Model predictive control of compressed air systems

Abstract

The present invention relates to a computer-implemented method for controlling a finite set of components fluidly connected to a common compressed air distribution system, the method comprising iteratively repeating the following steps: - receiving prediction data for the compressed air distribution system; - receiving characteristic data for each component of the component set; - determining one or more sets of continuously differentiable functions, each of the set of functions representing a unique operating sequence of the components of the component set; - selecting an optimal set of functions from the one or more sets of continuously differentiable functions, wherein the unique operating sequence represented by the optimal set satisfies the prediction data; - deriving configuration data for the component set from the optimal set of functions; and - configuring each component of the component set based on the configuration data.

Description

[Technical Field]

[0001] The present invention relates to the field of compressors, and more particularly to model predictive control of compressor chambers. [Background technology]

[0002] It is known that compressors are used to compress air or gas in one or more compression stages, which are then supplied to one or more consumers, the distribution of which takes place through a compressed air or gas system.

[0003] As the number of consumers can be huge and spatially distributed over a considerable area, for example in an industrial plant or a hospital, a central hub is usually installed from which the compressed air or gas is supplied.

[0004] Typically, a central hub contains one or more compressor rooms, each housing one or more compressors, as well as auxiliary equipment such as valves, filters, dryers, vessels, sensors, control components, and / or other devices for managing and / or controlling the compressor rooms. Pipes or ducts then exit the compressor room(s) to supply consumers. As the final part of the chain, the compressed air or gas is utilized by consumers for various uses.

[0005] Additionally, there may be another set of devices between the compressor and the consumer, such as safety valves, distribution valves, control sensors, or other devices for controlling and protecting the distribution of compressed air or gas.

[0006] The arrangements described above may also be referred to as compressed air or gas systems, which may therefore comprise one compressor supplying one consumer, but which may generally be considered to be broader and consequently comprise a large number of components, thereby constituting a complex system of elements interacting with one another.

[0007] In order to utilize a compressed air or gas system, its various elements must be controlled. It is already known to control the compressors individually by independent local control devices, whereby the different control devices are set to pre-set pressure values ​​and consequently switch the compressors on and off sequentially depending on the compressed air consumption.

[0008] Furthermore, methods of controlling a compressed air or gas system are known in which a number of communicable controllers control components forming part of the compressed air or gas system, whereby the components are controlled in such a way that no controller determines the operating state of components controlled by other controllers. WO 2008 / 009073 discloses such a method.

[0009] WO 2008 / 009072 discloses another method for controlling a compressed air unit consisting of multiple compressed air or gas networks with at least one commonly controllable component, whereby at least one commonly controllable component is controlled by at least one control device based on measurement data of at least one of the compressed air or gas networks.

[0010] However, a drawback of these control methods is that they operate solely based on the current state of the compressed air or gas system, i.e., they are unable to take into account any kind of prediction, which leads to suboptimal control and high energy costs. [Prior art documents] [Patent documents]

[0011] [Patent Document 1] International Publication No. 2008 / 009073 [Patent Document 2] International Publication No. 2008 / 009072 Summary of the Invention [Means for solving the problem]

[0012] The present invention aims to remedy the above-mentioned and other drawbacks. In a first aspect, the present invention relates to a computer-implemented method for controlling a finite set of components fluidly connected to a common compressed air distribution system, the method comprising: receiving forecast data representing predicted future pressure and / or air flow demands for the compressed air distribution system covering a forecast period; receiving characteristic data for each component of a set of components, the characteristic data including at least air flow data, air pressure data, and energy consumption data; determining one or more sets of continuously differentiable functions, each of the set of functions describing a pressure and / or air flow rate of the compressed air distribution system, each of the set of functions representing a unique operating sequence of components of the set of components that satisfies predicted future pressure and / or air flow rate data for at least an initial portion of a prediction period; selecting an optimal set of functions from the one or more sets of continuously differentiable functions, wherein the unique operating sequence represented by the optimal set satisfies the predicted future pressure and / or airflow data for at least a second portion of a prediction time period; - deriving configuration data for a set of components from the optimal set of functions; - configuring each component of the component set based on the configuration data; is repeated repeatedly.

[0013] The first step of the method involves receiving forecast data. In the context of the present disclosure, "forecast data" is understood as estimates of future values ​​of one or more process variables. In the case of a compressed air distribution system, the forecast data includes at least one of an estimated future pressure demand and / or an estimated future air flow demand. The forecast data covers at least a forecast period, which may have a duration of a few seconds, minutes, hours, days, or even longer. The duration of the forecast period may be changed with each iteration of the method. Preferably, the forecast data includes time series data, and estimates of future variables are provided for one or more distinct time instances during the forecast period. The forecast data may include estimates and / or estimated confidence intervals and / or estimated bounds for one or more process variables. The forecast data may be generated based on a model of the compressed air distribution system, historical and / or current process variable data, or other input data such as production schedules, maintenance schedules, calendar data, holiday data, or weather forecast data.

[0014] In a second step of the method, characteristic data is received. In the context of this disclosure, "characteristic data" is understood as data characterizing the technical or functional properties of one or more elements of the compressed air system. The characteristic data can be a mathematical model, a look-up table, measurement data, specifications, or any other form of data that can be interpreted by a person skilled in the art or by a suitable algorithm. The characteristic data includes data on at least each component of the set of components. The characteristic data for each component includes at least air flow rate data, air pressure data, and energy consumption data. For a particular compressor, it is useful to include in the characteristic data the operating region of the compressor. This operating region represents the allowable operating region of the compressor in the air pressure-air flow plane, and the energy efficiency is attributed to the compressor for each operating point within this region.

