Studies on Feedback Control of Cardiac Alternans

A beat-to-beat variation in the electric wave propagation morphology in myocardium is referred to as cardiac alternans and it has been linked to the onset of life threatening arrhythmias and sudden cardiac death. Experimental studies have demonstrated that alternans can be annihilated by the feedback modulation of the basic pacing interval in a small piece of cardiac tissue. In this work, we study the capability of feedback control to suppress alternans both spatially and temporally in an extracted rabbit heart and in a cable of cardiac cells. This work demonstrates real-time control of cardiac alternans in an extracted rabbit heart and provides an analysis of the control methodology applied in the case of a one-dimensional (1D) cable of cardiac cells. The real-time system control is realized through feedback by proportional perturbation of the basic pacing cycle length (PCL). The measurements of the electric wave propagation are obtained by optical mapping of fluorescent dye from the surface of the heart and are fed into a custom-designed software that provides the control action signal that perturbs the basic pacing cycle length. In addition, a novel pacing protocol that avoids conduction block is applied. A numerical analysis, complementary to the experimental study is also carried out, by the ionic model of a 1D cable of cardiac cells under a self-referencing feedback protocol, which is identical to the one applied in the experimental study. Further, the amplitude of alternans linear parabolic PDE that is associated with the 1D ionic cardiac cell cable model under full state feedback control is analyzed. We provide an analysis of the amplitude of alternans parabolic PDE which admits a standard evolutionary form in a well defined functional space. Standard modal decomposition techniques are used in the analysis and the controller synthesis is carried out through pole-placement. State and output feedback controller realizations are developed and the important issue of measurement noise in the controller implementation is addressed. The analysis of stabilization of the amplitude of alternans PDE is in agreement with the experimental results and numerical results produced by the ionic 1D cable of cardiac cells model. Finally, a discussion is provided in light of these results in order to use control to suppress alternans in the human myocardium.     

Predictive control of parabolic PDEs with boundary control actuation

This work focuses on predictive control of linear parabolic partial differential equations (PDEs) with boundary control actuation subject to input and state constraints. Under the assumption that measurements of the PDE state are available, various finite-dimensional and infinite-dimensional predictive control formulations are presented and their ability to enforce stability and constraint satisfaction in the infinite-dimensional closed-loop system is analyzed. A numerical example of a linear parabolic PDE with unstable steady state and flux boundary control subject to state and control constraints is used to demonstrate the implementation and effectiveness of the predictive controllers.     

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto-Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.     

Boundary control synthesis for a lithium‐ion battery thermal regulation problem

The thermal regulation problem for a lithium ion (Li‐ion) battery with boundary control actuation is considered. The model of the transient temperature dynamics of the battery is given by a nonhomogeneous parabolic partial differential equation (PDE) on a two‐dimensional spatial domain which accounts for the time‐varying heat generation during the battery discharge cycle. The spatial domain is given as a disk with radial and angular coordinates which captures the nonradially symmetric heat‐transfer phenomena due to the application of the control input along a portion of the spatial domain boundary. The Li‐ion battery model is formulated within an appropriately defined infinite‐dimensional function space setting which is suitable for spectral controller synthesis. The key challenges in the output feedback model‐based controller design addressed in this work are: the dependence of the state on time‐varying system parameters, the restriction of the input along a portion of the battery domain boundary, the observer‐based optimal boundary control design where the separation principle is utilized to demonstrate the stability of the closed loop system, and the realization of the outback feedback control problem based on state measurement and interpolation of the temperature field. Numerical results for simulation case studies are presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3782–3796, 2013     

Guaranteed cost distributed fuzzy observer‐based control for a class of nonlinear spatially distributed processes

The guaranteed cost distributed fuzzy (GCDF) observer‐based control design is proposed for a class of nonlinear spatially distributed processes described by first‐order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer‐based control design is developed in terms of a set of space‐dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed‐loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug‐flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013     

