Intro4u2u

KALMAN FILTERS

The purpose of a Kalman filter is to estimate the state of a system from meaurements which contain random errors. An example is estimating the position and velocity of a satelite from radar data. There are 3 components of position and 3 of velocity so there are at least 6 variables to estimate. These variables are called state variables. With 6 state variables the resulting Kalman filter is called a 6 dimensional Kalman filter.

In this introduction, we will start with a much simpler problem. We will start with a one dimensional Kalman filter. In other words we will assume we have only one variable to estimate.

This is a much easier problem to understand than the higher dimensional Kalman filter. It is very instructive to study this simpler example because you can intuitively see the reasoning behind the Kalman filter. Later this intuitive understanding will help in grasping what is going on in the more complicated filters.

You will notice that since I am typing this with a text editor, I cannot use subscripts, superscripts, greek letters etc. If you would prefer to see these lessons in the more usual math format and notation send an e mail to:

PDJoseph@compuserve.com

I will E mail you the first the first 4 lessons typed in Word using the Microsoft equation editor.

INTRODUCTORY LESSON

The one dimensional Kalman Filter

Suppose we have a random variable x(t) whose value we want to estimate at certain times t0 ,t1, t2, t3, etc. Also, suppose we know that x(tk) satisfies a linear dynamic equation

x(tk+1) = Fx(tk) + u(k) (the dynamic equation)

In the above equation F is a known number. In order to work through a numerical example let us assume F= 0.9

Kalman assumed that u(k) is a random number selected by picking a number from a hat. Suppose the numbers in the hat are such that the mean of u(k) = 0 and the variance of u(k) is Q. For our numerical example, we will take Q to be 100.

u(k) is called white noise, which means it is not correlated with any other random variables and most especially not correlated with past values of u.

In later lessons we will extend the Kalman filter to cases where the dynamic equation is not linear and where u is not white noise. But for this lesson, the dynamic equation is linear and w is white noise with zero mean.

Now suppose that at time t0 someone came along and told you he thought x(t0) = 1000 but that he might be in error and he thinks the variance of his error is equal to P. Suppose that you had a great deal of confidence in this person and were, therefore, convinced that this was the best possible estimate of x(t0). This is the initial estimate of x. It is sometimes called the a priori estimate.

A Kalman filter needs an initial estimate to get started. It is like an automobile engine that needs a starter motor to get going. Once it gets going it doesn’t need the starter motor anymore. Same with the Kalman filter. It needs an initial estimate to get going. Then it won’t need any more estimates from outside. In later lessons we will discuss possible sources of the initial estimate but for now just assume some person came along and gave it to you.

So we have an estimate of x(t0),which we will call xe. For our example

xe = 1000.

The variance of the error in this estimate is defined by

P = E [(x(t0) -xe)2]

where E is the expected value operator. x(t0) is the actual value of x at time t0 and xe is our best estimate of x. Thus the term in the parentheses is the error in our estimate.

For the numerical example, we will take P = 40,000.

Now we would like to estimate x(t1). Remember that the first equation we wrote (the dynamic equation) was

x(tk+1) = Fx(tk) + u(k)

Therefore, for k=0 we have

x(t1) = Fx(t0) + u(0)

Dr. Kalman says our new best estimate of x(t1) is given by

newxe = Fxe (equation 1)

or in our numerical example 900.

Do you see why Dr. Kalman is right. We have no way of estimating u(0) except to use its mean value of zero. How about Fx(t0). If our initial estimate of x(t0) = 1000 was correct then Fx(t0) would be 900. If our initial estimate was high, then our new estimate will be high but we have no way of knowing whether our initial estimate was high or low (if we had some way of knowing that it was high than we would have reduced it). So 900 is the best estimate we can make. What is the variance of the error of this estimate?

newP = E [(x(t1) - newxe)2]

Substitute the above equations in for x(t1) and newxe and you get

newP = E [(Fx(t0) + u -Fxe)2]

= E[F2(x(t0) - xe)2 ]+ E u2 + 2F E (x(t0)- xe)*u]

The last term is zero because u is assumed to be uncorrelated with x(t0) and xe.

So, we are left with

newP = PF2 + Q (Equation 2)

For our example, we have

newP = 40,000 X .81 + 100 = 32,500

Now, let us assume we make a noisy measurement of x. Call the measurement y and assume y is related to x by a linear equation. (Kalman assumed that all the equations of the system are linear. This is called linear system theory. In later lessons, we will extend the Kalman filter to non-linear systems.)

y(1) = Mx(t1) + w(1)

where w is white noise. We will call the variance of w, “R”.

