On positive systems with multivariable positive control: Process stabilization

A new approach—individual channel design (ICD)—to an enduring problem— multivariable feedback control—is presented. The approach is applications-oriented: it starts from the engineering premise that feedback control design is interactive; it involves an interplay between customer specification, uncertain plant characteristics, and the multivariable feedback design process itself. It is shown that individual signal transmission channels arise naturally from customer specification on selected plant outputs with no loss of structural (loop interaction) information. By invoking customer performance specification on different channels, highly successful single-input single-output classical (Nyquist-Bode) design is made possible. ICD is not a design method per se per se; rather it is a global structural framework wherein the possibilities and limitations for local-loop-shaping design (e.g. Bode or Nichols) of a particular plant are made apparent from the outset. Also, the conditions are established whereby channel gain and phase margins are robust measures of stability. In this way, a transparent, flexible and supportive design methodology is developed which directly aims to meet the users’ control requirements and is well-suited to the engineering context. An automotive gas turbine control case study illustrates the salient features of the processs of ICD.

The report discusses preliminary proof-of-concept research for using the Advanced Data Validation and Verification System (ADVVS), a new INEEL software package, to add validation and verification and multivariate feedback control to the operation of non-destructive analysis (NDA) equipment. The software is based on human cognition, the recognition of patterns and changes in patterns in time-related data. The first project applied ADVVS to monitor operations of a selectable energy linear electron accelerator, and showed how the software recognizes in real time any deviations from the optimal tune of the machine. The second project extended the software method to provide model-based multivariate feedback control for the same linear electron accelerator. The projects successfully demonstrated proof-of-concept for the applications and focused attention on the common application of intelligent information processing techniques.

The under-damped resonance phenomenon in grid-tied LCL-filtered inverters yields much difficulty in designing the controller. By adding one or more state feedback, the multi-variable feedback control methods are commonly used. However, the revealed studies are quite limited and cannot explain the essential mechanism of the multi-variable feedback control. In this paper, a systematic analysis method based on zero-placement is provided to detail the control mechanism of one family of multivariable feedback strategy. Through a combination of the easily-measured current and voltage states in LCL filters, a novel state variable of which the zeros can be assigned is produced. By assigning the zeros to cancel the resonance poles, the close-loop control based on the feedback of this novel state variable is easily designed and is capable of satisfactory dynamic. In summary, with the systematic analysis, a family of multi-variable feedback methods is deduced.

The main goal of this paper is to introduce a link between the thermodynamics and control systems theory. More precisely, the paper focuses on Lyapunov based control of process systems, specially the non isothermal Continuous Stirred Tank Reactors in a thermodynamic framework, using either the jacket temperature or the inlet molar flow rate as the only control input. As soon as the constraint on the total mass is considered and the reaction kinetics is a Lipschitz continuous function with respect to the temperature, it shows that the stabilization of thermal solicitations reciprocally entails the one of matter using La Salle’s invariance principle. As a consequence, these control problems can be solved if the closed loop Lyapunov functions are chosen to be proportional to the thermal part or material part of the so called thermodynamic availability function. Some numerical simulations for a first order chemical reaction with multiple steady states are given to validate our theoretical developments. The performance of the obtained nonlinear controllers with regard to the conversion rate is also discussed.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

Nonlinear Burn Control in Tokamak Fusion Reactors via Output Feedback

Multivariable uniform finite-time output feedback reentry attitude control for RLV with mismatched disturbance

This work proposes a control configuration and a nonlinear multivariable model‐based feedback controller for the reduction of thermal gradients inside the crystal in the Czochralski crystal growth process after the crystal radius has reached its final value. Initially, a mathematical model which describes the evolution of the temperature inside the crystal in the radial and axial directions and accounts for radiative heat exchange between the crystal and its surroundings and motion of the crystal boundary is derived from first principles. This model is numericully solved using Galerkin's method and the behaviour of the crystal temperature is studied to obtain valuable insights which lead to the precise formulation of the control problem, the design of a new control configuration for the reduction of thermal gradients inside the crystal and the derivation of a simplified 1‐D in a space dynamic model. Then, a model reduction procedure for partial differential equation systems with time‐dependent spatial domains (Armaou and Christofides, 1999) based on a combination of Galerkin's method with approximate inertial manifolds is used to construct a fourth‐order model that describes the dominant thermal dynamics of the Czochralski process. This low‐order model is employed for the synthesis of a fourth‐order nonlinear multivariable controller that can be readily implemented in practice. The proposed control scheme is successfully implemented on a Czochralski process used to produce a 0.7 m long silicon crystal with a radius of 0.05 m and is shown to significantly reduce the axial and radial thermal gradients inside the crystal. The robustness of the proposed controller with respect to model uncertainty is demonstrated through simulations.