Drag reduction in flow over a flat plate using active feedback control

This paper focuses on two-dimensional incompressible Newtonian fluid flow over a flat plate and studies the problem of reducing the frictional drag exerted on the plate using active feedback control. Several alternative control configurations, including both pointwise and spatially uniform control actuation and sensing, are developed and tested through computer simulations. All control configurations use control actuation in the form of blowing/suction on the plate and measurements of shear stresses along the plate. The simulation results indicate that the use of active feedback control, which employs reasonable control effort, can significantly reduce the frictional drag exerted on the plate compared to the open-loop values.     

Low‐order optimal regulation of parabolic PDEs with time‐dependent domain

Observer and optimal boundary control design for the objective of output tracking of a linear distributed parameter system given by a two‐dimensional (2‐D) parabolic partial differential equation with time‐varying domain is realized in this work. The transformation of boundary actuation to distributed control setting allows to represent the system's model in a standard evolutionary form. By exploring dynamical model evolution and generating data, a set of time‐varying empirical eigenfunctions that capture the dominant dynamics of the distributed system is found. This basis is used in Galerkin's method to accurately represent the distributed system as a finite‐dimensional plant in terms of a linear time‐varying system. This reduced‐order model enables synthesis of a linear optimal output tracking controller, as well as design of a state observer. Finally, numerical results are prepared for the optimal output tracking of a 2‐D model of the temperature distribution in Czochralski crystal growth process which has nontrivial geometry. © 2014 American Institute of Chemical Engineers AIChE J, 61: 494–502, 2015     

二元聚合物共混膜形貌与力学性能的计算机模拟

The effects of blend composition and micro-phase structure on the mechanical behavior of A/B polymer blend film are studied by coupling the Monte Carlo (MC) simulation of morphology with the lattice spring model (LSM) of micro mechanics of materials. The MC method with bond length fluctuation and cavity diffusion algorithm on cubic lattice is adopted to simulate the micro-phase structure of A/B polymer blend. The information of morphology and structure is then inputted to the LSM composed of a three-dimensional network of springs to obtain the mechanical properties of polymer blend film. Simulated results show that the mechanical response is mainly affected by the density and the composition of polymer blend film through the morphology transition. When a force is applied on the outer boundary of polymer blend film, the vicinity of the inner cavities experiences higher stresses and strains responsible for the onset of crack propagation and the premature failure of the entire system.     

Cellular Mechanisms of the Anti-Arrhythmic Effect of Cardiac PDE2 Overexpression

Background: Phosphodiesterases (PDE) critically regulate myocardial cAMP and cGMP levels. PDE2 is stimulated by cGMP to hydrolyze cAMP, mediating a negative crosstalk between both pathways. PDE2 upregulation in heart failure contributes to desensitization to β-adrenergic overstimulation. After isoprenaline (ISO) injections, PDE2 overexpressing mice (PDE2 OE) were protected against ventricular arrhythmia. Here, we investigate the mechanisms underlying the effects of PDE2 OE on susceptibility to arrhythmias. Methods: Cellular arrhythmia, ion currents, and Ca²⁺-sparks were assessed in ventricular cardiomyocytes from PDE2 OE and WT littermates. Results: Under basal conditions, action potential (AP) morphology were similar in PDE2 OE and WT. ISO stimulation significantly increased the incidence of afterdepolarizations and spontaneous APs in WT, which was markedly reduced in PDE2 OE. The ISO-induced increase in I_CaL seen in WT was prevented in PDE2 OE. Moreover, the ISO-induced, Epac- and CaMKII-dependent increase in I_NaL and Ca²⁺-spark frequency was blunted in PDE2 OE, while the effect of direct Epac activation was similar in both groups. Finally, PDE2 inhibition facilitated arrhythmic events in ex vivo perfused WT hearts after reperfusion injury. Conclusion: Higher PDE2 abundance protects against ISO-induced cardiac arrhythmia by preventing the Epac- and CaMKII-mediated increases of cellular triggers. Thus, activating myocardial PDE2 may represent a novel intracellular anti-arrhythmic therapeutic strategy in HF.     

