Eranda Harinath

Nonlinear model predictive control using polynomial optimization methods

This paper reviews and provides perspectives on the design of nonlinear model predictive control systems for polynomial systems. General nonlinear systems can often be rewritten exactly as polynomial systems or approximated as polynomial systems using Taylor series. This paper discusses the application of model predictive control (MPC) to these types of systems. After MPC problem for discrete-time polynomial systems is formulated as a polynomial program, moment-based and dual-based sum-of-squares (SOS) algorithms and their relationship are described as two promising methods for solving the polynomial programs to global optimality. Finally, future directions for research are proposed, including real-time, output-feedback, and robust/stochastic polynomial MPC.

Robust optimal control for the maximization of design space

A commonly applied procedure in the pharmaceutical industry is to determine the maximum allowable set of uncertain parameters-called the design space-that guarantees that the product quality attributes obtained by a manufacturing process are within the specific limits. Design spaces in industry are constructed without considering the effects of process dynamics or feedback control, which results in design spaces that poorly characterize the real operations. This paper presented approaches for determining the design space for a dynamic state-space model with linear fractional uncertainties and for synthesizing a linear feedback control law for a set of ellipsoidal quality attributes by using invariant set theory. The proposed method is illustrated in a simulation example.

Tablet coating by injection molding technology – Optimization of coating formulation attributes and coating process parameters

Graphical abstract Figure. No Caption available. Abstract We developed and evaluated a solvent‐free injection molding (IM) coating technology that could be suitable for continuous manufacturing via incorporation with IM tableting. Coating formulations (coating polymers and plasticizers) were prepared using hot‐melt extrusion and screened via stress‐strain analysis employing a universal testing machine. Selected coating formulations were studied for their melt flow characteristics. Tablets were coated using a vertical injection molding unit. Process parameters like softening temperature, injection pressure, and cooling temperature played a very important role in IM coating processing. IM coating employing polyethylene oxide (PEO) based formulations required sufficient room humidity (>30% RH) to avoid immediate cracks, whereas other formulations were insensitive to the room humidity. Tested formulations based on Eudrajit E PO and Kollicoat IR had unsuitable mechanical properties. Three coating formulations based on hydroxypropyl pea starch, PEO 1,000,000 and Opadry had favorable mechanical (<700 MPa Young’s modulus, >35% elongation, >95 × 104 J/m3 toughness) and melt flow (>0.4 g/min) characteristics, that rendered acceptable IM coats. These three formulations increased the dissolution time by 10, 15 and 35 min, respectively (75% drug release), compared to the uncoated tablets (15 min). Coated tablets stored in several environmental conditions remained stable to cracking for the evaluated 8‐week time period.

Model Predictive Control of Polynomial Systems

This chapter describes the design of nonlinear model predictive control (MPC) for polynomial systems. Polynomial systems arise in many applications, including in power generation, automotives, aircraft, magnetic levitation, chemical reactors, and biological networks. Furthermore, general nonlinear dynamical systems can usually be rewritten exactly as polynomial systems or approximated as polynomial systems using Taylor series. MPC for discrete-time polynomial systems is formulated as a polynomial program. Hierarchical semidefinite programing relaxation methods are discussed for solving these polynomial programs to global optimality. Then, the methods for fast polynomial MPC are described, including convexification formulations for input-affine systems and explicit algorithms using algebraic geometry methods. Methods are then described for converting general nonlinear dynamical systems into polynomial systems using Taylor’s theorem, and an illustrative simulation example is presented for the practical implementation of Taylor’s theorem for bounding control trajectories. Finally, future directions for research are proposed, including real-time, output-feedback, and robust/stochastic polynomial MPC.

Control and Systems Theory for Advanced Manufacturing

This chapter describes systems and control theory for advanced manufacturing. These processes have (1) high to infinite state dimension; (2) probabilistic parameter uncertainties; (3) time delays; (4) unstable zero dynamics; (5) actuator, state, and output constraints; (6) noise and disturbances; and (7) phenomena described by combinations of algebraic, ordinary differential, partial differential, and integral equations (that is, generalizations of descriptor/singular systems). Model predictive control formulations are described that have the flexibility to handle dynamical systems with these characteristics by employing polynomial chaos theory and projections. Implementations of these controllers on multiple advanced manufacturing processes demonstrate an order-of-magnitude improved robustness and decreased computational cost. Some promising directions are proposed for future research.

Demonstration of pharmaceutical tablet coating process by injection molding technology

We demonstrate the coating of tablets using an injection molding (IM) process that has advantage of being solvent free and can provide precision coat features. The selected core tablets comprising 10% w/w griseofulvin were prepared by an integrated hot melt extrusion-injection molding (HME-IM) process. Coating trials were conducted on a vertical injection mold machine. Polyethylene glycol and polyethylene oxide based hot melt extruded coat compositions were used. Tablet coating process feasibility was successfully demonstrated using different coating mold designs (with both overlapping and non-overlapping coatings at the weld) and coat thicknesses of 150 and 300 μm. The resultant coated tablets had acceptable appearance, seal at the weld, and immediate drug release profile (with an acceptable lag time). Since IM is a continuous process, this study opens opportunities to develop HME-IM continuous processes for transforming powder to coated tablets.

Maximization of ellipsoidal design space for continuous-time systems: A robust optimal control approach

In the pharmaceutical industry, it is common to determine the maximum allowable set of uncertain parameters - called the design space - that guarantees that the product quality attributes obtained by a manufacturing process are within specified limits. In industrial practice, design spaces are constructed without considering the effects of process dynamics or feedback control, which results in poor characterization of operations. This paper presents an approach for determining the design space for a continuous-time state-space model with linear fractional uncertainties and for simultaneously synthesizing a linear feedback controller. For a set of ellipsoidal quality attributes, a parameterization of the ellipsoidal design space is proposed. Then, a robust optimal control technique is presented to ensure the ellipsoidal quality attributes are satisfied while maximizing the volume of the ellipsoidal design space. The proposed approach is illustrated in a simulation example.

A robust dual-mode MPC approach to ensuring critical quality attributes in Quality-by-Design

In the Quality-by-Design (QbD) paradigm for pharmaceutical processes, critical quality attributes (CQAs) must meet specifications for all possible realizations of critical process parameters (CPPs) within a design space. During the startup of such a process, it is desired to begin meeting CQA specifications as quickly as possible and then robustly guarantee that specifications will continue to be met. This paper proposes a robust dual-mode model predictive controller (RDMPC) for meeting these objectives, for discrete-time linear systems with a linear fractional transformation (LFT) uncertainty description. The receding-horizon controller steers the system into a controlled invariant set in finite time, after which the terminal controller is applied to robustly guarantee specifications on CQAs for all time. The proposed control algorithm is demonstrated for a continuous stirred-tank reactor.