Static Feedforward Controller

Summary

Highlights

• Analyzing a static feedforward controller using a blending tank example. 🛢️
• Differentiating between feedforward and feedback control mechanisms. 🤔
• The role of P&ID diagrams in control system development. 🗺️
• Static controllers eschew dynamic complexities by focusing on steady-state balances. 🧮
• The screencast simplifies the creation of a static feedforward control equation. 📐
• Final steps involve converting control equations into practical signals for system implementation. 📡

Key Takeaways

• Understanding the basics of static feedforward controllers can greatly enhance process efficiency. ⚙️
• Feedforward control is vital when dealing with non-controllable streams in process systems. 🌊
• In static controllers, steady-state analysis is used, avoiding the complexity of dynamic models. 📊
• Creating accurate P&ID diagrams is crucial for visualizing control processes. 🎨
• Developing a static control equation involves smartly managing balance equations and eliminating variables. ✏️
• Translating control equations into real-life control signals is a necessary final step. 🔄

Overview

Chapters

• 00:00 - 00:30: Introduction to Static Feedforward Controller This chapter introduces the concept of a static feedforward controller using the example of a blending tank. The focus is on controlling the concentration of a desired solute exiting the tank, with emphasis on the controllable stream used for the feedback part of control.
• 00:30 - 01:00: Problem Statement and System Description In the chapter titled 'Problem Statement and System Description,' the focus is on addressing an issue with a second, uncontrolled stream entering a system. The composition and flow rate of this stream can vary, posing challenges for system control. The proposal includes using feed-forward control to manage this variability. The chapter suggests developing a P&ID (Piping and Instrumentation Diagram) based on the given information, and creating a static feed-forward controller. A discussion on static versus dynamic feed-forward controllers is also promised in this segment.
• 01:00 - 01:30: Developing the P&ID The chapter titled 'Developing the P&ID' covers the initial steps in creating a Piping and Instrumentation Diagram (P&ID) focusing on a mixed tank system. The system discussed includes two streams entering the tank and one stream exiting. An essential aspect of the process is the feedback control mechanism that adjusts the flow rate of one stream to control the composition in the tank. Additionally, the chapter highlights the necessity of measuring the flow rates.
• 01:30 - 02:00: Feedforward Controller Design In the chapter titled 'Feedforward Controller Design', a strategy is elaborated where two signals are sent to a single feedforward controller. The need for this approach arises because one of the streams in question cannot be controlled directly. By exploiting known relationships between the fluid and composition in the stream—expressed through balances—these factors can be mathematically related. This unified equation then forms the input signal for the feedforward controller, simplifying the control design.
• 02:00 - 02:30: Difference Between Static and Dynamic Controllers The chapter titled 'Difference Between Static and Dynamic Controllers' focuses on explaining the concept of static controllers. Initially, it discusses a feedback feedforward controller, emphasizing the integration of feedback and feedforward signals using a summing point. The chapter aims to prepare the ground for developing a static controller by first elucidating what it is. A static controller is described within the context of steady-state analysis, implying its reliance on constant parameters rather than dynamic responses. Prior to any detailed analysis of the system, it clarifies the premise of static control methodologies.
• 02:30 - 03:00: Planning the Static Controller In this chapter, the discussion focuses on the concept of static controllers in system design. Static controllers are highlighted as being particularly useful in situations where dynamic information is challenging to obtain or model. The chapter contrasts static analysis with dynamic analysis and advises that while dynamic analysis can be relatively straightforward for simple systems like a tank, static controllers are beneficial when developing mass balances is complex or information is sparse. The chapter also hints at additional considerations when planning static controllers, although these are not detailed in the provided transcript.
• 03:00 - 03:30: Mass and Component Balances The chapter discusses the concept of feed-forward control, emphasizing that it involves no feedback from the controlled variable to avoid introducing feedback elements into the analysis. The objective is to manage disturbances effectively. To develop a static control method, the chapter suggests utilizing mass and energy balances. It also includes defining flow rates and compositions, starting with defining W1.
• 03:30 - 04:00: Developing the Static Control Equation The chapter discusses the development of a static control equation. It introduces the flow rate of a stream with an attached valve with a fluid composition represented by X1, monitored by W2 and X2 for the Wild stream with feed-forward control.
• 04:00 - 04:30: Rearranging the Component Balance Equation The chapter delves into the concept of balance equations, focusing on both total mass balance and component balance. In a steady state analysis, it is established that the total mass balance is defined by the equation W1 + W2 = W. This is related to the component balance equation given by W1 x1 + W2 X2 = WX, where X represents mass fractions and W indicates the mass flow rate. The chapter may elaborate on how to apply these equations in practical scenarios.
• 04:30 - 05:00: Finalizing the Static Control Equation In this chapter, the focus is on finalizing the static control equation, wherein the objective is to ensure that the signal sent to the valve controlling W1 is appropriately regulated. The aim is to express W1 as a function primarily of the two disturbance variables, W2 and X2, along with any other necessary variables. Ideally, the equation would relate these variables directly to achieve the desired control.
• 05:00 - 05:30: Converting Variables for Control Systems In this chapter, titled 'Converting Variables for Control Systems,' the main focus is on rearranging component balances to solve for specific variables, such as W1, in control systems. The transcript discusses the feasibility of balancing components and illustrates rearranging a component balance equation to solve for W1 in terms of other variables. The chapter emphasizes the importance of examining other variables as needed in control systems.
• 05:30 - 06:00: Conclusion The chapter discusses the concept of eliminating variables in a mass balance equation. It mentions the relationship between two variables, W and W2, and the importance of using the total mass balance to connect them. The primary focus is on deciding which of the variables (W or W2) to eliminate from the equation.