[0015] The third step of the method involves determining one or more sets of continuously differentiable functions. The set of continuously differentiable functions includes one or more continuously differentiable functions, each representing a unique operating sequence of the components in the set of components. Each set includes at least one or more continuously differentiable functions representing the pressure and / or air flow rate of the compressed air system and the energy consumption of the components. The unique operating sequence of the components in each set is selected so that the pressure and / or air flow rate of the compressed air system meets the forecast data of the pressure and / or air flow rate demand for at least an initial portion of a forecast period. Preferably, the initial portion is longer than the sum of the period required to complete one iteration of the method and the period required to bring at least one compressor in the set of components from a stopped state to a steady-load state. Possible choices for the continuously differentiable functions and operating sequences of the components are disclosed in the remainder of this disclosure in connection with embodiments of the present invention.

[0016] The fourth step of the method involves selecting an optimal set from the one or more sets of continuously differentiable functions. The selection process is performed so that a unique operating sequence of components associated with the selected subset results in a compressed air system pressure and / or airflow rate that meets the forecast data for pressure and / or airflow rate demand for at least a second portion of the forecast period, the second portion being longer than an initial portion of the forecast period. Preferably, the unique operating sequence of components associated with the selected optimal set results in a compressed air system pressure and / or airflow rate that meets the forecast data for pressure and / or airflow rate demand throughout the entire forecast period. Preferably, the unique operating sequence of components associated with the selected optimal set results in a compressed air system energy consumption that is lower than the energy consumption associated with other operating sequences that meet the forecasted pressure and / or airflow rate demand. Those skilled in the art will appreciate that other optimization criteria can be used. Possible methods for selecting the optimal set are disclosed in the remainder of this disclosure and in connection with embodiments of the present invention.

[0017] The fifth step of the method is to derive configuration data from the selected optimal set. In the context of this disclosure, "configuration data" is understood as data that determines command inputs to be applied to one or more elements of the compressed air system to impose a selected unique operating sequence on the component set. The configuration data includes data for at least each component of the component set. Examples of configuration data include time instances when a particular compressor should be started, stopped, loaded, or unloaded, the speed at which a particular compressor should be operated, a valve position, or a time instance when a valve position should be changed, or the flow rate of a refrigeration circuit.

[0018] In a sixth step of the method, each member of the set is configured according to the configuration data.

[0019] An advantage of the method is that it allows for simultaneous control of a set of components in real time, taking into account not only the current state of the components and the compressed air distribution system, but also the predicted future demands of the compressed air distribution system.

[0020] While the method is applicable to all components of a compressed air distribution system, the remainder of this disclosure will uniquely use compressors as exemplary embodiments of components. Because compressors are generally the most critical, complex, and difficult to control components of a compressed air distribution system, those skilled in the art will understand that these are the most useful embodiments for illustrating the capabilities of the method without loss of generality.

[0021] Those skilled in the art will recognize that during normal operation, the compressor can be in one of three operating configurations or states. These states are as follows: - Standstill: during which the moving parts of the compressor that transfer energy to the compression medium, such as the impeller, scroll, piston, etc., are not in operation. Usually, in the standstill state, the motor that drives the moving elements of the compressor is stopped or the power transmission between the motor and the moving parts of the compressor is interrupted by a clutch. No-load state: During this time, the compressor is driven by the motor, and its moving parts operate to move a fluid that is discharged at the same pressure as the suction pressure. In a compressed air system, this can be achieved, for example, by including a bypass valve after the compressor's discharge that allows the compressor to discharge to the ambient air. Alternatively, the compressor's suction can be throttled, in which case the negligible air flow provided by the compressor can be discharged directly to the compressed air distribution system. The no-load state is usually an intermediate stage between the compressor's stopped and loaded state. In some applications, especially those using large compressors, the time it takes for the compressor to ramp up from stopped to its normal operating speed can be too long compared to the dynamics of the compressed air system's demand fluctuations. In such situations, the compressor can be kept in the no-load state whenever it is not needed. - Loaded condition: during which the compressor is driven by the motor, the moving parts of the compressor operate to move fluid which is discharged into the compressed air system against system back pressure. For purposes of this disclosure, a compressor is considered to be in a loaded condition when it is operating within its normal operating range and is not exceeding one or more of the following limits: surge, choke, power or speed.

[0022] Outside of normal operation, the compressor may be stalled, surged, choked, overspeed, or in other states, although these additional states will not be described in detail. However, those skilled in the art will understand from the remainder of this disclosure that the method according to the present invention can also address these states. Preferably, the method actively seeks to prevent these states. Furthermore, those skilled in the art will understand that other components of the compressed air distribution system can be represented by states, such as valves.

[0023] In one embodiment of the method according to the invention, each component of the component set is represented by a state machine (a mathematical modeling technique for describing discrete-state systems), also called a finite state machine or finite state automaton. For the purposes of the method, the state machine model of a component preferably includes at least the different states, information about how the states are interconnected, and time-dependent constraints associated with the states.

[0024] A unique sequence of operations for a finite set of components is associated with each set of continuously differentiable functions, so selecting the optimal set reduces to selecting the optimal sequence of operations for the components of the set.