M is some number whose value we know. We will use for our numerical example M = 1 , R= 10,000 and y(1) = 1200

Notice that if we wanted to estimate y(1) before we look at the measured value we would use

ye = M*newxe

for our numerical example we would have ye = 900

Dr. Kalman says the new best estimate of x(t1) is given by

newerxe = newxe + K*(y(1) -M*newxe)

= newxe + K*(y(1) - ye) (equation 3)

where K is a number called the Kalman gain.

Notice that y(1) - ye is just our error in estimating y(1). For our example, this error is equal to plus 300. Part of this is due to the noise, w and part to our error in estimating x.

If all the error were due to our error in estimating x, then we would be convinced that newxe was low by 300. Setting K=1 would correct our estimate by the full 300. But since some of this error is due to w, we will make a correction of less than 300 to come up with newerxe. We will set K to some number less than one.

What value of K should we use? Before we decide, let us compute the variance of the resulting error

E (x(t1) - newerxe)2 = E [x - newxe - K(y - M newxe)]2

= E [(x - newxe - K(Mx + w - M newxe)]2

= E [{(1 - KM)(x - newxe)2 +Kw}]2

= newP(1 - KM)2 + RK2

where the cross product terms dropped out because w isassumed to be uncorrelated with x and newxe. So the newer value of the variance is now given by

newerP = newP(1 - KM) 2 + R(K2) (equation 5)

If we want to minimize the estimation error we should minimize newerP. We do that by differentiating newerP withrespect to K and setting the derivative equal to zero and then solving for K. A little algebra shows that the optimal K is given by

K = M newP/[newP(M2) + R] (Equation 4)

For our example, K = .7647

newerxe = 1129

newerP = 7647

Notice that the variance of our estimation error is decreasing.

These are the five equations of the Kalman filter. At time t2, we start again using newerxe to be the value of xe to insert in equation 1 and newerP as the value of P in equation 2. Then we calculate K from equation 4 and use that along with the new measurement, y(2), in equation 3 to get another estimate of x and we use equation 5 to get the corresponding P. And this goes on computer cycle after computer cycle.

In the multi-dimensional Kalman filter, x is a column matrix with many components. For example if we were determining the orbit of a satellite, x would have 3 components corresponding to the position of the satellite and 3 more corresponding to the velocity plus other components corresponding to other random variables. Then equations 1 through 5 would become matrix equations and the simplicity and intuitive logic of the Kalman filter becomes obscured. The remaining lessons deal with the more complex nature of the multi-dimensional Kalman filter.

Objective

The broad objective of this research is the development, analysis, assessment and exploitation of a new form of model predictive control (MPC), Feedback MPC that is inherently robust in the face of uncertainty. Main objective is to devise a method, the complexity of which is considersbly less than that of dynamic programming, for achieving feedback model predictive control of constrained dynamic systems that is robust to a wide class of uncertainties (unknown disturbances, model error and state estimation error when output feedback is used).
What is model predictive control?

Model Predictive Control is an approach to controller design that involves on-line optimization calculations. The online optimization problem takes account of system dynamics, constraints and control objectives. Conventional model predictive control requires the solution of an open-loop optimal control problem, in which the decision variable is a sequence of control actions, at each sample time. Current control action is set equal to the first term of the optimal control sequence.

Model predictive control has a rich and unusual history. The main reason for the wide-scale adoption by industry of model predictive control is its ability to handle hard constraints on controls and states that arise in most applications. These constraints are particularly important in the petro-chemical industry where optimization of set points results in steady-state operation on, or close to, the boundary of the set of permissible states. Model predictive control is one of very few methods available for handling hard constraints, and it is precisely this fact that makes it so useful for the control engineer, particularly in the process industries where plants being controlled are sufficiently `slow’ to permit its implementation.
Robust Model Predictive Control

Since uncertainty often has a significant effect on stability and performance. Robust model predictive control requires, in principle, on-line solution of a min-max optimal control problem in which the decision variable is a sequence of control laws , that provides the feedback necessary for robustness, and the adversary is uncertainty. Naive inclusion of feedback leads to a dynamic programming problem of overwhelming complexity. The real challenge is to devise a method, the complexity of which is considerably less than that of dynamic programming, for achieving feedback model predictive control of constrained dynamic systems that is robust to a wide class of uncertainties.