Static Feedforward Controller Transcription

• 00:00 - 00:30 in this screencast we will analyze how to develop a static feed forward controller in order to show this we're going to take an example of a blending tank which is mixing two streams and our goal as the case with most blending tanks here is to control the concentration of the desired solute exiting the tank so there are two streams coming in one stream is controllable and we're utilizing it for the feed back part of the control
• 00:30 - 01:00 analysis however we have a second stream which is coming in from elsewhere and it's a florid that we cannot control and an issue here is that both the composition and the flow rate can vary so therefore it's been proposed to to utilize feed forward control for this so the questions asking us to develop a p and ID based on the information and secondly to develop a static feed forward controller we'll talk a little bit more about static versus Dynamic feed forward controllers when we get to that part of the question
• 01:00 - 01:30 so the first thing we'll do is develop the p and ID so for the p and ID we'll just first develop our tank we'll assume it's well mixed we'll have one stream coming in and a second stream coming in and then a stream coming out so the feedback control part is going to try to control the composition by adjusting the flow rate of one of the streams what also is going to happen is that we need to measure both the flow rate
• 01:30 - 02:00 and the composition of the other stream which can't be controlled in this case what we're going to do is these are going to go to a feed forward controller we're going to send both signals to one feed forward controller the reason why we're going to do this is that we know the fluid of this stream and the composition of the stream can be related together by the use of one or two balances so therefore we can have one equation which can relate both of them together and then this signal will be sent
• 02:00 - 02:30 as well towards the valve but then we'll add a summing Point here to show that it will take the sum of the feedback portion and the feed forward portion so here we have our feedback feed forward controller so for Part B we are looking at developing a static controller so before conducting any analysis on this system let's first discuss what a static controller is so a static controller is assuming that we are basing everything on a steady state analysis
• 02:30 - 03:00 so this means no transfer functions no derivatives and stuff along those lines for a case as simple as a tank it may behoove you to use a dynamic analysis the opposite of static just because the mass balances here are relatively straightforward however there are many cases where developing the mass balances could be a bit challenging or finding the information may not be available from a dynamic standpoint so therefore we use static controllers to handle that case an additional part here is to
• 03:00 - 03:30 remember that this is a feed forward controller so what this means is that we can take no information about the controlled variable otherwise it would introduce a part of feedback in this analysis which is not what we want to do here we want to be able to handle the disturbances appropriately so in order to develop a static control what we will take advantage of is either Mass Andor energy balances to do this work so to do this let's define a couple flow rates and compositions here we'll Define W1 as
• 03:30 - 04:00 the flow rate of the stream with the valve on it with a composition of fluid as X1 we'll have W2 and X2 for the Wild stream which will be monitored by the feed forward controller and we'll have W and X represent what is exiting the blending tank and our goal When developing a static controller here is to eliminate as many variables as possible so for our system here we'll have two balance of note two Mass
• 04:00 - 04:30 balances one will be a total mass balance and one will be a component balance the total mass balance again since we're doing a steady state analysis here this will just be that W1 + W2 = W and related is we'll have a component balance of W1 x1+ W2 X2 equal WX where X here since W is a mass flow rate xx1 and X2 are Mass fractions so if