[0025] In one embodiment of the method according to the invention, the step of determining one or more sets of continuously differentiable functions includes generating state space data representing possible operation sequences of the set of components. Because the state space is limited in dimensionality by the number of components in the set and the number of possible states per component, the state space representing the possible operation sequences is limited in dimensionality insofar as the number of allowable transitions per component is limited over a given time period. Thus, representing the components as state machines transforms the infinite space of possible operation sequences into a finite space that can be exhaustively searched.

[0026] Given a representation of a component by a state machine, the operational sequence of a component includes information about at least (i) the component's initial state, (ii) the state transitions the component will undergo, and (iii) the order in which the component will undergo these state transitions. The operational sequence of a component does not necessarily include the specific time instants at which the component will undergo a particular state transition. Thus, the set of operational sequences of a finite set of components controlled by the method of the present invention includes the set of operational sequences of each component in the set, and includes exactly one operational sequence for every component in the set. In contrast, the configuration data derived by the present method includes the operational sequences of the component set plus at least the time instants at which state transitions should occur during the prediction period.

[0027] In one embodiment of the method according to the invention, state space data representing possible operation sequences for the set of components is generated based on allowable state transitions from previous states of one or more components of the set to subsequent states of one or more components of the set. Because the allowable transitions depend on the current states of the components, there is always a finite number of allowable transitions. In this way, representing operation sequences as state transition sequences can further reduce the dimension of the state space in which the function sets are determined, thereby reducing the computational cost of the method.

[0028] In one embodiment of the method according to the invention, the state space data is pruned based on the value of at least one boundary condition or objective function, which pruning allows to further reduce the dimension of the state space in which the function set is determined, thereby reducing the computational cost of the method.

[0029] In one embodiment of the method according to the invention, the set of continuously differentiable functions according to the method can be written as (f(x,y),g(x,y)), where:

number

number

number

number

number

[0030] Those skilled in the art will understand that in the context of minimizing the energy consumption of a compressed air system, the objective function f includes a measure of the energy consumption of the system, such as the instantaneous energy consumption of the system or the total energy consumption over a forecast period. The objective function f can include additional terms that represent direct or indirect measures of the energy consumption or energy efficiency of the system. The objective function f can include other terms. Similarly, those skilled in the art will understand that the constraint functions g can include equations that model the components of the system or equations that describe process variables, such as pressure, air flow rate, air temperature, relative humidity, etc.

[0031] The step of selecting the optimal set of continuously differentiable functions involves the problem of minimizing f(x,y) subject to the boundary conditions lb≦g(x,y)≦ub, where the lower boundary lb and the upper boundary ub can include predicted future pressure and / or air flow demands, as well as additional boundary conditions imposed by the system or consumers connected to the system. For example, the boundary conditions can include a maximum temperature and / or a maximum relative humidity of the compressed air, or a maximum rotational speed of one or more compressors. This problem is a mixed-integer nonlinear problem.

[0032] In this embodiment, the step of selecting the optimal set of continuously differentiable functions then involves searching for at least a local minimum of the objective function f(x,y).

[0033] In one embodiment of the method according to the invention, the local minimum of the objective function is searched for using a branch and bound algorithm. The advantage of using a branch and bound algorithm is that it allows for systematic exploration and pruning of the state space.

[0034] In one embodiment of the method according to the invention, the time instants at which the components of the component set make particular state transitions of an action sequence are determined so as to obtain a local minimum of the objective function f(x,y). The method has two degrees of freedom for achieving optimal control. The first degree of freedom relates to the selection of the action sequence of the components of the component set. In the first degree of freedom, the available state space is explored, for example, using a branch and bound algorithm or other suitable technique. The second degree of freedom relates to the selection of the time instants at which the state transitions of the action sequence occur. To determine these time instants, it is necessary to solve a mixed-integer nonlinear problem of minimizing f(x,y) subject to the constraint lb≦g(x,y)≦ub.

[0035] In one embodiment of the method according to the invention, the characteristic data further comprises minimum start-up energy data and / or minimum active period data after start-up and / or average maintenance time for at least one component of the set of components.

[0036] In one embodiment of the method according to the invention, the step of iteratively repeating comprises repeating the method steps at discrete regular time intervals.

[0037] In one embodiment of the method according to the invention, the forecast period is time-dependent. The forecast period may change, for example, if the dynamic demand of the compressed air distribution system changes. If the dynamic demand fluctuations are small, the forecast data may cover a longer time period, and vice versa.

[0038] In one embodiment of the method according to the invention, the initial part of the prediction period is determined based on at least the maximum processing capacity of the data processing means executing the method.

[0039] A second aspect of the invention relates to a data processing system comprising means for carrying out the method according to the first aspect of the invention.

[0040] A third aspect of the invention relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to the first aspect of the invention.

[0041] A fourth aspect of the invention relates to a compressed air or gas system configured to be controlled in accordance with the method of the first aspect of the invention. [Brief explanation of the drawings]

[0042] [Figure 1] 1 shows a schematic representation of a compressed air system controlled in accordance with the present invention; [Figure 2a] 1 shows a schematic representation of a state machine of a compressor. [Figure 2b] 1 shows a schematic representation of a state machine of a compressor. [Figure 3a] 1 illustrates a schematic representation of a time switch employed in an embodiment of the present method to represent state transitions. [Figure 3b] 1 illustrates a schematic representation of a time switch employed in an embodiment of the present method to represent state transitions. [Figure 4a] 1 shows a flow diagram of an embodiment of a method according to the present invention; [Figure 4b] 1 shows a flow diagram of an embodiment of a method according to the present invention; [Figure 5a] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5b] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5c] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5d] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5e] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5f] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5g] 4 shows the results of an implementation of an embodiment of the method according to the invention. [Figure 5h] 4 shows the results of an implementation of an embodiment of the method according to the invention. DETAILED DESCRIPTION OF THE INVENTION

[0043] While the present disclosure will be described in terms of specific embodiments, these are intended to illustrate the present disclosure and are not to be construed as limiting. It is to be understood that the present disclosure is not limited by what is specifically shown and / or described, and that alternative or modified embodiments may be conceived in light of the overall teachings of the present disclosure. The drawings described are merely schematic and non-limiting.

