WO2009110900A1

WO2009110900A1 - Mass flow controller employing sliding mode control

Info

Publication number: WO2009110900A1
Application number: PCT/US2008/056005
Authority: WO
Inventors: Bradley C. Glenn; James H. Saunders; Anthony B. Kehoe; Jeffrey L. Whiteley; Todd Berger
Original assignee: Brooks Instrument, Llc
Priority date: 2008-03-06
Filing date: 2008-03-06
Publication date: 2009-09-11

Abstract

A mass flow controller (100) employing sliding mode control (SMC) is provided. The mass flow controller (100) includes a flow sensor (110) configured to generate one or more flow measurements of a fluid flow through the flow controller (100), a control valve (120) configured to control the fluid flow through the flow controller (100), and a controller (130) in communication with the flow sensor (110) and the control valve (120). The controller (130) is configured to receive the one or more flow measurements from the flow sensor (110), process the one or more flow measurements using a sliding mode control algorithm, and generate a valve setting to the control valve (120) in order to achieve a desired flow rate of the flow fluid through the flow controller (100).

Description

MASS FLOW CONTROLLER EMPLOYING SLIDING MODE

CONTROL

Background of the Invention

1. Field of the Invention

The present invention relates to a mass flow controller, and more particularly, to a mass flow controller employing sliding mode control.

2. Statement of the Problem

A mass flow controller is a device that can be used to measure and meter out fluids, including liquids and gases. Mass flow controllers are commonly used in semiconductor fabrication to measure out precise quantities of constituents, such as being used for measuring out quantities of gases for fabrication, for example. A mass flow controller must be able to accurately measure out very small mass quantities, such as precise masses of gas.

One type of mass flow controller is a thermal mass flow controller (TMFC). A TMFC determines a mass flow through a measure of heat transfer. To this end, a TMFC includes a heat source and one or more temperature sensor elements. The TMFC generates heat at one spot in a known fluid flow and measures the heat that is present at other points in the flow. For example, a measurement of the fluid temperature upstream of the heat source can be compared to a measurement of fluid temperature at a location that is downstream of the heat source. This thermal loss characteristic will change depending on the flow rate and the mass of the fluid flow. Therefore, the upstream and downstream temperature measurements can be compared in order to determine the amount of heat being carried away from the heat source, where the heat source generates a known quantity of heat. The TMFC therefore determines a mass flow rate of the fluid by measuring a heat transfer of the fluid. The mass flow measurement can subsequently be used to operate a valve that controls the flow of fluid. Consequently, the mass flow measurement can be used to regulate and meter out the fluid. The metering can be performed as the fluid flows through the mass flow controller. Control and metering of the fluid requires a high level of precision so that an exact amount of fluid is delivered by the mass flow controller. In semiconductor fabrication, for example, very precise levels of constituents are required. Control of the fluid flow needs to be very accurate and substantially instantaneous. In the prior art, control of the fluid flow is performed according to a proportional-integral-derivative (PID) process. The PID control process comprises three value determinations. The proportional (P) value determines the reaction to the current error factor. The integral (I) value determines a reaction value based on the sum of recent errors. The derivative (D) value determines a reaction value to the rate at which the error has been changing. The weighted sum of these three actions is used to adjust the fluid mass flow rate via a control valve. The PID control process reacts to and attempts to correct and/or eliminate a current error factor in order to generate a new valve setting. The PID control can be implemented in specific feedback circuitry or can comprise a general processor programmed according to PID control theory. A PID process control of a mass flow controller in the prior art has several drawbacks. A PID process control comprises reactive control that sees a change in condition and reacts to attempt to resume a previous state or condition. A PID process control for a mass flow controller in the prior art receives a mass flow measurement and a desired setpoint and determines an error factor that comprises a difference between the mass flow measurement and the setpoint. A PID process control attempts to maintain the mass flow measurement at the setpoint. The prior art PID process control does this by introducing a change to the control valve that is designed to eliminate the error factor.

Unfortunately, by looking at only the mass flow measurement, precise control of the fluid flow is difficult to attain. If the PID process control attempts to change the valve enough to completely eliminate the error factor, the PID process control can overshoot and the error factor can go from too much flow to too little flow, for example. Overshoot can lead to additional flow errors and can require multiple changes in the control valve in order to achieve the desired mass flow rate setpoint. Alternatively, if the amount of change in the control valve is conservative in order to avoid overshoot, the amount of valve change can end up being less than what is needed, resulting in undershoot. Undershoot can likewise require multiple changes to the control valve in order to iteratively achieve the mass flow rate setpoint. The multiple control valve changes can require excessive time and can lead to errors in the metered mass or amount of flow fluid. Overshoot and undershoot can both result in an inaccurate metering and delivery of the flow fluid.

Aspects of the Invention

In one aspect of the invention, a mass flow controller employing sliding mode control (SMC) comprises: a flow sensor configured to generate one or more flow measurements of a fluid flow through the flow controller; a control valve configured to control the fluid flow through the flow controller; and a controller in communication with the flow sensor and the control valve, with the controller configured to receive the one or more flow measurements from the flow sensor, process the one or more flow measurements using a sliding mode control algorithm, and generate a valve setting to the control valve in order to achieve a desired flow rate of the flow fluid through the flow controller. Preferably, the flow controller comprises a thermal mass flow controller and with the flow sensor comprising a thermal mass flow sensor configured to measure a thermal loss characteristic of the fluid flow. Preferably, receiving the one or more flow measurements comprises receiving a temperature measurement of the flow fluid, a pressure measurement, and a thermal loss characteristic measurement, and the controller is configured to process the temperature measurement, the pressure measurement, and the thermal loss characteristic measurement using the sliding mode control algorithm in order to generate the valve setting.