In order to overcome existing limitations of robust model predictive control, in our approach the predicted trajectory is replaced by a predicted tube in state space; the control policy (sequence of control laws) is linear in the tube, and the tube and the policy are chosen so that all realizations of the state lie within the tube. State and control constraints are easily handled.

The online optimal control problem requires is more complex than that for conventional model predictive control but the increase in complexity is relatively modest, permitting employment of this strategy in situations where robustness is required.

Model Predictive Control, or MPC, is an advanced method of process control that has been in use in the process industries such as chemical plants and oil refineries since the 1980s. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The models are used to predict the behavior of dependent variables (ie., outputs) of a dynamical system with respect to changes in the process independent variables (ie., inputs). In chemical processes, independent variables are most often setpoints of regulatory controllers that govern valve movement (eg., valve positioners with or without flow, temperature or pressure controller cascades), while dependent variables are most often constraints in the process (eg., product purity, equipment safe operating limits). The model predictive controller uses the models and current plant measurements to calculate future moves in the independent variables that will result in operation that honors all independent and dependent variable constraints. The MPC then sends this set of independent variable moves to the corresponding regulatory controller setpoints to be implemented in the process.

Despite the fact that most real processes are approximately linear within only a limitted operating window, linear MPC approaches are used in the majority of applications with the feedback mechanism of the MPC compensating for prediction errors due to structural mismatch between the model and the plant. In model predictive controllers that consist only of linear models, the superposition principle of linear algebra enables the effect of changes in multiple independent variables to be added together to predict the response of the dependent variables. This simplifies the control problem to a series of direct matrix algrebra calculations that are fast and robust.

When linear models are not sufficiently accurate because of process nonlinearities, the process can be controlled with nonlinear MPC. Nonlinear MPC utilizes a nonlinear model directly in the control application. The nonlinear model may be in the form of an empirical data fit (e.g. artificial neural networks) or a high fidelity model based on fundamentals such as mass, species, and energy balances. The nonlinear model may be linearized to derive a Kalman filter or specify a model for linear MPC. The time derivatives may be set to zero (steady state) for applications of real-time optimization or data reconciliation. Alternatively, the nonlinear model may be used directly in nonlinear MPC and nonlinear estimation (e.g. moving horizon estimation). A reliable nonlinear model is a core component of simulation, estimation, and control applications.

MPC is based on iterative, finite horizon optimization of a plant model. At time t the current plant state is sampled and a cost minimizing control strategy is computed (via a numerical minimization algorithm) for a relatively short time horizon in the future: [t,t + T]. Specifically, an online or on-the-fly calculation is used to explore state trajectories that emanate from the current state and find (via the solution of Euler-Lagrange equations) a cost-minimizing control strategy until time t + T. Only the first step of the control strategy is implemented, then the plant state is sampled again and the calculations are repeated starting from the now current state, yielding a new control and new predicted state path. The prediction horizon keeps being shifted forward and for this reason MPC is also called receding horizon control. Although this approach is not optimal, in practice it has given very good results. Much academic research has been done to find fast methods of solution of Euler-Lagrange type equations, to understand the global stability properties of MPC’s local optimization, and in general to improve the MPC method. To some extent the theoreticians have been trying to catch up with the control engineers when it comes to MPC.

Model Predictive Control (MPC) is a multivariable control algorithm that uses:

• an internal dynamic model of the process

• a history of past control moves and

• an optimization cost function J over the prediction horizon,

to calculate the optimum control moves.

The optimization cost function is given by:

ORIFICE SIZING CALCULATION

In this example, either calculate the head drop through an orifice of known diameter, or enter the head drop required and calculate the required size of orifice. The calculation applies to orifices where the orifice diameter is less than 0.3 of the pipe size.

How many times a day do we turn on a faucet? Do it now. First very slowly, and you will see glassy, orderly flow. If there is no wind or other disturbance, nothing will change. This is called laminar flow. A photo taken now will be identical to one taken half an hour later. Such a flow is deterministic; information about its future behavior is completely determined by specification of the flow at an earlier time. Now open the faucet to full on, or better still open a fire hydrant, or watch a smoke stack. Here, for this faster or larger scale motion, the flow pattern is changing all the time. Although its average motion is in one direction (sideways for the fire-hydrant, up for the smoke stack), within the flow there are irregularities everywhere. For example if you could train your eyes on a small speck of dust it would certainly move along but it would jitter as well, sometimes darting to one side, or up or down. Turbulent flow while proceeding in a particular direction, like laminar flow, has the added complexity of random velocity fluctuations. The flow patterns never repeat themselves. To convince yourself of this watch a smoke stack for a few minutes.

