THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY

There are several manufacturing processes where heat conduction is one of the key physical phenomena that influence the process performance. Such processes include molding operations, heat treatment, welding, flame bending etc. Typical temperature control implemented in these processes, at best involves independent multi-zone type regulation. (For example: barrel heaters in injection molding.) This thesis has addressed the problem of controlling entire temperature distributions in such processes. Several techniques developed in the theoretical literature on the control of distributed parameter systems (DPS) have been investigated for their applicability to manufacturing processes. An experiment has been setup using a scanned TIG torch to heat a rectangular specimen with several thermocouples embedded within it. A detailed simulation study was performed on a model of this experimental setup, to study the closed loop behavior of the model under different scenarios. The simulations used a linear quadratic gaussian (LQG) controller. The conclusion from this study was that the distribution of inputs and sensors in the controlled object had a significant impact on the performance of the controller in rejecting disturbances. However, there are no available techniques in the theoretical literature to adequately address the issue of optimally distributing inputs. This motivated the development of a technique for optimally distributing inputs across a controlled object. The technique comprises separating the space and time part of the governing partial differential equation, which results in the steady-state equation for heat conduction within the controlled object. The steady-state Green's function corresponding to this steady state heat conduction equation is determined. A quadratic performance index comprising a heat flux term and a temperature error term is defined over the spatial domain. A general form of a higher order cost functional is used along with the Green's function to set up the optimization problem. Variational calculus is used to determine the optimal heat flux distribution in steady state. This optimal heat flux distribution is in a linear proportional feedback form wherein the heat flux needed in steady state depends on the steady-state temperature error. Therefore such an approach can better adapt to model errors and external disturbances. Simulations have been performed on a rectangular solid to illustrate the optimal distribution technique based on the steady-state optimization. The constraints on the locations of the inputs and the types of disturbances considered were selected based on typical requirements in a resin transfer molding (RTM) or a compression molding application. The Green's functions were derived using a finite difference formulation for the heat conduction in the solid. The design of the heating was separated into two parts: In the first part, the heat flux locations and strengths were selected to satisfy the requirements on the steady-state performance. In the second part, additional heaters were introduced to improve the transient performance. In the first part of the design, the high gain (MIMO) obtained as a part of the steady-state analysis was rolled off using a first order frequency blending function. The MIMO Nyquist criterion was then used to determine if the closed loop system was stable. The break frequency for the frequency blending function is used as a controller design parameter and a suitable value is selected. The predictions of the MIMO Nyquist criterion have been verified by simulating the closed loop system. Additional heaters placed closed to the surface have been incorporated into the design using a cross-over network type design. The improvement in the transient performance has been demonstrated. The problem of accelerated cooling of hot-rolled steel has been addressed as a transient temperature distribution control problem. The major source of disturbance in this process is a variation in the initial temperature of steel. There are no measurements possible once the cooling process begins. The anomalous nature of the cooling process amplifies the variations in the initial temperature distribution, if not compensated for. To compensate for the variations in the initial conditions, a finite horizon quadratic performance index is setup. The resulting feedback form for the optimal solution is simulated on the model for the process, with the initial condition varied from the nominal initial condition. The simulated input is then used as an open-loop input to the process to compensate for the variations in the initial condition. Thesis Supervisor: Prof. David E. Hardt. Title: Professor of Mechanical Engineering, Massachusetts Institute of Technology. Committee: Prof. David E. Hardt (Chairman) Department of Mechanical Engineering MIT. Prof. Jung Hoon Chun Department of Mechanical Engineering MIT. Prof. Harris Doumanidis Department of Mechanical Engineering Tufts University. Dr. Kenneth W. Kaiser Charles Stark Draper Laboratory. Dr. Herschell B. Smartt Idaho National Engineering Laboratory.