Preferably, the sliding mode control algorithm includes a mechanical model. Preferably, the sliding mode control algorithm includes an electrical model. Preferably, the sliding mode control algorithm includes a fluid model. Preferably, the sliding mode control algorithm includes a fluid model including viscous flow modeling.

Preferably, the sliding mode control algorithm includes a thermal model. Preferably, the fluid model accounts for factional and/or turbulent losses in the flow controller.

Preferably, the fluid model accounts for factional and/or turbulent losses in an orifice of the control valve.

Preferably, the sliding mode control algorithm models the flow through the

orifice according to m_onfice = CA^Ip₁P₁ / ^pιf'^{k ~} (^P ₂ ' ?i )^(k+X)'^k ] •

Preferably, the sliding mode control algorithm accommodates a plurality of gases.

In one aspect of the invention, a mass flow control method comprises: receiving one or more flow measurements of a flow fluid from a mass flow sensor; processing the one or more mass flow measurements using a sliding mode control algorithm; and generating a valve setting to a control valve using the sliding mode control algorithm. Preferably, the flow sensor comprises a thermal mass flow sensor configured to measure a thermal loss characteristic of the fluid flow.

Preferably, receiving the one or more flow measurements comprises receiving a temperature measurement of the flow fluid, a pressure measurement, and a thermal loss characteristic measurement, and the processing further comprises processing the temperature measurement, the pressure measurement, and the thermal loss characteristic measurement using the sliding mode control algorithm in order to generate the valve setting.

Preferably, the sliding mode control algorithm includes a mechanical model. Preferably, the sliding mode control algorithm includes an electrical model. Preferably, the sliding mode control algorithm includes a fluid model.

Preferably, the sliding mode control algorithm includes a fluid model including viscous flow modeling.

Preferably, the sliding mode control algorithm includes a thermal model. Preferably, the fluid model accounts for factional and/or turbulent losses in the mass flow sensor and/or in the control valve. Preferably, the fluid model accounts for factional and/or turbulent losses in an orifice of the control valve.

Preferably, the sliding mode control algorithm models the flow through the

orifice according to m_onflce = CA^2_PiP_i{^[{PJ P_vγ^lk - {P₂ I P_v)^{k+l)lk \ .

Preferably, the method further comprises iteratively performing the receiving, processing, and generating.

Description of the Drawings

FIG. 1 shows a mass flow controller according to an embodiment of the invention.

FIG. 2 shows detail of the mass flow sensor according to an embodiment of the invention. FIG. 3 is a model of the control valve according to an embodiment of the invention.

FIG. 4 is a three-dimensional graph showing an orifice discharge coefficient (C_d) versus Reynolds number and versus the non-dimensional displacement of the valve plunger. FIG. 5 is a flowchart of a mass flow control method according to an embodiment of the invention.

FIG. 6 is a process flow diagram showing the processes of a SMC routine according to an embodiment of the invention.

FIG. 7 is a flowchart of a mass flow control method according to an embodiment of the invention.

Detailed Description of the Invention

FIGS. 1-7 and the following description depict specific examples to teach those skilled in the art how to make and use the best mode of the invention. For the purpose of teaching inventive principles, some conventional aspects have been simplified or omitted. Those skilled in the art will appreciate variations from these examples that fall within the scope of the invention. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of the invention. As a result, the invention is not limited to the specific examples described below, but only by the claims and their equivalents. FIG. 1 shows a mass flow controller 100 according to an embodiment of the invention. The mass flow controller 100 includes conduits 102, 103, and 104 that can conduct a fluid, including a liquid or a gas. The term fluid is used to describe any type of matter in any state that is capable of flow. It is to be understood that the term fluid applies to liquids, gases, and slurries comprising any combination of matter or substance to which controlled flow may be of interest. The mass flow controller 100 therefore can be located in a conduit and can regulate the delivery of the associated flow fluid.

The mass flow controller 100 includes a mass flow sensor 110, a control valve 120, and a controller 130. The mass flow sensor 110 and the control valve 120 can include the conduits 102, 103, and 104 and can regulate the fluid flow between the conduits 102 and 104.

It should be understood that the fluid flow can move through the mass flow controller 100 in either direction. Consequently, the mass flow sensor 110 can be located either upstream or downstream of the control valve 120.

The controller 130 performs an overall control process. The controller 130 is in communication with the mass flow sensor 110 and the control valve 120. The controller 130 receives measured values from the mass flow sensor 110. The controller 130 sends control signals to the control valve 120, such as a valve setting. Consequently, the controller 130 is configured to determine a fluid flow rate in the mass flow controller 100 and actuates the control valve 120 in order to achieve a predetermined mass flow rate of the flow fluid.

