10.450 Process Dynamics, Operations, and Control Lecture Notes -31 Lesson 31. Summing it all up 31.0 Context As engineers, we are to create, design, build, tinker, improve – and though progress may be halting and flawed by error, we continue in our charter to improve the conditions under which humans live. We do this by deploying our tools of analysis and synthesis. 31.1 Defining a system When faced with a problem, we often respond by abstracting it: marking off the relevant piece of the universe and identifying the important variables. inputs outputssystem The system has a boundary that marks out what is system, and what is not system. The rest of the universe influences the system by a set of input variables; the system responds by delivering a set of output variables back to the universe. Thus input and output are distinguished by causality. We continue our analysis by making some simplified description of the system – most often it is a mathematical description, a set of equations whose solution gives the output variables as a function of the input variables. The engineer seeks a model that can describe enough of the important behavior to a sufficient degree, and yet be solved at a reasonable cost. As in much of engineering work, this is an economic problem in which there are more ways to fail than to succeed. In studying chemical engineering, we learn to draw system boundaries around some connected region of space. The input and output variables are the flows of matter and energy across the system boundaries; in and out are clearly distinguished by the direction of flow. The model is our notion that energy and matter are conserved in their flow and transformation. Hence we have the material and energy balances that are so fundamental to chemical engineering practice. 31.2 Dynamic systems and control In 10.450, we have abstracted dynamic systems. Our boundaries are not always so clearly marked out in physical space, but the contents of the system usually comprise some collection of equipment. The input and output variables, however, are signals, indications, operations – not necessarily flows of matter and energy, and furthermore, not necessarily corresponding to the direction of flow. In considering a tank, we found 110.450 Process Dynamics, Operations, and Control Lecture Notes -31 that the output of interest was the liquid level in the tank, and one of the inputs was necessarily the outlet flow. In describing our dynamic systems by mathematical models, we did two major things: (1) we used linear approximations to the equations describing the system. This gave us a solution at a reasonable cost, and adequately described system behavior in the vicinity of a set point that we wished to maintain. (2) we resolved some of the structure inside the system boundaries to distinguish between a process and the additional equipment we contrived to control that process. Thus we had a few standard arrangements that served to describe a multitude of applications. system other inputs process final element sensor controller manipulated variable other outputs set point controlled variable The basic arrangement is feedback control – valuable because it always measures the output variable of interest and works to bring it to its desired value. We enhance feedback control by cascade and feedforward arrangements. Our 10.450 modeling and solution techniques included • linearizing equations around a reference condition by Taylor series approximations • arranging equations in standard forms to identify meaningful parameters in the equations • using basic elements (first order lags, dead times) and combinations (series, parallel, recycle) to represent more complicated systems • Laplace transforms, inverting by table of transform pairs, aided by partial fraction expansion of polynomials • block diagrams and Laplace-domain transfer functions, not only because it was a method of solution, but also because of the conceptual value • time-domain response to a few representative disturbances • summarizing the response to a sinusoidal disturbance in the frequency domain • explicit consideration of the stability limit Drawing an analogy to our steady-state experience, in which we might design and rate equipment (for example, design a new distillation column, 210.450 Process Dynamics, Operations, and Control Lecture Notes -31 or predict how an existing column might perform), we proceed to design and rate control systems for dynamic performance. That is we specify: • control objectives – how the system should behave, and how it must not behave • control structure – identify the controlled, manipulated, and disturbance variables, and the set point and control loops • control equipment – sensors, transducers, transmitters, valves • control tuning – setting the knobs so that the closed loop performs to achieve the objectives In all of this we remember that the controller and process are together one complex dynamic system, and that we make better choices of controller parameters as we understand more about the intrinsic dynamic behavior of the process. 31.3 Have fun and be good Analysis can be fun (it's an intense pleasure to see your model describing your system), and technical joy is one of the rewards of engineering as an activity. In doing our analyses, however, we should not be carried away to the point that we begin to believe it too much, nor forget the larger purpose of the analysis. That is, remember that a model is NOT reality, and know when to quit. Another distinction to keep in mind is the difference between model and method of solution. Do not start computing numbers so soon that you lose sight of the overall structure of the model, and what that structure can teach you about the system. Look for ways to break your model up so that valuable intermediate results are easily calculated, once you get to that stage. Remember that a variety of solution techniques may be available, and the best way to pick one is to have the model clearly defined.