Feedback control of hyperbolic distributed parameter systems

Hyperbolic distributed parameter systems (DPS) represent a large number of industrial processes with spatially nonuniform operating variable profiles. Research has been conducted to develop high-performance control strategies for these systems by exploiting their high-fidelity models. In this paper, a feedback control method that yields improved performance is proposed for DPS modelled by first-order hyperbolic partial differential equations (PDEs) using the method of characteristics. Simulation results show that this method can provide effective control for the systems modelled by a scalar PDE as well as a system of PDEs. Further, it can efficiently compensate the effect of model-plant mismatch and effectively reject the disturbances.     

Feedback control of dissipative PDE systems using adaptive model reduction

The problem of feedback control of spatially distributed processes described by highly dissipative partial differential equations (PDEs) is considered. Typically, this problem is addressed through model reduction, where finite dimensional approximations to the original infinite dimensional PDE system are derived and used for controller design. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ordinary differential equation (ODE) models using the method of weighted residuals. A common approach to this task is the Karhunen‐Loève expansion combined with the method of snapshots. To circumvent the issue of a priori availability of a sufficiently large ensemble of PDE solution data, the focus is on the recursive computation of eigenfunctions as additional data from the process becomes available. Initially, an ensemble of eigenfunctions is constructed based on a relatively small number of snapshots, and the covariance matrix is computed. The dominant eigenspace of this matrix is then utilized to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is recomputed with the addition of each snapshot with possible increase or decrease in its dimensionality; due to its small dimensionality the computational burden is relatively small. The proposed approach is applied to representative examples of dissipative PDEs, with both linear and nonlinear spatial differential operators, to demonstrate its effectiveness of the proposed methodology. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Behaviour of a Moving Droplet under Electrowetting Actuation: Numerical Simulation

Numerical simulation of droplet transport in microchannels under electrostatic actuation is investigated. Volume‐of‐Fluid (VOF) technique is employed, in which electrowetting effects are implemented through Lippmann's relation in the form of modified contact angles at the boundary. A velocity of about 35 mm/s is achieved with the actuation of 40 V. The droplet flow under electrowetting actuation is characterized for the majority of the process parameters such as actuation voltage, channel dimension, electrode size, and resultant velocity.     

Backstepping control of chemical tubular reactors

In this paper, a globally stabilizing boundary feedback control law for an arbitrarily fine discretization of a nonlinear PDE model of a chemical tubular reactor is presented. A model that assumes no radial velocity and concentration gradients in the reactor, the temperature gradient described by use of a proper value of the effective radial conductivity, a homogeneous reaction, the properties of the reaction mixture characterized by average values, the mechanism of axial mixing described by a single parameter model, and the kinetics of the first order is considered. Depending on the values of the nondimensional Peclet numbers, Damköhler number, the dimensionless adiabatic temperature rise, and the dimensionless activation energy, the coupled PDE equations for the temperature and concentration can have multiple equilibria that can be either stable or unstable. The objective is to stabilize an unstable steady state of the system using boundary control of temperature and concentration on the inlet side of the reactor. We discretize the original nonlinear PDE model in space using finite difference approximation and get a high order system of coupled nonlinear ODEs. Then, using backstepping design for parabolic PDEs we transform the original coupled system into two uncoupled target systems that are asymptotically stable in l²-norm with appropriate homogeneous boundary conditions. In the real system, the designed control laws would be implemented through small variations of the prescribed inlet temperature and prescribed inlet concentration. The control design is accompanied by a simulation study that shows the feedback control law designed with sensing only on a very coarse grid (using just a few measurements of the temperature and concentration fields) can successfully stabilize the actual system for a variety of different simulation settings (on a fine grid).     