The controller 130 can include a processing system 132. The processing system 132 can include a storage system 133. The storage system 133 can include a fluid temperature value 150, a fluid pressure value 151, a fluid thermal loss characteristic (TL) 152, a sliding mode control routine 153, a mass flow rate setpoint 154, and a valve setting 155. The storage system 133 can further include at least a fluids model 158, a mechanical model 156, and electrical model 157. Other variables and/or data structures can be included, and the above listing should not be construed as exhaustive. The mass flow sensor 110 can comprise any manner of mass flow sensor capable of measuring at least the fluid temperature (T), fluid pressure (P), and fluid thermal loss characteristic (TL) of the fluid flow. For example, the mass flow sensor 110 can comprise a thermal mass flow sensor that measures a mass flow rate ( m_semor ) by measuring and quantifying the thermal loss characteristic (TL) of the flow fluid.

In many mass flow controllers, a thermal mass flow sensor is used that includes a first temperature-sensing element positioned upstream of a heater element and a second temperature-sensing element positioned downstream of the heater element. The heater element heats the fluid. If the fluid is moving, some of the heat is moved away from the first temperature-sensing element and is moved downstream to the second temperature- sensing element, changing temperature measurements generated by the first temperature-sensing element and the second temperature-sensing element. Therefore, the cooling is affected by the mass flow rate of the fluid, wherein a thermal loss characteristic (such as a temperature difference between the first and second temperature-sensing elements) is related to the mass flow rate. Consequently, the sensed temperature difference is proportional to the mass flow rate of the fluid flowing through the mass flow sensor. In some embodiments, the first and second temperature- sensing elements comprise resistive elements that are wound about a sensor or bypass conduit at spaced-apart positions, each having a resistance that varies with temperature. However, other mass flow sensors are contemplated and are within the scope of the description and claims.

In some embodiments, the flow sensor 110 can include a bypass loop or passage 212, wherein only a portion of the flow is measured (see FIG. 2). The measurement of flow through the bypass passage 212 can be used to interpret or determine the flow rate of the full flow through the flow sensor 110.

The control valve 120 can comprise any manner of valve capable of being controlled by the controller 130. For example, the control valve 120 can comprise a solenoid valve. Alternatively, the control valve 120 can comprise a piezoelectric actuator or stepper actuator. However, other control valves are contemplated and are within the scope of the description and claims. The control valve 120 is modeled using models for the mechanical dynamics, the electrical dynamics, and the fluid dynamics. Each of these modeling processes is discussed separately below.

The fluid temperature value 150 can comprise a fluid temperature measurement received from the mass flow sensor 110. Likewise, the fluid pressure value 151 and the fluid thermal loss characteristic (TL) 152 can also be generated by and received from the mass flow sensor 110. These three values 150-152 comprise quantifications of the fluid flow through the mass flow controller 100.

The valve setting 155 comprises a valve actuation command that is transferred to the control valve 120 by the controller 130. The valve setting 155 therefore comprises a setting for the control valve 120 that achieves a proper fluid flow rate.

The fluids model 158, the mechanical model 156, and the electrical model 157 comprise models that are used by the sliding mode control routine 153 (see the discussion accompanying FIGS. 5-7). The models 156 through 158 are used to model the actions and reactions of the mass flow controller 100. The models can be used to model and predict operation of the mass flow controller 100. The models therefore can be used to generate the valve setting 155. Each of these models includes data that reflects the operation of and characteristics of the mass flow controller 100. The models can model the type and composition of the fluid, including characteristics such as density, viscosity, etc. The models can model changes in fluid characteristics with flow rate, pressure, temperature, and others. The models can model changes in fluid characteristics per the geometry of the mass flow sensor 110 and the control valve 120, including flow geometries, flow type/turbulence considerations, fluid viscosity, expansion/compression through the mass flow controller 100, and others. The models can model mechanical characteristics of the control valve 120, including reaction times, mechanical damping characteristics, opening/closing forces, opening/closing speeds, turbulent flow considerations, and others. The models can model electrical characteristics, including valve actuation current requirements, coil current levels versus actuation force, coil current levels versus actuation speeds, and others. It should be understood that the above listing is not exhaustive and other characteristics can alternatively or additionally be included in the modeling of the mass flow controller 100. The sliding mode control routine 153 can be executed by the processing system 132 in order to operate the controller 130. The sliding mode control routine 153 can receive data inputs from the flow sensor 110 and can generate data outputs to the control valve 120. The output includes the valve setting 155 that controls the actuation of the control valve 120. The sliding mode control routine 153 interacts with the fluids model 158, the mechanical model 156, and the electrical model 157 in order to generate and refine the valve setting value 155. The valve setting 155 therefore can control the amount of opening, rate of opening, etc., of the control valve 120. The valve setting 155 therefore can control the mass flow rate (m_sensor ) of the fluid flow through the mass flow controller 100.

In control theory, sliding mode control is a type of variable structure control where the dynamics of a non-linear system are altered via the application of a high- frequency switching control. This is a state feedback control scheme where the feedback is not a continuous function of time. The sliding mode control scheme involves following two basic steps. The first step comprises the selection of a hypersurface or a manifold such that the system trajectory exhibits desirable behavior when confined to this manifold. The second step comprises finding feedback gains so that the system trajectory intersects and stays on the manifold. The mass flow controller 100 according to an embodiment of the invention models the complete fluids system, unlike the prior art. In the prior art, such as in U.S. Patent No. 6,962,164 to Lull, only the valve orifice is modeled. The assumption in Lull is that modeling of fluid flow through just the valve orifice is satisfactory to accurately simulate the entire flow through a flow controller. In the prior art, controllers typically generate a gain value that is used to activate the solenoid valve (see equations 5 and 6 of Lull, col. 38, lines 48-57). The gain is used to force the error toward zero. Consequently, the larger the error (i.e., the larger the difference between the actual flow rate and the desired flow rate), then the larger the gain. The sliding mode control algorithm according to the invention is not merely a gain value. The sliding mode control algorithm according to the invention can take into account outside events and disturbances, wherein the sliding mode control algorithm can be at least partially predictive. In addition, the sliding mode control algorithm can take into account factors not included in a gain value, such as upstream and downstream fluid effects, including fluid drag, turbulence, and viscosity, for example.

