Vinay Kariwala

Multirate-Output-Feedback-Based LQ-Optimal Discrete-Time Sliding Mode Control

The traditional approach for sliding mode control design has been the design of a controller to achieve a predesigned sliding objective. However, not much research has been carried out on the design of the sliding surface. This note presents a technique for designing a sliding surface such that when confined to the surface, the closed-loop system has optimality in the linear quadratic sense. The paper also proposes a multirate-output-feedback-based controller that leads the system to the aforementioned optimal sliding mode.

Bidirectional branch and bound for controlled variable selection. Part I: principles and minimum singular value criterion.

The minimum singular value (MSV) rule is a useful tool for selecting controlled variables (CVs) from the available measurements. However, the application of the MSV rule to large-scale problems is difficult, as all feasible measurement subsets need to be evaluated to find the optimal solution. In this paper, a new and efficient branch and bound (BAB) method for selection of CVs using the MSV rule is proposed by posing the problem as a subset selection problem. In traditional BAB algorithms for subset selection problems, pruning is performed downwards (gradually decreasing subset size). In this work, the branch pruning is considered in both upward (gradually increasing subset size) and downward directions simultaneously so that the total number of subsets evaluated is reduced dramatically. Furthermore, a novel bidirectional branching strategy to dynamically branch solution trees for subset selection problems is also proposed, which maximizes the number of nodes associated with the branches to be pruned. Finally, by replacing time-consuming MSV calculations with novel determinant based conditions, the efficiency of the bidirectional BAB algorithm is increased further. Numerical examples show that with these new approaches, the CV selection problem can be solved incredibly fast.

Bidirectional Branch and Bound for Controlled Variable Selection Part II. Exact Local Method for Self-optimizing Control

Abstract The selection of controlled variables (CVs) from available measurements through enumeration of all possible alternatives is computationally forbidding for large-dimensional problems. In Part I of this work [Cao, Y., & Kariwala, V. (2008). Bidirectional branch and bound for controlled variable selection: Part I. Principles and minimum singular value criterion. Comput. Chem. Eng., 32 (10), 2306–2319], we proposed a bidirectional branch and bound (BAB) approach for subset selection problems and demonstrated its efficiency using the minimum singular value criterion. In this paper, the BAB approach is extended for CV selection using the exact local method for self-optimizing control. By redefining the loss expression, we show that the CV selection criterion for exact local method is bidirectionally monotonic. A number of novel determinant based criteria are proposed for fast pruning and branching purposes resulting in a computationally inexpensive BAB approach. We also establish a link between the problems of selecting a subset and combinations of measurements as CVs and present a partially bidirectional BAB method for selection of measurements, whose combinations can be used as CVs. Numerical tests using randomly generated matrices and binary distillation column case study demonstrate the computational efficiency of the proposed methods.

Bidirectional Branch and Bound for Controlled Variable Selection Part III: Local Average Loss Minimization

The selection of controlled variables (CVs) from available measurements through exhaustive search is computationally forbidding for large-scale processes. We have recently proposed novel bidirectional branch and bound (B3) approaches for CV selection using the minimum singular value (MSV) rule and the local worst-case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. Thus, CV selection by minimizing local average loss can be deemed as most reliable. In this work, the B3 approach is extended to CV selection based on local average loss metric. Lower bounds on local average loss and, fast pruning and branching algorithms are derived for the efficient B3 algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.

Plantwide control : recent developments and applications

The use of control systems is necessary for safe and optimal operation of industrial processes in the presence of inevitable disturbances and uncertainties. Plant-wide control (PWC) involves the systems and strategies required to control an entire chemical plant consisting of many interacting unit operations. Over the past 30 years, many tools and methodologies have been developed to accommodate increasingly larger and more complex plants. This book provides a state-of-the-art of techniques for the design and evaluation of PWC systems. Various applications taken from chemical, petrochemical, biofuels and mineral processing industries are used to illustrate the use of these approaches. This book contains 20 chapters organized in the following sections:

Brief paper: Fundamental limitation on achievable decentralized performance

A commonly accepted fact is that the diagonal structure of the decentralized controller poses fundamental limitations on the achievable performance, but few quantitative results are available for measuring these limitations. This paper provides a lower bound on the achievable quality of disturbance rejection using a decentralized controller for stable discrete time linear systems with time delays, which do not contain any finite zeros on or outside the unit circle. The proposed result is useful for assessing when full multivariable controllers can provide significantly improved performance, as compared to decentralized controllers. The results are also extended to the case, where the individual subcontrollers are restricted to be PID controllers.

Three dimensional digital holographic profiling of micro-fibers

A method to measure the size, orientation, and location of opaque micro-fibers using digital holography is presented. The method involves the recording of a digital hologram followed by reconstruction at different depths. A novel combination of automated image analysis and statistical techniques, applied on the intensity of reconstructed digital holograms is used to accurately determine the characteristics of the micro-fibers. The performance of the proposed method is verified with a single fiber of known length and orientation. The potential of the method for measurement of fiber length is further demonstrated through its application to a suspension of fibers in a liquid medium.

Decentralized Control of Solid Oxide Fuel Cells

Environmental concerns and limited availability of natural resources have made solid oxide fuel cells (SOFC) a promising alternative for large-scale electricity production. A control system is needed for SOFCs to meet operational objectives and ensure safe operation. Previous studies showed that the control of SOFC is challenging due to its slow response time, tight operating constraints and unavailability of some key measurements. In this work, simple yet reliable decentralized proportional-integral-derivative (PID) controllers are systematically designed based on a benchmark nonlinear dynamic model of SOFC . The design procedure involves selection of controlled variables (CVs), input-output pairing selection, and PID controller tuning. For CV selection, a novel method is proposed such that maintaining the CVs at constant setpoints facilitates constraint satisfaction for all key variables. Closed-loop simulations demonstrate that the proposed decentralized PI controllers are able to closely meet the control objectives of SOFC even in the presence of changing operating conditions.

Brief paper: Branch and bound method for multiobjective pairing selection

Most of the available methods for selection of input-output pairings for decentralized control require evaluation of all alternatives to find the optimal pairings. As the number of alternatives grows rapidly with process dimensions, pairing selection through an exhaustive search can be computationally forbidding for large-scale processes. Furthermore, the different criteria can be conflicting necessitating pairing selection in a multiobjective optimization framework. In this paper, an efficient branch and bound (BAB) method for multiobjective pairing selection is proposed. The proposed BAB method is illustrated through a biobjective pairing problem using selection criteria involving the relative gain array and the @m-interaction measure. The computational efficiency of the proposed method is demonstrated by using randomly generated matrices and the large-scale case study of cross-direction control.

On-line digital holographic measurement of size and shape of microparticles for crystallization processes

Crystallization is a widely used chemical process that finds applications in pharmaceutical industries. In an industrial crystallization process, it is not only important to produce pure crystals but also to control the shape and size of the crystals, as they affect the efficiency of downstream processes and the dissolution property of the drug. The effectiveness of control algorithms depend on the availability of on-line, real-time information about these critical properties. In this paper, we investigate the use of lens-less in-line digital holographic microscopy for size and shape measurements for crystallization processes. For this purpose, we use non-crystalline spherical microparticles and carbon fibers with known sizes present in a liquid suspension as test systems. We propose an algorithm to extract size and shape information for a population of microparticles from the experimentally recorded digital holograms. The measurements obtained from the proposed method show good agreement with the corresponding known size and shape of the particles.