• 04:30 - 05:00 we think about what we want to do here our goal is if we look at our diagram our goal is to send an appropriate signal to the valve which is controlling W1 so therefore what we want here is W1 to be a function of the two disturbance variables W2 and X2 and then other variables as needed so ideally we would be able to develop something which would just relate W1 to W2 and X2 only
• 05:00 - 05:30 however from a balance standpoint this may not be feasible so if we look at this from our component balance it would not be hard to rearrange the component balance to solve for W1 so we can rearrange our component balance such that W1 = WX - W2 X2 / X1 so if we look at this this is a perfectly valid equation here but remember our goal here is to look at other variables as needed
• 05:30 - 06:00 so we kind of want to eliminate them when possible and if we look at the right hand side we see the fact that W and W2 can be directly related to one another by the use of the total mass balance so what we're going to now do is is we're going to incorporate the total mass balance so in this case the question is which variable do we want to eliminate here W or W2 well since W2 is
• 06:00 - 06:30 one of the variables that is going to fluctuate we want to measure it that means it's really important for us to keep that in the equation so therefore what we're going to do here is eliminate W to make the algebra a little simpler we're actually going to move the X1 back you'll understand why in just a second we'll end up with W1 X1 we're then going to move the W1 term over w1x and this will equal w2x minus W2 X2 we now have
• 06:30 - 07:00 our equation however we are not done with our analysis here so what we'll have here When developing these static feed forward controls we have three types of variables the first is the controlled variable and remember the fact that we don't have the measurement of this controlled variable so therefore what we'll do is we'll represent it at the set point the second is the disturbance variable or variables here we'll just leave them as is because they are VAR which we are measuring using the
• 07:00 - 07:30 transmitters so therefore those are vales that we can continuously measure the third are other variables that are left other intermediate variables and here we'll just report them at their steady state position and this is often done by putting a bar over the variable so if we look at what we have here our controlled variable the variable we're trying to control is X our disturbance variables are W2 and X2 and if we look at what it's left that leaves us with
• 07:30 - 08:00 our other variable as X1 so therefore for our final answer putting this all together W1 will equal W2 a variable that we can measure multiplied by X set point set point value minus X2 a variable that we can measure divided by X1 I'm going to put a bar over that value because that will just take from its steady state value minus ex set point and this is the development of our static or steady state feed forward
• 08:00 - 08:30 controller so this would not allow us to for perfect control because it does not take into account time Dynamics but oftentimes we don't necessarily have that luxury so this provides a nice easy analysis in order to determine our transfer function in this case our constant value for our feed forward controller but an important point which we're not going to really go into here is this represents a start to the feed forward controller what's left here is we need to turn everything into signals
• 08:30 - 09:00 because remember that transmitters and control schemes don't report back 50 gallons per minute they report back particular signals 20% transmitter output 40% transmitter output Etc so therefore we have to be aware of information about the transmitters and depending on your process potentially the valves in order to put in a number inside the feed forward controller or an equation inside
• 09:00 - 09:30 the feed for controller because this represents an equation inside the feed forward controller that can be utilized for analysis so in this screencast we went through the procedure of how we can analyze a feed forward controller and develop an equation from a steady state balance to develop a static controller