The Lull patent breaks the orifice loss up into two terms, a viscous parallel plate pressure loss term (equation 1, see col. 36, line 41), and an inviscid pressure drop term at the orifice exit (equations 2 or 3, see col. 37, lines 2 and 8). The parallel plate (or viscous drag) term accounts for the pressure loss between the gap existing between the bottom of the valve plunger and the land area surrounding the valve orifice (see FIG. 16 of Lull). With the gap pressure loss accounted for, the Lull patent then uses the compressible form of Bernoulli's Equation (equations 2 or 3) to convert the pressure energy into kinetic energy (or mass flow). This pressure conversion process assumes that fluid friction is NOT present in the region downstream of the orifice. However, the assumption of frictionless flow is not valid.

In a real flow, the frictionless flow must be multiplied by an orifice discharge coefficient (C_d) to account for the internal viscous fluid losses, i.e., not all of the pressure is converted into kinetic energy or mass flow. For fully turbulent flows, the orifice discharge coefficient (C_d) is approximately (0.75). In flows which are not fully turbulent, the discharge coefficient becomes a function of the flow rate itself (or, more precisely, the Reynolds number). The Reynolds number dependence (and further a valve plunger height dependence) is accounted for herein by additional (and more thorough and complete) modeling. The modeling used herein employs a compressible orifice flow equation to model the fluid flow through the valve orifice (see Equation (9), below).

FIG. 2 shows detail of the mass flow sensor 110 according to an embodiment of the invention. In this embodiment, a main passage 211 extends between the conduit 102 and the conduit 103. In addition, a bypass passage 212 is connected to the main passage 211 at two locations and conducts a portion of the total gas flow. It should be understood that the bypass passage 212 is an optional feature and may not be included in all embodiments. Because the dimensions of the bypass passage 212 are known, a measurement of flow through the bypass passage 212 can be interpolated or processed in order to determine the overall flow through the mass flow sensor 110. To that end, a sensor 220 can be located on the bypass passage 212. The sensor 220 can perform any desired measurements, including mass and/or volume flow rate. In addition, the mass flow sensor 110 can include temperature and pressure sensors to measure a fluid thermal loss characteristic and a fluid pressure. FIG. 3 is a model of the control valve 120 according to an embodiment of the invention. In the figure, the flow path for the mass flow controller 100 is modeled as a tank with one inlet and one outlet. There is a porous media element 302 at the inlet and an orifice 304 at the outlet, modeling the control valve 120. The porous media element 302 models a laminar flow element (LFE). LFEs are used in flow bypass implementations, such as shown in FIG. 2, where a portion of the flow is measured in a bypass tube or conduit 212. A LFE is necessary in order to generate a pressure drop across the upstream and downstream ends of the bypass conduit 212, thereby forcing some of the flow through the sensor conduit. The fluid flow first passes through the porous media element 302 and into the internal volume. The flow then exits through the orifice 304 on the right side of the drawing. The orifice 304 can be blocked or unblocked by a plunger 306. The flow through the restrictor/porous media element can safely be assumed to be laminar flow. The pressure drop across the orifice 304 will be calculated via an orifice discharge coefficient and adiabatic expansion of the gas.

FLUID DYNAMICS

A simple linear equation can be used to model the laminar flow through a porous media element, used as an analogue for the air resistance through the system):

Where the ( ΔP_PM ) term is the pressure drop across the porous media element, the ( Q_act ) term is the actual gas flow through the porous media, the ( μ ) term is an absolute gas viscosity, and the (K) term is a porous media constant.

The pressure drop across the orifice is easily modeled via the orifice coefficient equation, which can be derived from fundamental first principles of one-dimensional compressible flow theory. The resulting equation for the non-choked (i.e., sub-sonic) flow of real gases through an orifice is:

m orifice = (2)

Where the ( m_onflce ) term is the mass flow rate (such as in kg/s) exiting the orifice, the ( C) term is the orifice flow coefficient (dimensionless), the ( A ) term is the cross- sectional area of the orifice (such as in m²), the (p_γ ) term is the upstream real gas density (in kg/m³), the (P₁) term is the upstream gas pressure (i.e., Pa, such as in kg/(m*s)), the (k ) term is the Ideal Gas specific heat ratio, the (P₂) term is the downstream gas pressure in the orifice (i.e., Pa, such as in kg/(m*s)), and the (T₁) term is the absolute upstream gas temperature (in degrees Kelvin).

When the gas velocity is choked, i.e., where P_out/P_m is less than or equal to P_cπti_cai,

where P_cπtlcal , the equation for the mass flow rate is:

The above explanation uses an upstream-to-downstream pressure ratio. It is not uncommon in the art for the above relationship to alternatively be expressed as a downstream-to-upstream pressure ratio. Either convention is accepted, but the notation must be consistently used. Choked flow refers to the situation in which the flow has attained sonic velocity.