[0044] References throughout this specification to "one embodiment" or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with an embodiment is included in one or more embodiments of the present disclosure. Thus, the appearances of the phrase "in one embodiment" or "in an embodiment" in various places throughout this specification do not necessarily all refer to the same embodiment, although they may. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, as will be apparent to one of ordinary skill in the art from this disclosure.

[0045] FIG. 1 shows a compressed air or gas system 100 comprising three compressors 101, 101′ and 101″ configured to supply compressed air or gas to a client network 105. The compressed air or gas system 100 further comprises a container or tank 103 for storing the compressed air or gas and a valve 104 connected to the client network 105. The client network 105 has one or more consumers. It should be further understood that the compressed air or gas system 100 may further comprise other devices such as dryers, filters, regulators and / or lubricators, however, hereinafter the invention will be described with reference to FIG. 1 as an arrangement of the compressed air or gas system 100. In FIG. 1, solid lines indicate fluid connections and dotted lines indicate data connections.

[0046] Each of the compressors 101, 101', 101" is locally controllable by a respective controller 102, 102', 102". Furthermore, to efficiently control the compressed air or gas system 100, the controllers 102, 102', 102" are to be controlled in a coordinated manner. In other words, each of the controllers 102, 102', 102" is avoided from individually controlling the respective compressors 101, 101', 101". However, the controllers 102, 102', 102" are directed by the main controller 106 such that the overall performance and efficiency of the compressed air or gas system 100 is improved.

[0047] The master controller 106 may be located near the controllers 102, 102', 102'', or may be located remotely relative to the compressed air or gas system 100. Alternatively, one of the controllers 102, 102', 102'' may be configured to act as a master controller that controls all of the compressors 100, 100', 100''.

[0048] The main controller 106 handles the operation, switching, and idling costs of the compressed air or gas system 100, thereby reducing wear on the different equipment components and simultaneously optimizing energy consumption. To this end, the main controller 106 utilizes an embodiment of a method according to the present invention. The main controller 106 receives characteristic data 110 describing technical or functional characteristics of one or more elements of the compressed air system. This characteristic data can be obtained from a database, a model, measurements made on one or more elements of the compressed air system 105, or any other suitable means. Furthermore, the main controller 106 also receives forecast data 120 describing future predicted air flow and / or pressure demands of at least the client network. Again, this forecast data can be obtained from a database, a model, measurements made on one or more elements of the compressed air system 100 or the client network 105, or any other suitable means. Based on the characteristic data 110, the prediction data 120, and the method of the present invention, the main controller 106 sends configuration data 130 to the controllers 102, 102', 102'' to coordinate the control of the compressors 101, 101', 101''.

[0049] 2a and 2b show schematic representations of a compressor state machine 200, 200''. The state machine 200 of FIG. 2a includes three possible states: loaded 201, unloaded 202, and stopped 203. Each state includes at least two parameters:

number

number

number

[0050] 2a also shows state transitions to adjacent states: transition 204 from unloaded state 202 to loaded state 201, transition 205 from loaded state 201 to unloaded state 202, transition 206 from unloaded state 202 to stopped state 203, and transition 207 from stopped state 203 to unloaded state 202. Each transition includes at least a parameter indicating the time required to complete the transition, corresponding to transitions 204, 205, 206, and 207, respectively.

number

[0051] The state machine 200'' of Figure 2b has only two possible states: loaded 201 and stopped 203. As a result, the state machine 200'' of Figure 2b has only two possible state transitions: loaded to stopped 208 and stopped to loaded 209. The state machine 200 also allows transitions 208 and 209, but these are not shown in Figure 2a to avoid cluttering the figure.

[0052] Compared to the state machine representation 200 of FIG. 2a, the state machine 200″ of FIG. 2b offers lower computational complexity due to the reduced number of states and transitions. Representing a compressor with a state machine 200″ may be advantageous when available computing power is insufficient to determine the optimal operating sequence of the compressors in real time using the state machine representation 200. Such a situation may arise, for example, when multiple compressors need to be controlled simultaneously or when the air flow demand of a compressed air system changes strongly and unpredictably. The tradeoff of the reduced number of degrees of freedom of the state machine 200″ may be that finer control of the compressors is not possible. Additionally, some compressors may not be able to transition from a stopped state to a loaded state immediately.

[0053] Embodiments of the method of the present invention can use either of both state machines to represent compressors in a set of compressors. In addition, the method can use both representations simultaneously, representing some compressors in the set by state machines with three states while representing other compressors in the set by state machines with only two states. Also, during execution of the method, the method can dynamically switch between both state machine representations to represent one or more compressors, thereby dynamically changing the balance between execution speed and control precision of the method.

[0054] Finally, those skilled in the art will appreciate that the method of the present invention is not limited to representing compressors solely by state machines containing two or three states, but that more states (each state representing a distinct operating regime of the compressor) can be added to the state machine. Thus, the above description applies equally to state machine representations containing four or more states.