Fluid flow that is slow tends to be laminar. As it speeds up a transition occurs and it crinkles up into complicated, random turbulent flow. But even slow flow coming from a large orifice can be turbulent; this is the case with smoke stacks. Engineers and scientists don’t like to say “fast” or “slow” or “small” and “big” since there is no reference. Small compared to what? Big compared to what? Since turbulence is altogether a different type of fluid flow to laminar flow, it is desirable to be able to quantify under what conditions it occurs.

Let us re-do the faucet experiment in a more systematic way. We have shown that as the speed, V, increases, transition to turbulence will occur. Now, instead of using water in your pipes, replace it with honey. Assuming you could provide a large enough pressure, even for fast flow the motion would remain laminar. If you do not wish to do this experiment, stir a spoon rapidly in a cup of water and then at the same speed (working hard) in a cup of honey. Honey has a higher viscosity than water and the viscosity resists transition to turbulence: while the water is turbulent, the honey remains laminar at the same speed. Finally, put a nozzle on your tap and constrict the water flow into a fine glass capillary tube. Here too the flow can be made to go quite fast without it becoming turbulent. Our experiments suggest that laminar flow occurs for low speeds, small diameters, low densities and high viscosities, while turbulent flows occur for the opposite conditions: high speeds, large diameters, high densities and low viscosities. Now viscosity is a measurable fluid property (as is its density, temperature, etc.). We will discuss it more in a moment, but we often use the “kinematic viscosity,” which is the viscosity divided by the density. Its unit is m^2/s. Notice its dimensions are the same as a length multiplied by a velocity. If the fluid speed is V (m/s), the orifice diameter is d (m) then we can write the following dimensionless ratio

Re is the Reynolds number, named after Osborne Reynolds who did systematic experiments, of a similar type to those described above, one hundred years ago. Notice that if V or d (or both) are small and the viscosity is large, Re will be small. For this case the flow will be laminar. Increase d or V or decrease the viscosity, and Re will increase. Reynolds found that for flow in a pipe it did not matter which of the three particular parameters he varied in this dimensionless group: as long as Re was less than approximately 2300, the flow was laminar. Above this value, turbulence would invariably occur. This is a general result since it allows us to vary the type of fluid, flow speed and pipe diameter without having to use the words “large” or “fast”, etc. Moreover, since Re is dimensionless, it does not matter which system of units are used (S.I., Engineering, etc.) so long as they are the same throughout. We can now talk of high Reynolds number flow or low Reynolds number pipe flow, knowing that in this context low means somewhat less than 2000. The kinematic viscosity of water is approximately 10^{-6} m^2/s (that of honey is about 10^{-3} m^2/s, 1000 times greater than that of water). Thus if the pipe diameter is say 1 cm, the speed at which the Reynolds number is 2000, is 0.2 m/s or approximately 0.4 mph, a rather slow speed. Water undergoes transition to turbulence at low speeds. Most of the water flows we see, such as in streams and rivers, are indeed turbulent.

Air too is a fluid, its viscosity, \nu, is approximately 10^{-3} m^2/s. This is a higher viscosity than that of water. This rather counter-intuitive fact is due to the great differences in density of the two fluids. Water has a density of approximately 1000 kg/m^3; the air density is 1.2 \, kg/m^3. Thus part of the “viscous feeling” we have when we pull our fingers through water is really due to inertia — we are having to move the water away from our hands and this also provides resistance. For this reason we need to remember the difference between the dynamic viscosity and the kinematic viscosity. The dynamic viscosity of water is approximately 10^{-3} kg/(m s) while that of air is 1.2 \times 10^{-5} kg/(m s). Thus the dynamic viscosity of water is higher than that of air, in keeping with our intuitive notion.

While the transition from laminar to turbulent flow occurs at a Reynolds number of approximately 2300 in a pipe, the precise value depends on whether any small disturbances are present. If the experiment is very carefully arranged so that the pipe is very smooth and there are no disturbances to the velocity and so on, higher values of Re can be obtained with the flow still in a laminar state. However, if Re is less than 2300, the flow will be laminar even if it is disturbed. Thus 2300 is the value the Re below which turbulence will not occur in a pipe. Moreover, if the flow has a different geometry, such as flow in a square duct, or over a turbine blade, transition will occur at different values of Re. The essential point is that flows become turbulent at high Reynolds numbers where “high” means much greater than unity.