This can occur in both fully and partially open plunger situations. Assuming ideal gas behavior, steady state choked flow occurs when the ratio of the absolute upstream

pressure to the absolute downstream pressure is equal to or greater than

where k is the specific heat ratio of the gas (sometimes called the isentropic expansion factor and denoted as (γ). For many gases, (k) ranges from about 1.09 to about 1.41,

and therefore ranges from 1.7 to about 1.9, which means that choked

flow usually occurs when the absolute source vessel pressure is at least 1.7 to 1.9 times as high as the absolute downstream pressure.

If desired, the inlet density in Equations (2) and (3) can be eliminated via an Ideal Gas Law, and the Ideal Gas law limitation can be obviated via the compressibility factor. This results in equations that are equivalent to Equations (2) and (3) but different in form. Conservation of mass can be used to develop a transient fluids model for the flow geometry depicted in FIG. 3. The resulting equation, dM/dt = [MassFlowln - MassFlowOut], can be simplified by application of Equations (1-3) and the Ideal Gas Law, resulting in:

P , ( R * T , * M λ

Where the ( dM I dt ) term is rate of change of mass within the body, the ( P_mlet ) term is inlet pressure to the body, the ( T_mlet ) term is the inlet gas temperature, the ( M ) term is instantaneous mass within the body, the ( V ) term is the internal storage volume of the body, the ( m_onfice ) term is the orifice mass flow rate (obtained from Equations (2) or (3), as appropriate), the ( k ) term is a restrictor porous media constant, and the ( μ ) term is the absolute gas viscosity. As with Equations (2) and (3) the limitations imposed by the Ideal Gas Law in Equation (4) can be obviated via use of the compressibility factor.

In most applications turbulent flow is assumed for the orifice discharge coefficient and the orifice discharge coefficient is assumed to be independent of plunger position (i.e., a "full open" plunger). This situation is generally not present in most operating flow controllers, so the orifice discharge must be modified to account for both Reynolds number and plunger height (gap) dependencies. Both effects can be accounted for, to within a reasonable approximation, via similitude, i.e., dimensional analysis.

Combining the power of dimensional analysis with a combination of experimental and numerical data, the orifice discharge coefficient ( C _d ) can be correlated as function of both the Reynolds Number and the dimensionless plunger position. The particular form used for the product is: C_d = a * (l - e-^ )* Re^fe (5)

Where the ( Re ) term is Reynolds number and is based on the actual orifice diameter, the (a ) term is a fit coefficient that is strictly a function of the dimensionless plunger displacement (x_d), the (b ) term is a fit coefficient that is strictly a function of the dimensionless plunger displacement (x_d), the ( k ) term is a fit coefficient that is strictly a function of the dimensionless plunger displacement (x_d), and the (x_d) term is the dimensionless plunger displacement [i.e., (actual plunger displacement)/(orifice diameter)].

Two different functional forms were chosen to fit ( a ) and ( b ). For ( a ), the function form is a sigmoid, while a modified power law fit was use for the ( b ) term, i.e.: a_t - a_h , _Λ a = ^ + _{1 +} ;₍^_)/w (6) and:

b = b_n * l + b, * x. V)

Where the (a_b) term can be a numerical value of about (-0.0616), the (a_t) term can be a numerical value of about (0.92437), the (x₀) term can be a numerical value of about (0.12071), the (w) term can be a numerical value of about (0.05714), the (b₀) term can be a numerical value of about (0.39045), the (b^ term can be a numerical value of about (13.16144), the (b₂) term can be a numerical value of about (0.79720), and the (k) term can be a numerical value of about (-3.72947). It should be understood that the above functional fit for C_d, and the associated numerical coefficients, represent only one particular embodiment. The form of the C_d fit and/or associated numerical coefficients can be varied as needed.

The control objective is to regulate mass flow in the presence of source pressure perturbations. For now, it is assumed that coil voltage of the solenoid valve is the control input. Recalling the equations of motion that describe the entire system are as follows:

X₁ = x₂ (8)

I = J. !L₁- VgL_xJ (H)

L(x) L(x) dx

The variable (e) is introduced as the error between the actual mass flow and the desired or setpoint of the device. The following sliding surface is defined as: s = k_le + k₂e + e (12)

or:

^■ _ d ^Um^m _ss_ee_nn_sSoo_rr ^ ^■ _} , d ^um^ln _ss_ee_nn_ss_oo_rr R ^JWT P ^λ_₁m_n f D __ R ^JWT\ m, Juf \ _ _m ( r n \ \ ( ] ά\ dx dp_dv V {RT_mμκ [ ^m V

The control is chosen as [V = Vsign(s)] where V is the valve coil voltage and when the sliding mode is enforced, s=0, and: e = -k_ιe- k₂έ (16)

The (Ic₁) and (k₂) terms are design constants chosen as the desired convergence rate of the controller 130. It should be understood that the sliding surface (s) is a function of (m ), (X₁), (x2), (p_dv), and (p_in). However, the only measured variables are the mass flow rate of fluid ( m_sensor , the mass flow rate obtained from the mass flow sensor 110 which will include any necessary adjustments to account for the flow bypass 212 if present), the inlet pressure (p_in), and the electrical current (i), thus motivating the need for observers in the system in order to determine the valve plunger displacement (x). Observers are mathematical relationships used to obtain the value for process control variables that are not directly measured. For example, the system can measure the inlet pressure and not the dead volume pressure (the dead volume pressure is the upstream pressure for the orifice). Equation (19) below is an observer equation that can be solved to obtain the dead volume pressure, without measurement of the dead volume pressure. However, the dead volume pressure is needed in order to predict the flow through the orifice.

