Duncan A. Mellichamp

An adaptive nonlinear predictive controller

Abstract The design and implementation of a new adaptive nonlinear predictive controller is presented using a general nonlinear model and variable transformations. The resulting controller is similar in form to standard linear model predictive controllers and can be tuned analogously. Alternative, the controller can be tuned using a single parameter. The design is computationally efficient. The controller is updated on-line without recalculating the controller gain matrix, which involves a matrix inversion. The new controller is compared to a PI controller and to an adaptive linear predictive controller through simulations of a continuous stirred-tank reactor. The effects of modeling errors on the new controller are also shown with simulations

A unified derivation and critical review of modal approaches to model reduction

Six of the most commonly-used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables. In this representation, the derivation and the cross-comparison of the various methods are greatly facilitated. Each method is then analysed to determine key characteristics, i.e. (i) steady-state agreement, (ii) initial-value agreement, (iii) independence of the reduced model on the choice of retained state variables and inputs, and (iv) eigen vector orientation. Realistic, large-scale systems are used to evaluate the static and dynamic characteristics of each model reduction method numerically. These studies reveal some important, and often unrecognized, weaknesses of several traditional techniques and confirm the strength of the newly-developed technique of Litz.

An Adaptive Nonlinear Predictive Controller

The design and implementation of a new adaptive nonlinear predictive controller is presented using a general nonlinear model and variable transformations. The resulting controller is similar in form to standard linear model predictive controllers and can be tuned analogously. This design allows the controller to be updated on-line without recalculating the controller gain matrix, which involves a matrix inversion. The new controller is compared to a PI controller and to an adaptive linear predictive controller through simulations.

Optimal stabilizing controllers for bilinear systems

A new method for the design of stabilizing controllers for multivariable bilinear systems is presented. The design method is based on a Liapunov stability theorem and the solution of a Liapunov equation. The resulting non-linear control globally asymptotically stabilizes the closed-loop system and minimizes a generalized quadratic performance index. The effect of the weighting matrices on the closed-loop response is analysed. Simulation results demonstrate that the new design technique provides better control than linear feedback. Moreover, the linear feedback can destabilize the closed-loop system depending on the initial conditions, whereas the new control strategy results in global asymptotic stability.

A comparison of the optical projection lithography simulators in SAMPLE and PROLITH

This paper documents important algorithmic details not available in the open literature, and illustrates differences and similarities between the SAMPLE and PROLITH programs using representative lithography systems as examples. Numerical comparisons demonstrate that the aerial images calculated by SAMPLE and PROLITH are in generally good agreement. At high numerical resolution, the programs provide the same qualitative lithographic information, including latent images and edge profile results; however, significant degradation occurs at lower restorations. Adequate results are obtained using a vertical resolution smaller than one-twentieth of the theoretical standing-wave wavelength. Significant disagreement is found in the output of the post-exposure bake algorithms where SAMPLE predicts much lower standing-wave amplitude attenuation effects. >

A self-tuning controller for systems with unknown or varying time delays†

A SISO self-tuning controller with a Smith-predictor type time delay compensator (STC-TDC) is proposed to handle processes with unknown or varying time delays. Two numerical examples comparing PI control, the standard STC of Clarke and Gawthrop, the self-tuning Dahlin algorithm of Vogel and Edgar, and the STC-TDC show that the new approach performs best for both setpoint and load changes when process time delay changes occur. A third example shows that the STC-TDC matches the extended stability characteristics of the alternative approach due to Kurz and Goedecke but is computationally much simpler.

Use of scatterometric latent-image detector in closed-loop feedback control of linewidth

The use of a diffraction-based latent image detector during the post-exposure bake (PEB) step for a chemically amplified resist system was investigated and its use in a feedback control strategy was examined. A calibration between intensity of light diffracted from the wafers during PEB and the final post-develop linewidth was determined. Using this relationship, two feedback control strategies were tested. One method altered the PEB time to compensate for unmeasured process disturbances and drive the linewidth to its target. The other method involved altering of the develop time. We found that using the post-exposure bake monitor in a feedback control system can improve wafer-to-wafer and lot-to-lot variability to below that which has been possible through conventional SEM measurements.

Dynamic analysis and control of a tubular autothermal reactor at an unstable state

Abstract The dynamic behavior of an autothermal reactor with internal countercurrent heat exchange is represented by a relatively simple mathematical approximat which retains essentially all of the steady state and dynamic features of real reactors. The system of partial differential equations is discretized in space by the method of orthogonal collocation and the convergence of the eigenvalues of the linearized model is found to be extremely difficult to achieve in the unstable region near blow-off. Different model reduction techniques are investigated and compared. Modal control with state or output feedback and a single manipulated input is used an attempt to stabilize the system. A technique based on a low-order collocation model provides good control action, whereas most of the conventional, approximate methods fail to stabilize the unstable model of the reactor. The features of the stable, closed-loop system are confirmed through simulated reactor transient tests.

On controlling an autothermal fixed-bed reactor at an unstable state—III: Model reduction and control strategies which avoid sstate estimation

Abstract A simplified approach for the control of fixed-bed reactors is discussed. Key elements include: (i) careful modeling of the reactor to obtain a lumped approximation with good internal structure (i.e. appropriate coupling between inputs and state variables through the different response modes); (ii) a major reduction in model size to an accurate, low-order form; (iii) derivation of a control algorithm for the low-order model; and (iv) direct application to the full-order system without the use of state estimation. The success of this approach is rooted in the choice of modeling techniques and of a model reduction procedure. The powerful new reduction method of Litz is evaluated here. Applications of the technique to a simulated unstable autothermal reactor are demonstrated for the case of modal control with incomplete state feedback. Results point to a high probability of success in subsequent experimental tests.

A generalized structural dominance method for the analysis of large-scale systems

The structural dominance method of Litz is generalized to aid in determining not only the dominant modes, as in the original method, but also the most sensitive state variables and the most effective inputs of a linear, large-scale system. Through the addition or modification of a number of features, the utility of the method to the control system designer has been greatly enhanced. These include: (a) avoiding the gain normalization procedure of the original method (which eliminates information on input/output sensitivity), (b) definition of input- and state-variable normalization elements (so as to permit evaluation of variable sensitivities by direct numerical comparison), and (c) generalization of a time-weighting technique (to assist in determining minimum order of the reduced system model). With the range of measures provided in the generalized method, the system designer can now introduce both subjective and objective criteria quite naturally into the selection of a control structure (choice of meas...