W. Fred Ramirez

Obtaining smoother singular arc policies using a modified iterative dynamic programming algorithm

Dynamic programming is a very powerful technique for the optimization of dynamic systems. With the ready availability of high-speed computers and the development of the iterative dynamic programming (IDP) algorithm, a feasible alternative to the calculus of variations approach to the optimal control problem is now available. Inherent in the IDP algorithm is the application of piecewise constant discretized controls. This often leads to singular optimal control policies that are highly active. The aim of this research is to modify the IDP algorithm to reduce the control energy variations that are typical of IDP while at the same time developing policies that are very close to the true optimal control. This is achieved by including a filter within the IDP procedure. Two types of filtering schemes are considered: a median filter and a first-order filter. Application of this modified algorithm to two bioreactor systems that yield singular optimal control profiles is presented and the usefulness of this scheme...

Simultaneous measurement of the thermal conductivity and thermal diffusivity of unconsolidated materials by the transient hot wire method

This paper describes a new design for the transient hot wire method that can obtain the thermal conductivity and thermal diffusivity of unconsolidated materials. In this method, the thermal conductivity is determined from the slope of the temperature rise versus time of an electrically heated wire. The temperature rise is detected as the unbalanced voltage of a precision Wheatstone bridge. This voltage is read by a microcomputer via a high‐speed analog‐to‐digital converter. The instrument was designed so that measurements can be taken over a temperature range of 20–200 °C and a pressure range of atmospheric down to 10 mTorr. Tests using glycerin indicate an accuracy of 1% for the conductivity and 6% for the diffusivity and a precision of 0.4% for the conductivity and 4.5% for the diffusivity. Measurements have also been made on materials such as 50‐μ glass beads and unconsolidated spent oil shale.

Optimal Injection Policies for Enhanced Oil Recovery: Part 1 Theory and Computational Strategies

The theory of optimal control of distributed-parameter systems is presented for determining the best possible injection policies for EOR processes. The optimization criterion is to maximize the amount of oil recovered at minimum injection costs. Necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagins weak minimum principle. A gradient method is proposed for the computation of optimal injection policies.

Photopolymerized, Multilaminated Matrix Devices with Optimized Nonuniform Initial Concentration Profiles To Control Drug Release

This paper describes a novel approach to obtain desired release profiles from diffusion-controlled matrix devices by employing nonuniform initial concentration profiles theoretically and experimentally. Theoretically, a model was developed to examine the effect of nonuniform initial concentration profiles on matrix release behavior, and an optimization technique was investigated to determine suitable nonuniform initial concentration profiles which provide desired release patterns. Experimentally, release rates of an organic dye from photopolymerized matrix devices were measured to test the application of these mathematical techniques and the efficacy of photolaminated matrices in approximating the optimized release behavior. All system parameters were measured by independent experiments, and the experimental release data agree very well with the computed results.

Chapter 8 – SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

The aim of this chapter is to discuss finite-difference techniques for the solution of partial differential equations. It presents various techniques for pure convection problems, pure diffusion or dispersion problems, and mixed convection diffusion problems. It illustrates each case with common physical examples. It also introduces Special techniques for one- and two-dimensional flow through porous media. It also introduces the method of weighted residuals. Low-order weighted residual approximations work well when the solution varies smoothly over the entire domain of the trial function. When there are rapid changes over a varying portion of the domain, then the method requires high-order approximations. In that case, the finite-difference approach is more effective. Convective-diffusion problems are particularly difficult for the weighted residual method, whereas pure conduction problems can be treated very efficiently by this approach.

Use of volume averaging for the modeling of thermal properties of porous materials

Abstract The thermal conductivity and thermal diffusivity of single and two-phase materials were measured using the transient hot wire method. The mathematical basis for the use of this method for measurements on single phase materials is well documented. Thermal property measurements on two-phase materials are more complex to analyse than those of single phase materials. A mathematical model based on volume averaging was developed to predict measured values of the effective thermal properties of two-phase materials.

Optimal state and parameter identification. An application to batch fermentation

Abstract Simultaneous state and parameter identification is a problem that has not been addressed very often nor successfully in the past. In this work I present a general algorithm for coupling state variable and model parameter identification. A specific system that requires the simultaneous identification of process states and model parameters is that of batch beer fermentation. Results show the advantages in coupling a sequential parameter identification algorithm with the Kalman filter state identification algorithm. Such a combined algorithm has the capability of accurately estimating the entire state of the process even when some model parameters are uncertain. This strategy of using the best deterministic process information coupled with sequential updating can be successfully applied to many chemical and biochemical processing problems including batch beer fermentation.

Dynamic hybrid neural network model of an industrial fed-batch fermentation process to produce foreign protein

An industrial pharmaceutical company has provided industrial pilot scale fed-batch data from a biological process used to produce a foreign protein from fed-batch fermentation. This process had proven difficult to control due to the complex behavior of the bacteria after induction. Because of the difficulty of modeling the process fundamentally, neural networks are an attractive alternative. To capture dynamic systems a gray box model approach of parameter function neural networks was used. The parameter function neural network approach has been able to capture well this pilot scale fed-batch fermentation process. In order to obtain accurate training data, the data sets were fit and smoothed using smoothing cubic spline functions. Neural networks were found for the five critical parameter functions of growth rate, glucose consumption rate, oxygen consumption rate, acetate production rate, and protein production rate. Relatively simple networks were used in order to capture process behavior and not the significant noise in the industrial scale pilot data. Simulations using the neural network parameters predicted dynamic response data well.

State controllability and optimal regulator control of time-delayed systems

An important recent advance in the solution of the optimal regulator control problem for time-delayed systems is extended here to multivariable systems and to systems which exhibit multiple time delays. The state equations are partitioned into discrete and continuous portions through a state transformation such that the solution of the optimal regulator problem reduces to finding a steady-state controller gain based on both a discrete and continuous Riccati matrix. The discrete Ricatti matrix is found independently of the continuous solution due to the partitioning of the state equations, and it is not necessary to solve the system of partial differential Riccati equations which arise in the traditional solution of the linear quadratic regulator (LQR) problem for time-delayed systems. In addition, through this state transformation it becomes possible to extend the standard state controllability tests to time-delayed systems. It is shown that the controllability of the transformed state space is necessary for a feasible solution to the optimal regulator problem for time-delayed systems. This is an important test to determine the practicality of various time-delayed system realizations. Numerical examples illustrate the application of the technique to systems exhibiting multiple time delays, multivariable systems and time-series models. It is shown that the classic Wood-Berry distillation model realization does not possess state controllability properties which explains why this system has been historically difficult to control using feedback techniques.

Use of optimal control theory to optimize carbon dioxide miscible-flooding enhanced oil recovery

Abstract Optimal control theory is used to determine optimal injection strategies that maximize the profitability of the carbon dioxide enhanced oil recovery process. Based upon a modified black oil model, a comparative study was made to determine how optimization can improve upon currently practiced injection policies of a single carbon dioxide slug, simultaneous injection of CO 2 and water, and WAG injection. The results show that optimal slug volumes of carbon dioxide can be computed. Also, the wellbore pressure is shown to be an important control variable affecting the optimal performance of a carbon dioxide flood.