OBSERVER DESIGN

P_dv -h(m_onfice -m_onfiJ (19)

Where the (^Λ) symbol denotes the state estimates, the (I₁, I₂, I₃, and I₄) terms are design constants, and the (m_onfice ) term is an estimate of the flow rate using the orifice equations, i.e., equations (2-7).

MECHANICAL DYNAMICS

Mechanically, the control valve 120 is modeled as a mass spring damper system. It is necessary to include the spring compression preload on the valve plunger to properly characterize the opening current (i) of the valve. In order to do so, the following variables are introduced: x, the relative position of the plunger and X_p, the relative position of the seat of the upper guide spring. Both positive directions are device as upward. Therefore, the mechanical dynamics can be described as:

MX = F_MAG +K_u (x_p - x) - K_Lx -Bx (21)

x = ^ + ^(x -x) -^x--x (22) m m m m To match the opening current of the coil to the model, it is necessary to find the initial position of the upper guide spring seat X_p0. To do so, set Equation (21) equal to zero in order to generate:

" ⁼ ^ MAG + ^u \^Xp ^{~ X}SEΛT ) ^~ "^L^XSEΛT \^^J

Where: F T_^UAr = 1 ^ 1 -2 = 1 ^-1 T-i-2 ( /2/-.4 Λ \)

2 ox 2 (C₂ - airgap) and where C₁ and C₂ are empirical constants determined from data. K_u is the upper guide spring constant, K_L is the lower guide spring constant, B is a damping coefficient, and X_SEAT is the amount the plunger lower guide spring is compressed at the initial condition. Therefore, an arbitrary X_SEAT is defined which will vary with each lower guide spring and can solve for an initial (x_po), the amount the upper guide spring is compressed in the initial state. 1 C γ _ ^~ ^ 27 (^C₂ -ai ■rgap ^) ^'° ^{+ K}» (^X*MT ) + ^KL^XSEAT

^Xp0 ^~ _κ \^ZJ) Where i₀ is the opening current for the control valve 120 and the air gap is chosen to be about 0.025 inch, the maximum travel of the valve plunger. This assures that the control valve 120 opens at the correct opening current.

ELECTRICAL DYNAMICS

* =J-(v -iR -i^) (26)

Where the (i) term is the electrical current in the solenoid, the (V) term is the voltage, the (R) term is the electrical resistance, and the (L) term is the inductance, and where: L(X) = —Q — (27)

(C₂ - X)

FIG. 4 is a three-dimensional graph showing the orifice discharge coefficient (C_d) versus Reynolds number and versus the non-dimensional displacement of the valve plunger (i.e., the plunger height). The orifice discharge coefficient (C_d) depicted in this figure includes both the parallel plate pressure drop and the orifice loss term. Combining the parallel plate pressure drop and orifice loss terms into one single term is strictly valid only for incompressible flow. However, as the SMC algorithm only needs a reasonably accurate representation of the solution manifold, the incompressible orifice coefficient will work well when used for implementing the SMC algorithm in incompressible flow. FIG. 5 is a flowchart 500 of a mass flow control method according to an embodiment of the invention. In step 501, one or more flow measurements are received from a mass flow sensor. For example, a fluid temperature measurement, a fluid pressure measurement, and a fluid thermal loss characteristic can be received from the mass flow sensor. The one or more flow measurements can comprise measurements of a fluid flow through the mass flow controller 110. However, other and/or additional measurements of the fluid flow can be employed.

In step 502, the one or more flow measurements are processed using a sliding mode control routine/algorithm. The sliding mode control routine comprises a predictive algorithm that takes into account multiple factors. The sliding mode control routine can include processing the one or more flow measurements in order to predict fluid flow characteristics and processing to predict valve operational characteristics, including mechanical dynamics and electrical characteristics, such as characteristics of an electrically actuated control valve and magnetic characteristics of an electrical/magnetic actuator device. In step 503, a valve setting is generated to the control valve. The valve setting comprises a valve actuation position for the control valve. The valve setting can further include a valve actuation speed, if desired. The valve setting therefore comprises a valve actuation that can be employed to achieve a desired mass flow rate through the mass flow controller. FIG. 6 is a process flow diagram showing the processes of the SMC routine 153 according to an embodiment of the invention. The process flow diagram of this figure shows detail of the SMC processing, such as in steps 502 of FIG. 5, above, and in step 704 of FIG. 7, below. The process flow diagram shows an electrical subsystem process 64, a mechanical subsystem block 65, a thermal sensor subsystem block 66, a fluids subsystem block 67, a control subsystem block 68, and a difference block 69. The process flow diagram further shows an analog-to-digital (AJO) conversion block 61 and a digital-to-analog (D/ A) conversion block 62.