[0055] 3a and 3b show schematically two types of time switches that can be used in embodiments of the present method to represent the state transitions of one or more compressors as a function of time. Both of these types of time switches follow a sigmoid function:

number

[0056] 3a shows a schematic representation 200 of a state machine representation of a compressor having three states: loaded, unloaded, and stopped, designated by the numerals 201, 202, and 203, respectively. At the beginning of a time period, the compressor is in loaded state 201, which is mathematically shown to have a value equal to 1. By definition, the different states of a state machine are mutually exclusive, so the compressor cannot be in either an unloaded or stopped state. This is mathematically imposed by requiring that the sum of the values ​​of all of the machine's states must equal 1.

[0057] In FIG. 3a, a series of operations is imposed on the compressor, including a state transition from a loaded state 201 to an unloaded state 202. Therefore, a time switch 224 is introduced around a first switching time 220, which transitions the loaded state from value 1 to value 0 and the unloaded state from value 0 to value 1. Also, during the switching period, the sum of the values ​​of all states remains equal to 1. Prior to the initiation of the time switch 224, the state of the state machine 200 is known. Therefore, the period from the initial time to the initiation of the time switch 224 is the state determination period 222 of the machine 200. Because this state machine is in a known state adjacent to the time switch 224, a time switch with this same property will be referred to as an “adjacent switch” in the remainder of this disclosure. An adjacent switch can be imposed on the state machine only adjacent to the state determination period, i.e., after the period when the state of the machine is known. Note that the concept of an adjacent switch can also be used retroactively; an adjacent switch can be imposed before the state determination period. This is useful when the final state of the machine at the end of the period is known, rather than the initial state of the machine.

[0058] After completion of time switch 224, machine 200 must remain in no-load state 202 for a minimum time 210. Thus, the machine is in a state determination period 222 for at least the minimum time 210 after initiation of time switch 224. After this period has elapsed, machine 200 is in a state indeterminate period 223 (during which the machine's state variables can have any value as long as the sum of their values ​​equals one), and may optionally, but not necessarily, undergo another state transition, such as a transition around a second switch time 221.

[0059] Mathematically, imposing adjacent time switches on a state machine is achieved by imposing the following set of equations on the constraint function g(x,y):

number

number

number

[0060] FIG. 3b shows a schematic representation of a state machine 200″ for a compressor having two states, loaded and off, designated 201 and 203, respectively. At the beginning of the time period, the state of the compressor is unknown. At switch time 220, a time switch 225 is introduced that transitions the machine to the loaded state 201. Because the compressor must remain in the loaded state for a minimum time 210, the state of the compressor is known during this period. The introduction of time switch 225 therefore results in a state determination period 222 during which the state of machine 200″ is known and the values ​​of its state variables are fixed. The length of this period 222 is equal to the minimum period required for the machine to remain in a particular state. However, after the end of the minimum period or before the initiation of time switch 225, machine 200″ is in a state uncertainty period 223. Because the introduction of the time switch 225 is independent of knowledge of the state of the machine 200'' and can therefore occur anywhere in the time period, a time switch with this same characteristic will be referred to as a ``free-floating switch'' in the remainder of this disclosure.

[0061] Mathematically, imposing a floating time switch on a state machine is achieved by imposing the following set of equations on the constraint function g(x,y):

number

[0062] Embodiments of the method can be implemented with adjacent switches or floating switches, or a combination of both. Both types of switches can be further extended to include tolerances around the ramp so that the state variable can attain an integer value after the switch is complete. This is useful when other constraints prevent the state variable from transitioning between integer values.

[0063] Figure 4a shows a flow diagram of one embodiment of the method according to the invention. Before each iteration of the method, an initialization step 300 is performed. During this initialization step, queues and containers are created. At this point, the queues and containers are empty.

[0064] The first step in the iterative method is a data collection step 301. During this data collection step, both characteristic data for one or more compressors and predictive data for the compressed air system are collected.

[0065] In step 302, the queue is updated. During the first iteration of the method, this updating involves creating an initial set of continuous differentiable equations (f(x,y), g(x,y)) subject to the boundary condition lb≦g(x,y)≦ub and the associated problem of minimizing f(x,y). This set of equations and the associated problem are added as items to the queue. During the second and subsequent iterations of the method, the updating step 302 can serve different purposes, as will be further explained during the disclosure of the present embodiment.

[0066] Because the method of the present invention is intended for real-time control of one or more compressor sets, the method runs for a finite amount of time. This amount of time can be constant or variable based on known characteristics of the system. For example, the method can calculate a maximum amount of time to run for each iteration based on received forecast data. Timer 303 tracks the time elapsed during the execution of the computational portion of the method; if the computation time exceeds a predetermined maximum time, timer 303 interrupts the calculation and causes the method to proceed to the next iteration.

[0067] During execution of the method, items corresponding to sets of continuous differentiable equations (each representing a unique operating sequence of the compressor and their associated minimization problem) may be added to or removed from the queue. In step 304, the method checks whether the queue still contains items. If the queue is empty, step 304 causes the method to proceed to the next iteration step before the maximum amount of time for the iteration has elapsed.

[0068] In step 305, the method attempts to solve one or more items in the queue using a branch and bound algorithm, which is shown in detail in Figure 4b. The branch and bound algorithm adds fully solved items to a container, and the algorithm can also add partially solved items to the queue and / or remove items from the queue.

[0069] When the method exits the computation loop, either because the maximum duration of one iteration has expired or because the queue is empty, the method checks whether the container contains a completely solved solution in step 306. If so, in step 308, the optimal solution, meaning the solution with the lowest cost of the objective function f(x,y), is selected from the container.

