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MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303)Spring 2008For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.MANUFACTURING PROCESSES AND PROCESS CONTROL David E. Hardt Laboratory for Manufacturing and Productivity Massachusetts Institute of Technology February , 1996 The following paper outlines a basic modeling paradigm for manufacturing process control. Once the model is defined, three distinctly different modes of process control are described based on this model The model then leads to a control taxonomy for manufacturing processes. Model Definition All manufacturing processes have but two outputs: • Geometry (macroscopic shape of the product) • Properties (all intrinsic material properties) These two outputs completely define the performance of the product, and the design specifications that it must meet. All processes also involve the transformation of material from an initial geometry and set of properties to the final outputs. This transformation is accomplished through the application (or removal) of energy, distributed about the surface or volume of the material. The source of this “directed energy” is the manufacturing machine or equipment. Thus, we can first define a manufacturing process as the interaction of equipment with a material to transform the material to the desired outputs geometry and properties. This model is shown in block diagram form in Fig 1. Outputs Energy Geometry Properties Equipment Material Fig. 1 The Relationship of Equipment and Material in a Manufacturing Process Since all transformations are driven by and governed by the equipment, the only control over the process (other than changing the material itself) is through the equipment. Thus, the control inputs to the process are those equipment inputs that modulate the intensity and distribution of the energy input to the material. In other words, during the operation of the process, the only accessible means of controlled change is the equipment inputs. This leads to the process model shown in Fig. 2 Energy Equipment Material Machine Inputs Outputs Geometry Properties Fig. 2 Process Model with Equipment Inputs Shown To help define internal variables in the process as well as the inputs and outputs, the basic output causality of the process model is shown in Fig. 3 using a simple functional relationship between the process output vector Y and the parameters of the process . Y = () The equipment inputs u are separated as a subset of the parameters that are accessible, certain and “manipulable” in a “reasonable” time frame relative to the basic process execution time. Y = (,u) The vector  can be further broken down into two categories: • Material Parameters • Equipment Parameters Within both equipment and material parameters, we are interested in the thermodynamic state and the constitutive properties of each. For example, the equipment states will be the power pairs: force-velocity, pressure-flow, temperature- entropy (or heat flow) voltage-current, and chemical potential-extent of reaction. Material states can be the same quantities within the material. By contrast, the equipment properties govern how and when the energy is applied. Thus, the geometric, mechanical, thermal and electrical properties of the equipment determine its constitutive properties. Constitutive properties for the material are the well-known quantities such as stiffness, yield point, melting point, viscosity, etc. Fig. 3 Development of A Process Model for Control Y = process outputs  = process parameters = the process transformation function. The parameter vector  is progressively broken down into distur-bances () and inputs (u) David E. Hardt 1/31/05 1 �� �� In general, the states of the equipment and material change over the course of the process as energy is applied, whereas the constitutive properties tend to remain unchanged. However, the energy focused on the material often causes significant changes in the constitutive properties. Indeed the process outputs as defined above can be thought of as the terminal mechanical states and constitutive properties for the material. Modes of Process Control There are several ways in which processes are controlled, ranging from off-line sensitivity reduction to real-time output control. In all cases, the objective is to minimize the effect of disturbances (i.e. ) on the output Y. This basic objective is captured by the first order variation equation: Y Y Y =  + u u where: Y = variation of the output Y = disturbance sensitivity of the process  = parameter disturbances Y u = input-output sensitivity or “gain” u = equipment input changes To minimize the basic variation of Y we can: • design and operate the process to have low disturbance sensitivities (minimize Y/). This is the goal of process optimization. • design or control the equipment to minimize parameter variations  This is the goal of Statistical Process Control (SPC) • counteract  by appropriate changes in u, most typically through the use of feedback control to minimize Y over an appropriate frequency range Sensitivity and Parameter Optimization One means of characterizing the properties of a process is to quantify the effect of variations in the parameters on the outputs. This “generalized sensitivity function” takes the matrix form: �Y If such sensitivity functions are known, the process can then be tuned or “optimized” so as to minimize these functions. This control method is shown schematically in Fig. 4 In this control method the objective is to select nominal values of parameters  such that the sensitivity of the output to disturbances �Y is minimized. (Note that no inherent feedback loop exist here; thus changes in  will not be directly compensated for.) Fig. 4 Optimization of  to minimize the effect of  Statistical Process Control SPC is actually a process diagnosis tool that tries to determine if process disturbances () that are non-random in nature exist. This is done by examining the statistics of output data sampled from the process. If such disturbances are found, SPC provides no prescrip-tion for action, but implies that the disturbance should be eliminated. This is


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MIT 2 830J - Modes of Process Control

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