The A/D conversion block 61 receives and digitizes a supply pressure input (Supply Pressure), i.e., a pressure upstream of the control valve 120. The A/D conversion block 61 receives and digitizes a thermal loss characteristic (Thermal

Sensor) which varies according to the mass flow rate and is used to determine the mass flow rate. The A/D conversion block 61 receives and digitizes a valve current consumption measurement (Valve current) of the electrical current consumed by the control valve 120. The A/D conversion block 61 receives and digitizes a mass flow rate setpoint (Massflow SP). The supply pressure measurement and the thermal loss characteristic are received from the mass flow sensor 110. The valve current consumption measurement can be measured by the control valve 120 or can be measured by another component, such as by the controller 130, for example. The mass flow rate setpoint (Massflow SP) comprises a desired or predetermined mass flow rate. The mass flow rate setpoint (Massflow SP) can be stored in the controller 130. The mass flow rate setpoint (Massflow SP) can be calculated or derived by the controller 130. The mass flow rate setpoint (Massflow SP) can be inputted into the controller 130 by an operator or can be received from another device, for example.

The D/ A conversion block 62 receives a measured mass flow rate (Massflow Indicator) and a valve setting/command (Valve Command) and generates and outputs analog versions of both values. Alternately, inputs and outputs to and from the thermal mass flow controller can be of a different physical form or format, such as digital communications or pulse- width modulation protocols.

The electrical subsystem block 64 receives as inputs a plunger displacement (x), a valve plunger speed (dx/dt), a voltage (V) of an electromagnet component of the control valve 120, and an electrical current (current) of the electromagnet component. The voltage (V) and electrical current (current) can comprise measured values while the plunger displacement (x) and valve plunger speed (dx/dt) values can comprise calculated or determined values. The electrical subsystem block 64 processes the plunger displacement (x), the valve plunger speed (dx/dt), the voltage (V), and the electrical current (current) in order to determine a magnetic force value (fmag) that represents the magnetic force generated on the valve plunger by the electromagnet component of the control valve 120. The electrical subsystem block 64 subsequently generates as output the magnetic force value (fmag).

The mechanical subsystem block 65 receives as inputs a magnetic force value (fmag) from the electrical subsystem block 64 and a mass flow error (MF error) from the difference block 69. The mass flow error (MFerror) comprises an error difference between the mass flow estimate (Massflow Est) and the measured mass flow (Massflow), which comprises a difference between the mass flow rate that is supposed to be occurring as compared to the mass flow rate as it is being measured. The mechanical subsystem block 65 processes the received magnetic force value (fmag) in order to determine the plunger displacement (x) and in order to determine a valve plunger speed (dx/dt). The mechanical subsystem block 65 processes the received mass flow error (MFerror) using a mechanical model. The mechanical subsystem block 65 further determines from the mechanical model how to move the valve plunger. The mechanical subsystem block 65 subsequently generates as outputs the valve plunger speed (dx/dt), the valve plunger position (Valve Position), and the plunger displacement (x). The plunger displacement (x) comprises a distance the valve plunger has moved closing- wise from a fully open position where the control valve 120 is a normally-open (NO) type valve. Alternatively, the plunger displacement (x) comprises a distance the valve plunger has moved opening-wise from a fully closed position where the control valve 120 is a normally-closed (NC) type valve.

The thermal sensor subsystem block 66 receives as an input the digital thermal loss characteristic (TL) outputted by the A/D conversion block 61. The thermal sensor subsystem block 66 processes the thermal loss characteristic (TL) in order to determine the measured mass flow rate (Massflow) of the fluid (i.e., m_semor ). The processing can include employing a thermal model of the fluid in order to generate the measured mass flow rate (Massflow) from the thermal loss characteristic (TL). The thermal sensor subsystem block 66 subsequently generates and outputs the measured mass flow rate (Massflow) representative of a fluid mass flow through the mass flow sensor 110. The fluids subsystem block 67 receives as inputs the valve plunger position (Valve Position) generated by the mechanical subsystem block 65, a fluid supply pressure (Psupply) from the pressure sensor, and a measured mass flow rate (Flow or Massflow). The fluids subsystem block 67 processes the valve plunger position (Valve Position), the fluid supply pressure (Psupply), and the measured mass flow rate (Flow) in order to determine an estimated mass flow rate (Massflow Est) for the current value of the valve plunger position (Valve Position). The fluids subsystem block 67 subsequently generates as an output the mass flow rate estimate (Massflow Est). Consequently, when the commanded valve position changes, the estimated mass flow rate (Massflow Est) will be updated. The mass flow rate estimate (Massflow Est) comprises an estimated mass flow rate for a newly calculated valve setting/command being sent to the control valve 120.

The control subsystem block 68 receives as inputs the measured mass flow rate (Massflow) and the mass flow rate setpoint (FlowSP). The control subsystem block 68 processes the measured mass flow rate (Massflow) and the mass flow rate setpoint (FlowSP) in order to determine a valve setting for commanding the control valve 120. The control subsystem block 68 subsequently generates and outputs a valve setting/command (Vcmd) that is destined for the control valve 120. The valve setting/command (Vcmd) includes a valve current specification that controls a valve position/opening.

The difference block 69 generates a mass flow difference or error signal (MFerror) between the estimated mass flow rate (Massflow Est) generated based on the commanded valve plunger position and the measured mass flow rate (Massflow) as measured from the thermal loss characteristic detected in the mass flow sensor 110.