[0070] Alternatively, if the container is empty, step 307 selects a (partially solved) optimal solution from the queue and derives configuration data from this optimal solution. In this case, the optimal solution does not cover the entire range of the forecast period for which forecast data is available, so uncertainty remains as to whether the selected operating sequence can meet the predicted pressure and / or airflow demand. This issue can be addressed in a post-processing step in step 307. Such a post-processing step can apply multiple criteria to identify the risk that an incomplete operating sequence will not be able to meet the predicted pressure and / or airflow demand. For example, it can check whether all compressors in the set can be loaded for the remainder of the forecast period for which the item is not fully solved. If the selected optimal solution meets the post-processing criteria, it can be retained. Otherwise, it can be rejected, and another solution from the queue can be selected as the optimal solution.

[0071] Configuration data is then derived from this optimal solution, and the compressors of the system are configured based on the configuration data in step 309. This completes one iteration of the method.

[0072] When the second iteration of the method begins, the first step is again data collection step 301. However, at this point, the queue and container are not necessarily empty. If the container contains items, these items are added to the queue and the container is emptied. The items in the queue are then shifted in time. If an item in the queue does not match the updated state of the compressor, the item is removed from the queue. Finally, the items in the queue are updated with new forecast data.

[0073] 4B shows a flow diagram of one embodiment of the branch and bound algorithm 305. The input to the branch and bound algorithm is a queue that holds unsolved or partially solved problems (also called items), where each problem corresponds to a unique sequence of operations for the compressor. The output of the branch and bound algorithm is an updated queue and container. The branch and bound algorithm relies on three separate algorithms: a selection algorithm that selects an item from the queue, a branching algorithm that branches the item, and a solution algorithm that solves the item.

[0074] In step 400, a selection algorithm selects an item from the queue. The algorithm can use one of several criteria to determine which item to select. Examples of such criteria are: Best-first: The algorithm always selects the item with the smallest value of the objective function f(x,y). This approach is easy to implement and can obtain the optimal solution in the least amount of computation time without using heuristics. However, it may take longer than other criteria to obtain the first solution that is feasible and completely solved over the entire forecast period. Alternating Best-First: This algorithm builds on the best-first algorithm. Instead of searching the whole tree, the tree is split and the best-first algorithm is applied to each split of the tree, alternating. For trees with very long branches, this is a good option for getting a good solution in less time than the "best-first" approach. · Breath first: The algorithm picks the item at the beginning of the queue. Depth-first: The algorithm selects the partially solved item that has already been solved for the longest time period. After reaching a feasible, fully solved solution, the method can explore the rest of the queue using further approaches. Weighted depth and cost: The algorithm balances between optimizing computation speed with a "depth-first" approach and minimizing a cost function with a "best-first" approach. This approach is usually faster than the "depth-first" approach but yields fewer optimal solutions, and is slower than the "depth-first" approach but yields more optimal solutions. Heuristics: Heuristics are defined that try to estimate the direction the algorithm should go in. These heuristics can be application based.

[0075] The algorithm may switch between one or more of the above criteria between different iterations of the method. The algorithm may switch between or combine one or more of the above criteria during a single iteration of the method.

[0076] In step 401, the branching algorithm creates a branch from the item selected from the queue in step 402. The created branch is therefore a "child" of the initially selected item, which is the "parent." In this context, generating a branch means adding one state transition to the parent's action sequence, thereby creating a new, unique action sequence and a new associated mathematical problem. Mathematically, generating a branch involves adding a set of equations representing a time switch to the parent's constraint function g(x,y). These equations are described in connection with Figures 3a and 3b.

[0077] The state transitions that can be added to an existing operation sequence are limited by the basic state machine representation. It may be possible to generate multiple branches from a single parent. However, the branching algorithm does not necessarily generate all possible branches. For example, the branching algorithm may only branch from the compressor that is least solved in time, i.e., the machine that still has the greatest state uncertainty over the prediction period. Alternatively, the branching algorithm may only branch from the compressor that causes the greatest energy consumption. The branching algorithm may combine different branch generation strategies within one iteration or switch between branch generation strategies between multiple iterations of the method. The branch generation strategy employed may be specifically adapted to the basic application.

[0078] In relation to Figures 3a and 3b, two types of time switches are introduced: adjacent switches and floating switches. The branch generation algorithm determines the type of switch to introduce to impose state transitions. In the context of model predictive control, adjacent switches are preferred. Because the initial state is known, the use of adjacent switches allows for a time-forward solution, reaching a feasible solution for the initial part of the time period early in the calculation phase. As a result, the branching process can be interrupted before reaching a complete solution, provided that the feasibility of the partially solved problem is guaranteed for the unsolved time horizon. In compressor control, this can be achieved by post-processing, which requires all compressors to be loaded for the unsolved time horizon.

[0079] In contrast, floating switches create more branches and are therefore computationally expensive. However, in some special cases, using floating switches can lead to faster solutions. One such case is when the unconstrained state variables are already close to integer values ​​at a particular time. Furthermore, a further drawback of using floating switches is their implementation complexity, requiring dedicated algorithms to calculate possible switching paths between two different states to ensure that infeasible partial solutions are not generated.

[0080] After the branches are generated, the solution algorithm will attempt to resolve all branches. Step 402 checks whether all branches have been resolved. If so, the branch and bound algorithm ends and the method returns to time check step 303 in Figure 4a. If all generated branches have not been resolved, the method proceeds to the solution algorithm in step 403.