A linear low‐order state space dynamic model for a catalytic butane hydrogenolysis reactor which has been fitted to reactor dynamic data is used to develop a multivariable linear quadratic feedback control algorithm for regulatory control of the reactor exit concentrations using temperature measurements only. Kalman filter theory is used to obtain state estimates for the system. The control algorithm developed is implemented on the pilot plant reactor in a series of DDC control studies. The controller is shown to perform very well and considerably better than a single loop PI controller with a feedback on the hot spot temperature. Performance is evaluated both under the normal stochastic disturbances in the system and under a severe deterministic load disturbance. Exit concentrations predicted by the model and used in the performance index are shown to compare very favorably with actual concentrations obtained from a process gas chromatograph.

A major difficulty in multivariable control design is the cross-coupling between inputs and outputs which obscures the effects of a specific controller on the overall behavior of the system. This paper considers the application of neural networks in decoupling multivariable output feedback controllers. Simulation results are presented to show the feasibility of the proposed technique.

The ovarian system exhibits nonlinear dynamics which is modeled by a set of coupled nonlinear differential equations. The paper proposes adaptive fuzzy control based on differential flatness theory for the complex dynamics of the ovarian system. It is proven that the dynamic model of the ovarian system, having as state variables the LH and the FSH hormones and their derivatives, is a differentially flat one. This means that all its state variables and its control inputs can be described as differential functions of the flat output. By exploiting differential flatness properties the system’s dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop’s Lyapunov function to be a negative one. Moreover, Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.

The objective of this work is to automatically regulate glycemia of Type 1 Diabetes Mellitus (T1DM) avoiding both hyperglycemia and hypoglycemia risks. A positive state feedback controller was designed previously to regulate Blood Glucose Concentration (BGC) in the fasting phase maintaining the system in the positively invariant set (PIS). The drawback of this positive controller is that when tested in the postprandial phase it couldn’t avoid hyperglycemia. Therefore, in this work, the positive state feedback controller was developed to avoid both hypoglycemia and hyperglycemia maintaining the system inside the PIS. Meal disturbance is estimated by a sliding mode perturbation observer to be included in the control law. Such that meal effect is canceled early enough preventing glycemia from raising to hyperglycemia, but the positivity of the new controller isn’t guaranteed. Therefore, a hybrid controller is designed to switch to the previous positive controller whenever the new controller has a negative action. A positive control is essential in this problem since the control input (insulin) can only be infused and it cannot be taken back from the bloodstream in case of any overdoses. The hybrid positive controller is tested in silico on five virtual T1DM patients. The results shown that the average percentage of time for glycemia over 180mg/dl (3.6%), normal range (80-120mg/dl) (78.2%), and below (80mg/dl) (0%) from overall simulation time. In conclusion, the hybrid positive control law succeeded to maintain the system inside the PIS avoiding hypoglycemia and preventing hyperglycemia keeping BGC in normal range rejecting meal disturbance.

Based on a brief review on current harmonics generation mechanism for grid-connected inverter under distorted grid voltage, the harmonic disturbances and uncertain items are immersed into the original state-space differential equation of grid-connected inverter. A new algorithm of global current harmonic rejection based on nonlinear backstepping control with multivariable internal model principle is proposed for grid-connected inverter with exogenous disturbances and uncertainties. A type of multivariable internal model for a class of nonlinear harmonic disturbances is constructed. Based on application of backstepping control law of the nominal system, a multivariable adaptive state feedback controller combined with multivariable internal model and adaptive control law is designed to guarantee the closed-loop system globally uniformly bounded, which is proved by a constructed Lyapunov function. The presented algorithm extends rejection of nonlinear single-input systems to multivariable globally defined normal form, the correctness and effectiveness of which are verified by the simulation results.

The eigenstructure assignment scheme for robust multivariable state feedback control is extended to redundantly actuated dynamical systems. The fact that the plants that are atleast square allow for the exact assignment of an arbitrary orthonormal set of closed loop eigenvectors makes this methodology attractive for feedback controller design poorly modeled dynamical systems. For second order mechanical systems, a partial eigenstructure assignment methodology is presented which simplifies the scheme of pole assignment for real target sub-modal matrix. An optimal allocation strategy is derived for redundant control inputs to minimize an integral cost function. A novel adaptive aggregation procedure is introduced to handle problems with very high redundancy in actuation. The aggregation approach along with the eigenstructure assignment methodology is applied to the wing morphing problem. The robust redundant actuation procedure is demonstrated on a mathematical model constructed from the wind tunnel test data of the novel morphing wing model designed and developed at Texas A & M University.

This paper explores the application of modern feedback control technology to the regulation of the reactive ion etching process. Currently, this process is run open-loop, except for the PID controller to regulate pressure. We investigate the utility of additional measurements for the purpose of feedback control to improve process performance and robustness. First, we compare a feedback controller that regulates V<SUB>bias</SUB> and chamber pressure to one that regulates V<SUB>bias</SUB> and fluorine. We show that the fluorine controller yields better control of etch rate; this result is to be expected since fluorine is more closely related to the chemical etching process than is pressure. Our second study compares various controllers that regulate V<SUB>bias</SUB> and fluorine using the conductance throttle and applied RF power. We show that multivariable feedback controllers that can compensate for process coupling by coordinating control inputs have advantages over decentralized controllers consisting of two independent feedback loops.