FIG. 7 is a flowchart 700 of a mass flow control method according to an embodiment of the invention. In step 701, a fluid temperature measurement is received. The fluid temperature measurement comprises a temperature (T) of the fluid as it flows through the mass flow sensor.

In step 702, a fluid pressure measurement is received. The fluid pressure measurement comprises a pressure (P) of the fluid as it flows through the mass flow sensor.

In step 703, a fluid thermal loss characteristic measurement is received from the mass flow sensor. The fluid thermal loss characteristic measurement comprises a temperature loss in the fluid substantially due to the mass flow rate of the fluid.

In step 704, the fluid temperature measurement, the fluid pressure measurement, and the fluid thermal loss characteristic measurement are processed with a sliding mode control algorithm/routine in order to generate a valve setting. The sliding mode control algorithm can comprise one or more models, as previously discussed. A model can include modeling of various characteristics of the mass flow sensor, including characteristics of both a mass flow sensor and an associated control valve. Processing these measurements with a model, including a model for fluid dynamics, mechanical dynamics, and/or electrical dynamics provides a predictive function of mass flow rate for a valve actuation. Processing these measurements with a model provides a highly accurate valve setting. The valve setting comprises a setting or actuation level for the control valve in order to achieve a predetermined mass flow rate through the mass flow controller.

In step 705, the generated valve setting is transferred to the control valve. The control valve will be subsequently actuated according to the valve setting. The control valve will control the mass flow rate of the flow fluid through the mass flow controller.

Claims

What is claimed is:

1. A mass flow controller (100) employing sliding mode control (SMC), comprising: a flow sensor (110) configured to generate one or more flow measurements of a fluid flow through the flow controller (100); a control valve (120) configured to control the fluid flow through the flow controller

(100); and a controller (130) in communication with the flow sensor (110) and the control valve (120), with the controller (130) configured to receive the one or more flow measurements from the flow sensor (110), process the one or more flow measurements using a sliding mode control algorithm, and generate a valve setting to the control valve (120) in order to achieve a desired flow rate of the flow fluid through the flow controller (100).

2. The mass flow controller (100) of claim 1, with the flow controller (100) comprising a thermal mass flow controller (100) and with the flow sensor (110) comprising a thermal mass flow sensor (110) configured to measure a thermal loss characteristic of the fluid flow.

3. The mass flow controller (100) of claim 1, with receiving the one or more flow measurements comprising receiving a temperature measurement of the flow fluid, a pressure measurement, and a thermal loss characteristic measurement, wherein the controller (130) is configured to process the temperature measurement, the pressure measurement, and the thermal loss characteristic measurement using the sliding mode control algorithm in order to generate the valve setting.

4. The mass flow controller (100) of claim 1, with the sliding mode control algorithm including a mechanical model.

5. The mass flow controller (100) of claim 1, with the sliding mode control algorithm including an electrical model.

6. The mass flow controller (100) of claim 1, with the sliding mode control algorithm including a fluid model.

7. The mass flow controller (100) of claim 1, with the sliding mode control algorithm including a fluid model including viscous flow modeling.

8. The mass flow controller (100) of claim 1, with the sliding mode control algorithm including a thermal model.

9. The mass flow controller (100) of claim 1, wherein the fluid model accounts for frictional and/or turbulent losses in the flow controller (100).

10. The mass flow controller (100) of claim 1, wherein the fluid model accounts for frictional and/or turbulent losses in an orifice (304) of the control valve (120).

11. The mass flow controller (100) of claim 1, wherein the sliding mode control algorithm models the flow through the orifice (304) according to

m orifice = .

12. The mass flow controller (100) of claim 1, wherein the sliding mode control algorithm accommodates a plurality of gases.

13. A mass flow control method, comprising: receiving one or more flow measurements of a flow fluid from a mass flow sensor; processing the one or more mass flow measurements using a sliding mode control algorithm; and generating a valve setting to a control valve using the sliding mode control algorithm.

14. The method of claim 13, with the flow sensor comprising a thermal mass flow sensor configured to measure a thermal loss characteristic of the fluid flow.

15. The method of claim 13, with receiving the one or more flow measurements comprising receiving a temperature measurement of the flow fluid, a pressure measurement, and a thermal loss characteristic measurement, with the processing further comprising processing the temperature measurement, the pressure measurement, and the thermal loss characteristic measurement using the sliding mode control algorithm in order to generate the valve setting.

16. The method of claim 13, with the sliding mode control algorithm including a mechanical model.

17. The method of claim 13, with the sliding mode control algorithm including an electrical model.

18. The method of claim 13, with the sliding mode control algorithm including a fluid model.

19. The method of claim 13, with the sliding mode control algorithm including a fluid model including viscous flow modeling.

20. The method of claim 13, with the sliding mode control algorithm including a thermal model.

21. The method of claim 13, wherein the fluid model accounts for frictional and/or turbulent losses in the mass flow sensor and/or in the control valve.

22. The method of claim 13, wherein the fluid model accounts for frictional and/or turbulent losses in an orifice of the control valve.

23. The method of claim 13, wherein the sliding mode control algorithm models the

flow through the orifice according to m_onfice = G^p₁P₁ (-^-)[(P₂ /P₁)²'* -(P₂ /P₁)^⁺¹*'*

V ft — 1

24. The method of claim 13, wherein the sliding mode control algorithm accommodates a plurality of gases.

25. The method of claim 13, further comprising iteratively performing the receiving, processing, and generating.