[0081] In step 403, the solution algorithm attempts to solve a specific problem associated with a unique sequence of movements. Mathematically, this problem is the minimization of an objective function f(x,y), subject to the constraints lb≦g(x,y)≦ub, where:

number

number

number

number

number

[0082] Typically, in the first substep of the solution algorithm, the linear relationship in MINLP is calculated by dividing the objective and constraint functions into the relaxation variables

number

number

number

number

number

number

[0083] In step 404, the algorithm checks whether the problem is integer feasible (i.e., whether the constraints can be satisfied when the state variables are restricted to integer values). In addition, step 404 also checks whether the cost of the objective function of the branch is lower than the lowest objective cost achieved by any other fully solved branch. If both conditions are not met, the particular branch is discarded in step 405. If they are, the method checks in step 406 whether this branch is fully solved, i.e., whether the machine states are constrained for the entire time period of the prediction horizon for which prediction data was available. If the branch is fully solved, the associated operation sequence and objective cost are stored in a container in step 407. If the branch is not fully solved, the branch is added to a queue in step 408. In the next iteration of the branch-and-bound algorithm, this branch is selected as the parent to branch from.

[0084] 5a-5i show the results of an implementation of an embodiment of the method according to the invention. In the embodiment of FIGS. 5a-5h, the compressor set comprises three machines designated U1, U2, and U3, represented by state machines 200, 200', and 200'', respectively. Machines 200 and 200' are assumed to have three accessible states: loaded 201, unloaded 202, and stopped 203. Machine 200'' is assumed to have only two accessible states: loaded 201 and stopped 203. Forecast data for the compressed air network connected to the three compressors is available for a forecast period 126. The forecast data includes a forecast of future air flow demand 121 and a forecast of future minimum and maximum pressure demands 123 and 124. Note that for clarity of the figures, not all reference numbers are assigned to all subplots of the figures.

[0085] FIG. 5a initially shows machines 200 and 200″ in a loaded state 201 and machine 200′ in a stopped state 203. Machine 200′ must be forced to remain in the stopped state for at least one time iteration. This may occur, for example, because the machine was previously in the stopped state and the minimum amount of time in the stopped state has not yet expired. However, machines 200 and 200″ can change states from the beginning of the time period. The cross symbols indicate values ​​calculated by the branch and bound algorithm for calculated airflow 122, calculated pressure 125, and state variables. During state determination period 222, the state of the machine is known and the calculated state variables are constrained state variables 131. In contrast, during state uncertainty period 223, the state of the machine is not known and the calculated state variables are unconstrained state variables 132.

[0086] The solution in Figure 5a contains an uncertainty period 223 and is therefore only partially solved. The branching algorithm assumes that the greatest gain can be achieved by adding state transitions on machine 200'', creates two branches, represented in Figures 5b and 5c, from the existing partial solution of Figure 5a, and adds these branches to a queue. After creating the branches in Figures 5b and 5c, the parent, represented in Figure 5a, is discarded.

[0087] In the branch of FIG. 5b, a transition 208 from a loaded state to a stopped state is imposed on machine 200″. Because machine 200″ is stopped, it must remain stopped for a minimum amount of time 210. The solution algorithm determines that, due to the absence of a stopped state, machine 200 must be constrained in a loaded state for the entire time period. Furthermore, the solution algorithm determines that even if machine 200′ transitions from a stopped state to a loaded state, the compressor set cannot meet the minimum pressure demand 123 for time period 127. Therefore, the branch of FIG. 7b is infeasible and is removed from the queue.

[0088] In contrast, in the branch of FIG. 5c, machine 200″ remains in loaded state 201. The solution algorithm determines that under these conditions, it is optimal for machine 200′ to remain constrained to the stopped state until approximately 300 seconds, while it is optimal for machine 200″ to remain constrained to the loaded state until approximately 600 seconds. This operating sequence allows the compressor to meet the predicted future airflow and pressure demands. Therefore, the branch is feasible. Because the time period of the branch includes a state uncertainty region 223, the branch is not fully solved and remains in the queue. Because the state of machine 200 is unconstrained for any portion of the time period, machine 200 is the least solved. Therefore, the branching algorithm assumes that the greatest gain can be achieved by adding a state transition to machine 200, creates two branches, represented in FIGS. 5d and 5e, from the existing partial solution of FIG. 5c, and adds these branches to the queue. After creating the branches of FIGS. 5d and 5e, the parent, represented in FIG. 5c, is discarded.

[0089] In the branch of Figure 5d, machine 200 is initially constrained in a loaded state, while in the branch of Figure 5e, a state transition 205 to an unloaded state is imposed on machine 200. After resolution, both branches are partially solved, shown to be feasible, and kept in the queue. Because the objective function cost is lower for the sequence of operations in Figure 5e than for the sequence of operations in Figure 5d (not shown), the branch of Figure 5d is discarded, and the branching algorithm decides to branch from the sequence of Figure 5e. Because machine 200 is still the least solved of the three machines, the branching algorithm decides to branch by imposing additional state transitions on machine 200, which are added to the queue and create two new branches, represented in Figures 5f and 5g. After the branches of Figures 5f and 5g are created, the parent represented in Figure 5e is discarded.

[0090] In the branch of Figure 5f, this additional state transition is transition 204 from the unloaded state to the loaded state, and in the branch of Figure 5g, this additional state transition is transition 206 from the unloaded state to the stopped state. Both branches are executable. The cost of the objective function is lower for the sequence of operations in Figure 5g than for the sequence of operations in Figure 5f (not shown). Therefore, the branch of Figure 5f is discarded and the branch of Figure 5g is added to the queue.