Air motion is invariably turbulent. Consider a smokestack (which to a first approximation is mostly air). If its diameter is say 3 m, then V must be less than 6.6 mm/s (0.015 mph) for it to be laminar! There is no such thing as a laminar smokestack. Clouds too are usually turbulent. Here we determine the Reynolds number using an approximate characteristic dimension of the cloud such as its height or width. Assuming the cloud dimension is say 500 m, and its characteristic internal motion is say 5 m/s, then taking the kinematic viscosity to be 10^{-5} m^2/s (it is approximately the same for water vapor as it is for air), the Re = (500 x 5)/10^{-5} = 2.5 x 10^8. A high value indeed. No wonder cumulus clouds always have a random, puffy looking turbulent structure (see also the plume generated by Mt. St. Helens in the picture above).
Turbulent Flow
When the flow is turbulent, the flow contains eddying motions of all sizes, and a large part of the mechanical energy in the flow goes into the formation of these eddies which eventually dissipate their energy as heat. As a result, at a given Reynolds number, the drag of a turbulent flow is higher than the drag of a laminar flow. Also, turbulent flow is affected by surface roughness, so that increasing roughness increases the drag.

Transition to turbulence can occur over a range of Reynolds numbers, depending on many factors, including the level surface roughness, heat transfer, vibration, noise, and other disturbances. To understand why this is so, and to appreciate the role of the Reynolds number in governing the stability of the flow, it is helpful to think in terms of a spring-damper system such as the suspension system of a car. Driving along a bumpy road, the springs act to reduce the movement experienced by the passengers. If there were no shock absorbers, however, there would be no damping of the motion, and the car would continue to oscillate long after the bump has been left behind. So the shock absorbers, through a viscous damping action, dissipate the energy in the oscillations and reduce the amplitude of the oscillations. If the viscous action is strong enough, the oscillations will die out very quickly, and the passengers can proceed smoothly. If the shock absorbers are not in good shape, the oscillations may not die out. The oscillations can actually grow if the excitation frequency is in the right range, and the system can experience resonance. The car becomes unstable, and it is then virtually uncontrollable.

In fluid flow, we often interpret the Reynolds number as the ratio of the inertia force (that is, the force given by mass x acceleration) to the viscous force. At low Reynolds numbers, therefore, the viscous force is large compared to the inertia force, and the flow behaves in some ways like a car with a good suspension system. Small disturbances in the velocity field, created perhaps by small roughness elements on the surface, or pressure perturbations from external sources such as vibrations in the surface or strong sound waves, will be damped out and not allowed to grow. This is the case for pipe flow at Reynolds numbers less than the critical value of 2300 (based on pipe diamter and average velocity), and for boundary layers with a Reynolds number less than about 200,000 (based on distance from the origin of the layer and the freestream velocity). As the Reynolds number increases, however, the viscous damping action becomes comparatively less, and at some point it becomes possible for small perturbations to grow, just as in the case of a car with poor shock absorbers. The flow can become unstable, and it can experience transition to a turbulent state where large variations in the velocity field can be maintained. If the disturbances are very small, as in the case where the surface is very smooth, or if the wavelength of the disturbance is not near the point of resonance, the transition to turbulence will occur at a higher Reynolds number than the critical value. So the point of transition does not correspond to a single Reynolds number, and it is possible to delay transition to relatively large values by controlling the disturbance environment. At very high Reynolds numbers, however, it is not possible to maintain laminar flow since under these conditions even minute disturbances will be amplified into turbulence.

Turbulent flow is characterized by unsteady eddying motions that are in constant motion with respect to each other. At any point in the flow, the eddies produce fluctuations in the flow velocity and pressure. If we were to measure the streamwise velocity in turbulent pipe flow, we would see a variation in time as shown in figure 14.

Figure Velocity at a point in a turbulent flow as a function of time.

We see that the velocity has a time-averaged value \bar U and a fluctuating value u’, so that \bar U is not a function of time, but u’ is.

