Mayuresh V. Kothare

Robust constrained model predictive control using linear matrix inequalities

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to explicitly deal with model uncertainty. In this paper, the authors address the robustness issue in MPC by directly incorporating the description of plant uncertainty in the MPC problem formulation. The plant uncertainty is expressed in the time-domain by allowing the state-space matrices of the discrete-time plant to be arbitrarily time-varying and belonging to a polytope. The existence of a feedback control law minimizing an upper bound on the infinite horizon objective function and satisfying the input and output constraints is reduced to a convex optimization over linear matrix inequalities (LMIs). It is shown that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing.

Brief An efficient off-line formulation of robust model predictive control using linear matrix inequalities

The practicality of model predictive control (MPC) is partially limited by its ability to solve optimization problems in real time. Moreover, on-line computational demand for synthesizing a robust MPC algorithm will likely grow significantly with the problem size. In this paper, we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained MPC algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off-line one within another in state space. This off-line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed-loop system and substantial reduction of the on-line MPC computation. The controller design is illustrated with two examples.

Anti-windup design for internal model control

This paper considers linear control design for systems with input magnitude saturation. A general anti-windup scheme which optimizes nonlinear performance, applicable to MIMO systems, is developed. Several examples, including an ill-conditioned plant, show that the scheme provides graceful degradation of performance. The attractive features of this scheme are its simplicity and effectiveness.

Brief Multiplier theory for stability analysis of anti-windup control systems

We apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti-windup bumpless transfer (AWBT) schemes. For appropriate choices of the multipliers, we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities (LMIs). We show that a number of previously reported attempts to analyze AWBT stability, using seemingly diverse techniques such as the Popov, circle and off-axis circle criteria, the optimally scaled small-gain theorem (generalized @m upper bound) and describing functions can all be generalized within the framework of this paper.

Efficient robust constrained model predictive control with a time varying terminal constraint set

Abstract An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N =0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.

Novel microfluidic interconnectors for high temperature and pressure applications

Reliable microfluidic interconnectors are one of the basic building blocks of integrated fluidic and chemical reaction systems-on-chip. Though many ideas have been proposed and implemented in the literature for creating different kinds of macro-to-micro fluidic connections, development of integrated on-chip connectors for high temperature and pressure microfluidic applications has not been properly studied. Such connectors will be indispensable in true on-chip chemical processing applications for reactions which require more severe operating conditions than those possible using currently available interconnection techniques. In this paper we present novel microfluidic interconnects that can be used in applications involving operating temperatures of up to 275 °C and pressures in excess of 315 Psi (21.43 atm). The only wetted surfaces in this design are teflon, silicon and pyrex glass, making the design inert to most chemicals. High-pressure leakage, pull-out and high-temperature durability tests conducted on the interconnect show that the connections obtained are superior to those reported in the literature using other techniques. Structural analysis of the interconnect is carried out to illustrate the effect of interconnect geometry on strength and high-pressure performance.

Towards a palladium micro-membrane for the water gas shift reaction: microfabrication approach and hydrogen purification results

A novel palladium-based micromembrane is reported that can be used for hydrogen gas separation in a miniature fuel processor for micro fuel cells. The micromembrane structure is built in a silicon substrate, using standard MEMS microfabrication processes. Four layers, viz. copper, aluminum, spin-on-glass (SOG) and palladium form the composite membrane. Copper, aluminum and SOG layers provide structural support for the palladium film. Copper can act as catalyst in the water gas shift reaction that converts unwanted carbon monoxide gas into hydrogen. Palladium is used to separate hydrogen from other gases present. The micromembrane selectively separates hydrogen from a 20:80 hydrogen:argon gas mixture by weight even at room temperature. The diffusion of hydrogen through palladium is enhanced at higher temperatures and pressures, closely following the predictions from Sieverts law. Future applications of this micromembrane for simultaneous water gas shift reaction and hydrogen separation are discussed.

Control of a solution copolymerization reactor using multi-model predictive control

We study the control of a solution copolymerization reactor using a model predictive control algorithm based on multiple piecewise linear models. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function which has finite and infinite horizon cost components and uses multiple linear models in its predictions. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and takes the system to the final operating point. Simulation results on an industrial scale methyl methacrylate vinyl acetate solution copolymerization reactor model demonstrate the ability of the algorithm to rapidly transition the process between different operating points.

A System-on-a-Chip Implementation for Embedded Real-Time Model Predictive Control

This paper presents a hardware architecture for embedded real-time model predictive control (MPC). The computational cost of an MPC problem, which relies on the solution of an optimization problem at every time step, is dominated by operations on real matrices. In order to design an efficient and low-cost application-specific processor, we analyze the computational cost of MPC, and we propose a limited-resource host processor to be connected with an application-specific matrix coprocessor. The coprocessor uses a 16-b logarithmic number system arithmetic unit, which is designed using cotransformation, to carry out the required arithmetic operations. The proposed architecture is implemented by means of a hardware description language and then prototyped and emulated on a field-programmable gate array. Results on computation time and architecture area are presented and analyzed, and the functionality of the proposed architecture is verified using two case studies: a linear problem of a rotating antenna and a nonlinear glucose-regulation problem. The proposed MPC architecture yields a small-in-size and energy-efficient implementation that is capable of solving the aforementioned problems on the order of milliseconds, and we compare its performance and area requirements with other MPC designs that have appeared in the literature.

A co-processor FPGA platform for the implementation of real-time model predictive control

In order to effectively control nonlinear and multivariable models, and to incorporate constraints on system states, inputs and outputs (bounds, rate of change), a suitable (sometimes necessary) controller is model predictive control (MPC). MPC is an optimization-based control scheme that requires abundant matrix operations for the calculation of the optimal control moves. In this work we propose a mixed software and hardware embedded MPC implementation. Using a codesign step and based on profiling results, we decompose the optimization algorithm into two parts: one that fits into a host processor and one that fits into a custom made unit that performs the computationally demanding arithmetic operations. The profiling results and information on the co-processor design are provided