Characterization of single-walled carbon nanotube mats and their performance as electromechanical actuators

Carbon nanotube mats (buckypapers) were prepared from three commercial grades of single-walled carbon nanotubes (SWCNTs) and by two processing variants (i.e. filtration of centrifuged and uncentrifuged dispersions). Material properties such as Young’s modulus, tensile strength, electrical conductivity, electrical capacitance, specific surface area and morphology were investigated and put in relation to the in-plane actuation performance in an aqueous electrolyte (1 M NaCl). A dynamic mechanical analyzer was adapted for actuation strain measurements on the samples under various tensile prestress levels. High SWCNT purity and dispersibility were found to be crucial for preparing dense and strong cohesive mats with good actuation performance.     

3D-Printed Poly(acrylic acid–vinylimidazole) Ionic Polymer Metal Composite Actuators

Ionic polymer–metal composites (IPMC)—constructed using an ionic polymer sandwiched between metal electrodes—have shown great potential for the fabrication of soft actuators. IPMC architectures have many advantages including low actuation voltage, fast response, basic control, and relatively light weight. Poly(acrylic acid) (PAA)-based ion exchange membranes are of particular interest for IPMC devices due to their large ion exchange capacity and ease of preparation; however, they suffer from relatively weak mechanical strength. Here, PAA-based soft actuators are synthesized with enhanced mechanical properties and proton conductivity through the incorporation of hydrogen bonding interactions with imidazolium groups via copolymerization with 1-vinylimidazole. In addition to examining the impact of composition on physiochemical (swelling, glass transition, decomposition, Young's modulus, etc.) and electrochemical (specific capacitance) properties, an additive manufacturing process, digital light projection (DLP), is utilized to fabricate complex geometries demonstrating the potential for the fabrication of IPMC devices with complex actuation modalities. Planar DLP 3D-printed IPMC actuators of varied polymer compositions are fabricated with activated carbon and copper electrodes, and their actuation performance is evaluated in air, where large bending deformation is observed (14°–37°).     

Dynamic optimization of dissipative PDE systems using nonlinear order reduction

This article presents computationally efficient methods for the solution of dynamic constraint optimization problems arising in the context of spatially distributed processes governed by highly dissipative nonlinear partial differential equations (PDEs). The methods are based on spatial discretization using the method of weighted residuals with spatially global basis functions (i.e., functions that cover the entire domain of definition of the process and satisfy the boundary conditions). More specifically, we perform spatial discretization of the optimization problems using the method of weighted residuals with analytical or empirical (obtained via Karhunen-Loève expansion) eigenfunctions as basis functions, and combination of the method of weighted residuals with approximate inertial manifolds. The proposed methods account for the fact that the dominant dynamics of highly dissipative PDE systems are low dimensional in nature and lead to approximate optimization problems that are of significantly lower order compared to the ones obtained from spatial discretization using finite-difference and finite-element techniques, and thus, they can be solved with significantly smaller computational demand. The resulting dynamic nonlinear programs include equality constraints that constitute a low-order system of coupled ordinary differential equations and algebraic equations, which can then be solved with combination of standard temporal discretization and nonlinear programming techniques. We employ backward finite differences (implicit Euler) to perform temporal discretization and solve the nonlinear programs resulting from temporal and spatial discretization using reduced gradient techniques (MINOS). We use two representative examples of dissipative PDEs, a diffusion-reaction process with constant and spatially varying coefficients, and the Kuramoto-Sivashinsky equation, a model that describes incipient instabilities in a variety of physical and chemical systems, to demonstrate the implementation and evaluate the effectiveness of the proposed optimization algorithms.     