The eddies interact with each other as they move around, and they can exchange momentum and energy. For example, an eddy that is near the centerline of the pipe (and therefore has a relatively high velocity), may move towards the wall and interact with eddies near the wall (which typically have lower velocities). As they mix, momentum differences are smoothed out. This process is superficially similar to the action of viscosity which tends to smooth out momentum gradients by molecular interactions, and turbulent flows are sometimes said to have an equivalent eddy viscosity. Because turbulent mixing is such an effective transport process, the eddy viscosity is typically several orders of magnitude larger than the molecular viscosity. The important point is that turbulent flows are very effective at mixing: the eddying motions can very quickly transport momentum, energy and heat from one place to another. As a result, velocity differences get smoothed out more effectively than in a laminar flow, and the time-averaged velocity profile in a turbulent flow is much more uniform than in a laminar flow (see figure 4).

As a result of this mixing, the velocity gradient at the wall is higher than that seen in a laminar flow at the same Reynolds number, so that the shear stress at the wall is correspondingly larger. This observation is in agreement with the fact that the losses in a turbulent flow are much higher than in a laminar flow, and therefore the pressure drop per unit length will be greater, which is reflected in a larger frictional stress at the wall

Rotary vane vacuum pumps move fluid through the pump using a rotating assembly in the pumping chamber. Typically there are two or more rotating vanes that move the gas or fluid from inlet to outlet. Rotary vane vacuum pumps are positive displacement pumps. The volume of fluid that is transferred by rotary vane pumps depends upon the size of the housing and the area between each adjacent vane. Larger pumps may have additional impeller vanes. As the rotor turns, the ends of the vane barely touch the housing creating a seal from inlet to outlet. The inlet and outlet are often perpendicular, however for vacuum service applications two inlets may be used, one for air supply and the other for the pumped media. The fluid is pressurized as the volume between the vanes lessens during one half-cycle and is suctioned through an intake port during the other half-cycle.

The movement of the media through the pump can be broken down into three phases in rotary vane pumps: 1) Air or fluid moves through the inlet also known as open to inlet (OTI). 2) The vane rotates clockwise or counterclockwise and seals the media between the vanes and the housing wall also known as closed to inlet and outlet (CTIO). With fluids, this volume should remain constant throughout the cycling process. Gases and/or air may be compressed in this phase causing the pressure to increase before the next phase. 3) The media is moved through to the outlet. This is also referred to as the open to outlet (OTO) volume. The rotor blades are positioned to contain a specific volume of air or fluid. The cyclical movement of the vane creates a smooth flow as the fluid is transferred through the pumping chamber. Generally, materials can be chosen for the vane. For example, carbon vanes can be used with inert gases and a variety of other media types. The vane can be internal or external, rigid or flexible.

The manufacturer for rotary vane vacuum pumps can often give the displacement of the pump. The surface dimensions of the housing and rotary assembly may be considered when calculating flow rate. In some rotary vane pumps, as the flow rate increases, the pressure in the pump chamber increases. Various requirements may be needed including vacuum service or air compression. As with most rotary pumps, the viscosity of the media will affect the speed of the drive chosen. The flow rate is also proportional to the motor speed. Magnetic drive, belt drive or direct drive can be chosen for powering rotary vane pumps.

Rotary vane vacuum pumps can be used in a number of applications providing a pressure or vacuum source for laboratory applications and as well as other automation applications. Smaller sizes may have a maximum flow of 3 LPM with pressures ranging from 80-120mbar.move fluid through the pump using a rotating assembly in the pumping chamber. Typically there are two or more rotating vanes that move the gas or fluid from inlet to outlet. Rotary vane vacuum pumps are positive displacement pumps. The volume of fluid that is transferred by rotary vane pumps depends upon the size of the housing and the area between each adjacent vane. Larger pumps may have additional impeller vanes. As the rotor turns, the ends of the vane barely touch the housing creating a seal from inlet to outlet. The inlet and outlet are often perpendicular, however for vacuum service applications two inlets may be used, one for air supply and the other for the pumped media. The fluid is pressurized as the volume between the vanes lessens during one half-cycle and is suctioned through an intake port during the other half-cycle.