[0091] At this point, the maximum computation time for one iteration of the method may have elapsed. No branches have been fully resolved. Therefore, the method will select the item from the queue with the lowest objective cost, which is the sequence of operations in Figure 5g. This sequence will be applied to the compressor.

[0092] Then, at the start of the next iteration, all items in the queue must be shifted in time so that the start of their time period coincides with the start of the new time period in the prediction data. Figure 5h shows the sequence of Figure 5g shifted in time. Here, machines 200 and 200' are initially stopped, and machine 200'' is initially loaded. If any other sequences are in the queue at this point, they are also shifted in time. However, if these other sequences become infeasible because their new initial state does not match the new initial state of the compressor, they are discarded as well. The sequence of Figure 5h, which is currently being applied to the compressor, is the only item remaining in the queue. The branch-and-bound algorithm will create a branch from this item and attempt to solve it. [Explanation of symbols]

[0093] 100 Compressed Air System 101 Compressor 102 Control device 103 Container 104 Valve 105 Client Network 106 Main control unit 110 Characteristic Data 120 forecast data 121 Predicted Air Flow Demand 122 Calculated Air Flow Rate 123 Predicted Minimum Pressure Demand 124 Estimated Maximum Pressure Demand 125 Calculated Pressure 126 Forecast Period 127 period 130 Configuration Data 131 Constrained State 132 Unconstrained State 200 State Machine 201 Load condition 202 No load condition 203 Stopped 204 Transition from unloaded to loaded state 205 Loaded to unloaded transition 206 Transition from no-load state to stop state 207 Transition from unloaded to loaded state 208 Transition from Loaded State to Stopped State 209 Transition from Stopped to Loaded Minimum time to stay in 210 state 220 Switching Time 221 Next Switch Time 222 Restricted Zone 223 Unrestricted Zone 224 adjacent switches 225 Floating Switch 300 Method Initialization Step 301 Data Collection Steps 302 Queue Update Step 303 Time Check Step 304 Queue Check Step 305 Branch and Bound Algorithm 306 Container Check Step 307 Solution Selection Step from Queue 308 Solution Selection Step from Container 309 Compressor Configuration Steps 400 Item Selection Algorithm 401 Branching Algorithm 402 Branch Check Step 403 MINLP solver steps 404 Feasibility Check Step 405 Branch discard step 406 Solution Check Step 407 Additional steps to the container 408 Enqueue Step

Claims

1. 1. A computer-implemented method for controlling a finite set of components fluidly connected to a common compressed air or gas distribution system, comprising: receiving forecast data representing predicted future pressure and / or air flow demands for said compressed air or gas distribution system covering a forecast period; receiving characteristic data for each component of the set of components, the characteristic data including at least air flow data, air pressure data, and energy consumption data; determining a set of a plurality of continuously differentiable functions, each of said set of functions including a function describing pressure and / or air flow rate of said compressed air or gas distribution system and a function describing energy consumption or energy efficiency of said compressed air or gas distribution system, each of said set of functions representing a unique operating sequence of said components of said set of components that will meet said predicted future pressure and / or air flow rate demand for at least an initial portion of said prediction time period; selecting an optimal set of functions from the set of multiple continuously differentiable functions, wherein the unique sequence of operations represented by the optimal set meets the predicted future pressure and / or airflow demand for at least a second portion of the prediction time period; deriving configuration data for the component set from the optimal set of functions; configuring each component of the set of components based on the configuration data; A method of repeatedly repeating the above.

2. The method of claim 1 , wherein each component of the component set is represented by a state machine.

3. The method of claim 2 , wherein the step of determining the set of multiple continuously differentiable functions comprises generating state space data representing possible motion sequences of the component set.

4. 4. The method of claim 3, wherein the state space data is generated based on allowable state transitions from previous states of one or more components of the component set to subsequent states of one or more components of the component set.

5. The method of claim 3 or 4, further comprising pruning the state space data based on at least one boundary condition or objective function value.

6. 6. The method of claim 1, wherein each of the set of functions includes an objective function that describes the energy usage or energy efficiency of the compressed air or gas distribution system, and wherein selecting the optimal set of functions includes searching for at least a local minimum of the objective function.

7. The method of claim 6 , wherein the local minimum is found using a branch and bound algorithm.

8. The method of claim 6 that relies on claim 4 or claim 7 that relies on claim 4, wherein the local minimum of the objective function is sought by determining the time instants at which the components of the component set undergo the state transitions of the operation sequence represented by the optimal set of functions.

9. 9. The method of claim 1, wherein the characteristic data further comprises minimum start-up energy data and / or minimum active period data after start-up and / or average maintenance time for at least one component of the set of components.

10. 10. The method of claim 1, wherein the step of repeatedly repeating comprises repeating at discrete regular time intervals.

11. The method of claim 1 , wherein the prediction period is time-dependent.

12. 12. The method of claim 1, further comprising determining the initial portion of the forecast period based on at least a maximum processing capacity of a data processing means executing the method.

13. A data processing system comprising means for carrying out the method of any one of claims 1 to 12.

14. A computer program comprising instructions that, when the program is executed by a computer, cause the computer to carry out the method of any one of claims 1 to 12.

15. 13. A compressed air or gas system configured to be controlled in accordance with the method of any one of claims 1 to 12.

Images