Temperature distribution reconstruction in Czochralski crystal growth process

A mechanical geometric crystal growth model is developed to describe the crystal length and radius evolution. The crystal radius regulation is achieved by feedback linearization and accounts for parametric uncertainty in the crystal growth rate. The associated parabolic partial differential equation (PDE) model of heat conduction is considered over the time‐varying crystal domain and coupled with crystal growth dynamics. An appropriately defined infinite‐dimensional representation of the thermal evolution is derived considering slow time‐varying process effects. The computational framework of the Galerkin's method is used for parabolic PDE order reduction and observer synthesis for temperature distribution reconstruction over the entire crystal domain. It is shown that the proposed observer can be utilized to reconstruct temperature distribution from boundary temperature measurements. The developed observer is implemented on the finite‐element model of the process and demonstrates that despite parametric and geometric uncertainties present in the model, the temperature distribution is reconstructed with the high accuracy. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2839–2852, 2014     

Modelling of a clinker rotary kiln using operating functions concept

Modelling and parameter identification of complex dynamic systems/processes is one of the main challenging problems in control engineering. An example of such a process is clinker rotary kiln (CRK) in cement industry. In the prevailing models independently of which structure is used to describe the kiln's dynamics and the identification algorithm, parameters are assumed to be centralised and constant while the CRK is well known as a distributed parameter system with a strongly varying dynamic through time. In this work, the kiln's dynamic is described in the form of a state‐space representation with three state variables using a system of partial differential equations (PDE). The structure is chosen so that it can easily be embedded in classical state‐space control algorithms. The parameters of the PDE system are called operating functions since their numerical values vary with respect to different operating conditions of the kiln, to their position in the kiln, and through time. A phenomenological approach is also proposed in this paper to identify the operating functions for a given steady‐state operation of the kiln. The model is then used to perform a semi‐dynamic simulation of the process through manipulating main process variables.     

Phosphodiesterases Expression during Murine Cardiac Development

3′-5′ cyclic nucleotide phosphodiesterases (PDEs) are a large family of enzymes playing a fundamental role in the control of intracellular levels of cAMP and cGMP. Emerging evidence suggested an important role of phosphodiesterases in heart formation, but little is known about the expression of phosphodiesterases during cardiac development. In the present study, the pattern of expression and enzymatic activity of phosphodiesterases was investigated at different stages of heart formation. C57BL/6 mice were mated and embryos were collected from 14.5 to 18.5 days of development. Data obtained by qRT-PCR and Western blot analysis showed that seven different isoforms are expressed during heart development, and PDE1C, PDE2A, PDE4D, PDE5A and PDE8A are modulated from E14.5 to E18.5. In heart homogenates, the total cAMP and cGMP hydrolytic activity is constant at the evaluated times, and PDE4 accounts for the majority of the cAMP hydrolyzing ability and PDE2A accounts for cGMP hydrolysis. This study showed that a subset of PDEs is expressed in developing mice heart and some of them are modulated to maintain constant nucleotide phosphodiesterase activity in embryonic and fetal heart.     

Precision Control of Programmable Actuation of Thermoresponsive Nanocomposite Hydrogels with Multilateral Engineering

Hydrogels capable of stimuli-responsive deformation are widely explored as intelligent actuators for diverse applications. It is still a significant challenge, however, to “program” these hydrogels to undergo highly specific and extensive shape changes with precision, because the mechanical properties and deformation mechanism of the hydrogels are inherently coupled. Herein, two engineering strategies are simultaneously employed to develop thermoresponsive poly(N-isopropyl acrylamide) (PNIPAm)-based hydrogels capable of programmable actuation. First, PNIPAm is copolymerized with poly(ethylene glycol) diacrylate (PEGDA) with varying molecular weights and concentrations. In addition, graphene oxide (GO) or reduced graphene oxide (rGO) is incorporated to generate nanocomposite hydrogels. These strategies combine to allow the refined control of mechanical and diffusional properties of hydrogels over a broad range, which also directly influences variable thermoresponsive actuation. It is expected that this comprehensive design principle can be applied to a wide range of hydrogels for programmable actuation.