The movement of the media through the pump can be broken down into three phases in rotary vane pumps: 1) Air or fluid moves through the inlet also known as open to inlet (OTI). 2) The vane rotates clockwise or counterclockwise and seals the media between the vanes and the housing wall also known as closed to inlet and outlet (CTIO). With fluids, this volume should remain constant throughout the cycling process. Gases and/or air may be compressed in this phase causing the pressure to increase before the next phase. 3) The media is moved through to the outlet. This is also referred to as the open to outlet (OTO) volume. The rotor blades are positioned to contain a specific volume of air or fluid. The cyclical movement of the vane creates a smooth flow as the fluid is transferred through the pumping chamber. Generally, materials can be chosen for the vane. For example, carbon vanes can be used with inert gases and a variety of other media types. The vane can be internal or external, rigid or flexible.

The manufacturer for rotary vane vacuum pumps can often give the displacement of the pump. The surface dimensions of the housing and rotary assembly may be considered when calculating flow rate. In some rotary vane pumps, as the flow rate increases, the pressure in the pump chamber increases. Various requirements may be needed including vacuum service or air compression. As with most rotary pumps, the viscosity of the media will affect the speed of the drive chosen. The flow rate is also proportional to the motor speed. Magnetic drive, belt drive or direct drive can be chosen for powering rotary vane pumps.

Rotary vane vacuum pumps can be used in a number of applications providing a pressure or vacuum source for laboratory applications and as well as other automation applications. Smaller sizes may have a maximum flow of 3 LPM with pressures ranging from 80-120mbar.

Hand pumps and foot pumps are manually operated pumps that can driven by hand or foot via a handle or lever.  This manual external force actuates an internal mechanism, which increases pressure for moving fluids such as gas, chemicals, or water. Hand lever and foot pedals are pushed up or down to begin the pump cycle, often requiring one stroke to draw the fluid and another stroke to discharge it, as is typical in many displacement pumps.

Hand pumps and foot pumps are generally of hydraulic and pneumatic design.  Hydraulic hand pumps and foot pumps are used to manually pressurize a hydraulic system and for instrument calibration.  Pneumatic hand pumps and foot pumps are designed for testing and instrument calibration.  A fluid reservoir is generally supplied with hydraulic and pneumatic hand pumps as an integral part of the pump or an independent part.  It holds a quantity of fluid for the pump to use to power hydraulic or pneumatic cylinders.

Hand pumps and foot pumps may also be called drum pumps, which will require handles, levers, and plungers to begin dispensing the fluid from a pail, drum, or tank.  Drum pumps may mount manually or with a clamp. Although the actual hand pumps may be portable and lighter in weight, it may be preferable to keep the pail, drum or barrel stationary due to the properties of the fluid and the pumping environment.

Hand pumps and foot pumps can be of reciprocating or rotary types. Most rotary types use a drive rather than a lever or crank.  In reciprocating type hand pumps, a hydraulic or pneumatic piston is used to create the pressure needed to move the media. Hand pumps can also be diaphragm pumps as in marine applications where seawater is pumped from the bilge.  Diaphragm hand pumps are displacement pumps that use a rubber disk to alternate air or fluid.  The diaphragm is actuated by the pressures or vacuums created during the pump cycle.

Hand pumps and foot pumps are portable and field operable where electric drives may not be available.  A gage is often attached to hand pumps to measure pressure.  Calibration hand pumps can be sold as a kit or will require calibration instruments, indicators, gages, and other instrumentation.

Industrial liquid handling pumps are classified in many different ways. They are distinguished by materials of construction, media pumped, industries or applications served, pressure and flow levels, and physical orientation. For this product area, however, industrial liquid handling pumps are distinguished by the media pumped and the fluid motive mechanism, which can be separated into two broad categories of pumping action: dynamic and displacement.

Dynamic or kinetic industrial liquid handling pumps operate by imparting energy into the fluid, frequently by increasing its velocity to a level greater than that allowed by the fluid outlet port. This energy is thereby converted to higher pressure. Displacement pumps compress fluid mechanically by decreasing the volume of a chamber that contains the fluid. Many configurations of piston-cylinder combinations, diaphragm oscillation, and rotating members are used to achieve this compression. While many ranges of flow and pressure capabilities are available for all industrial liquid handling pumps, dynamic pumps are characterized by the ability to produce high flow rates.

Displacement industrial liquid handling pumps are distinguished by their comparatively high-pressure capabilities. Specific pump types include axial, bladder, cantilever, centrifugal, circumferential piston, diaphragm, double diaphragm, dosing or metering, drum, gear, hand, jet, linear, lobed rotor, manual, peristaltic, piston or plunger, radial piston, rocking piston, rotary vane, regenerative blower, screw, scroll, syringe, and turbine. Other types of displacement industrial liquid handling pumps may also be available.

