresponding to physical quantities of said compressor system, the model is supplemented at least by a first virtual valve, the first virtual valve being virtually coupled to an inlet or an outlet of the compressor system, the first virtual valve having an opening level that is variable, the opening level of the first virtual valve being a first supplemental state variable of the model the first virtual is added to the model for the control of the anti-surge valve, not included in the compressor system.

2. The method of claim 1, wherein the model is configured so that the first supplemental state variable of the model has only a first value and a second value, the first value corresponding to the first virtual valve being completely closed and the second value corresponding to the first virtual valve being completely open.

3. The method of claim 2, wherein the model is configured so that the first supplemental state variable of the model changes from the first value to the second value or from the second value to the first value abruptly.

4. The method of claim 1, wherein the model is supplemented by a second virtual valve, the first virtual valve being virtually coupled to an inlet of the compressor system, the second virtual valve being virtually coupled to an outlet of the compressor system, the second virtual valve having an opening level that is variable, the opening level of the second virtual valve being a second supplemental state variable of the model.

5. The method of claim 4, wherein the model is configured so that the second supplemental state variable of the model has only a first value and a second value, the first value corresponding to the second virtual valve being completely closed and the second value corresponding to the second virtual valve being completely open.

6. The method of claim 5, wherein the model is configured so that the second supplemental state variable of the model changes from the first value to the second value or from the second value to the first value abruptly.

7. The method of claim 1, wherein the compressor system comprises a compressor and wherein surge of the compressor is limited or avoided only by acting on anti-surge valve.

8. The method of claim 1 , wherein for performing control of the anti-surge valve in the compressor system, the control being predictive and based on a model, characterized by the fact that the model being a physical nonlinear model of said compressor system, is based on N state variables,

N-l or N-2 of the plurality of state variables corresponds to physical quantities of said compressor system,

1 or 2 of the plurality of state variables corresponds non-measurable disturbances acting on the compressor system.

9. The method of claim 8, wherein the model is configured so that a first non-measurable disturbance is modelled as an opening level of a first valve coupled to an inlet of the compressor system, wherein the model is configured so that the first non-measurable disturbance is modelled as constant in time within a calculation time step.

10. The method of claim 8, wherein the model is configured so that a second non-measurable disturbance is modelled as an opening level of a second valve coupled to an outlet of the compressor system, wherein the model is configured so that the second non-measurable disturbance is modelled as constant in time within a calculation time step.

11. The method of claim 8, wherein the compressor system comprises a compressor and wherein surge of the compressor is limited or avoided only by acting on said valve.

12. A compressor plant (1000) comprising a compressor system (100) and a control unit (200), wherein the compressor system (100) comprises: a compressor (10), an electric motor (20) driving in rotation the compressor (10), an anti-surge valve (30) fluidly coupling an inlet and an outlet of the compressor (10), a measuring arrangement (40); wherein the control unit (200) is configured to control opening/closing of the anti-surge valve (30) based on measurements carried out by the measuring arrangement (40); wherein the control unit (200) is configured to carry out the method of claim 1.

13. The compressor plant (200) of claim 12, wherein the control unit (200) comprises: an observer (210) having inputs coupled to the measuring arrangement (40) and having outputs, and a controller (220) having inputs coupled to the outputs of the observer (210) and an output coupled to the anti-surge valve (30); wherein the observer (210) is configured to generate and output values of state variables of a physical model of the compressor system (100) starting from measurements from the measuring arrangement (40), wherein the controller (220) incorporates the physical model of the compressor system (100) and is configured to generate an output signal starting from at least the values of the state variables from the observer (210).