Industrial liquid handling pumps are designed to work with specific fluids and/or applications. Some pumps may be suitable for multiple applications. Common fluids and applications for industrial liquid handling pumps include general-purpose fluid transfer, chemicals, cryogenic materials, food processing, fuel or oil, high temperature fluids, high viscosity fluids, hydraulic fluid, medical or surgical fluids, refrigerants, sludge or sewage, slurry, solids or gravel, thermoplastics, and water.

Specifications to consider when selecting industrial liquid handling pumps include maximum flow rate, maximum pressure, maximum temperature, and maximum power drive. Flow capacity must be specified separately for air or gas and liquid pumps. Maximum pressure refers to the maximum level of air pressure generated at the pump outlet. Typically, units are referenced to one atmosphere, as in psig or psi gauge. Maximum flow may not occur at maximum pressure. Depending on the pump style, maximum temperature can refer to either maximum fluid temperature being pumped, or the upper limit of ambient conditions. Maximum drive power is the rated power of the motor or engine which drives the industrial liquid handling pumps.

Cryogenic pumps are designed to move coolants and cryogenic liquids. They are built to withstand and operate in extremely cold temperatures. Cryogenic pumps feature hermetically sealed designs to minimize heat leakage from the motor or contamination by process fluids into the cryogenic fluid.

Long shaft cryogenic pumps are designed with the pump motor and mounting flange separated from the pump impeller by a long shaft. The pump impeller is submerged in the cryogen or freezing liquid. This minimizes the leaking of heat from the motor into the frozen or freezing cryogenic fluid. Long shaft cryogenic pumps may be welded or bolted to a variety of cryogenic equipment, including dewars and cryostats. A dewar is a specially insulated container designed to store liquefied gases, such as the liquid nitrogen used as a coolant in cryogenic applications. A cryostat is a device used to maintain the temperature of the coolant. A centrifugal pump is typically used to transfer cryogenic liquids between a storage tank or tanker car because of their ability to produce and maintain a high flow rate.

Cryogenic pumps may also be submersible. A submersible cryogenic pump is frequently used in applications where heat leak is not the most important factor. Submersible cryogenic pumps are used as pumps in vehicles that use liquefied natural gas or in the liquid hydrogen propellant system in a rocket. Cryogenic pumps for use in extremely cold environments are usually constructed with a vacuum housing to provide a barrier between the motor and the cryogenic fluid. Cryogenic pumps are used to circulate coolant in a variety of applications, including cooling high temperature superconducting cables or magnets, for cooling synchrotron beamline crystals, and as pumps in prototype slush hydrogen applications.

Specialty vacuum pumps are specialty or proprietary products and accessories related to vacuum pumps. Specialty vacuum pumps include portable, handheld, and miniature vacuum pumps; low power or 12-volt vacuum pumps, and a variety of other devices. Specialty vacuum pumps also include low power electric pumps for use in vehicles. A 12 volt vacuum pump is commonly used to create the vacuum necessary for operating power brakes. This type of electric vacuum pump is also used in other portable or battery-powered devices.

Specialty vacuum pumps are used for many different industrial and scientific applications, including purification of chambers in chemical or semiconductor manufacturing, degassing fume areas in laboratories, and for holding components in place during machining processes. A specialty vacuum pump used for handheld applications may include devices for bleeding brake lines on cars and trucks. A hand vacuum pump often employs a trigger-style design, allowing an operator to easily disengage the vacuum. Other specialty vacuum pumps include miniature or even microscopic pumps for use in small apparatus or motors. A mini vacuum pump may be battery-powered and used in robotic applications or in applications where space is limited.

Specialty vacuum pumps for other types of applications include rotary vane vacuum pumps and liquid ring vacuum pumps. A rotary vane vacuum pump consists of a hollow body with a rotating cylinder that is mounted off-axis with two opposing vanes. The motion of the turning rotor causes the volume present between the two vanes and the hollow body of the pump to vary at each half turn. Rotary vane vacuum pumps are used in all kinds of vacuum applications, including thin film deposition and other semiconductor processes. A liquid ring vacuum pump consist of a rotating impeller with multiple blades mounted in a pump housing. As the impeller rotates, centrifugal force moves a liquid against the outside wall, forming a seal. Liquid ring vacuum pumps work like a piston, compressing the gas in the chamber as the impeller moves toward the top of the pump housing