Closed-loop Balancing Research Articles

Scalable computation of energy functions for nonlinear balanced truncation

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A computational challenges that has so far prevented its deployment on large-scale systems is that the energy functions required for characterization of controllability and observability are solutions of various high-dimensional Hamilton–Jacobi–(Bellman) equations, which are computationally intractable in high dimensions. This work proposes a unifying and scalable approach to this challenge by considering a Taylor-series-based approximation to solve a class of parametrized Hamilton–Jacobi–Bellman equations that are at the core of nonlinear balancing. The value of a formulation parameter provides either open-loop balancing or a variety of closed-loop balancing options. To solve for the coefficients of Taylor-series approximations to the energy functions, the presented method derives a linear tensor system and heavily utilizes it to numerically solve structured linear systems with billions of unknowns. The strength and scalability of the algorithm is demonstrated on two semi-discretized partial differential equations, namely the Burgers and the Kuramoto–Sivashinsky equations.

Closed-Loop Capacitor Voltage Balancing Scheme for Modular Multilevel Converters Operated in Switching-Cycle Balancing Mode

Modular Multilevel Converters (MMCs) have attracted tremendous research interest for high/medium-voltage applications due to their superior features of scalability and modularity. While successfully commercialized for a few applications, MMCs are hampered in their further widespread adoption due to voluminous cell capacitors. Recently a new switching-cycle-balancing control was proposed. It has the potential to balance cell capacitor voltages in the timescale of a switching period by alternating circulating current multiple times in a switching cycle. This greatly decreases the required cell capacitance and also enables MMC dc-dc operation. Yet, the capacitor voltage balancing effectiveness is susceptible to non-ideal factors like parameter and measurement errors. Therefore, a closed-loop balancing scheme is critical to fully achieve effective switching-cycle balancing. However, due to the very high frequency circulating current alternations, subsequent extremely fast regulation, and heavily coupled control parameters, the closed-loop balancing control presents a huge challenge. The letter aims to address these challenges and develop an effective closed-loop voltage balancing scheme. The mathematical foundations of the proposed control are laid, and the proposed scheme is verified using a custom-built 10 kV SiC MOSFET-based MMC under 18 kV dc-link voltage.

Performance Evaluation of Balancing Bicopter using P, PI, and PID Controller

Due to potential features of unmanned aerial vehicles for society, the development of bicopter has started to increase. This paper contributes to the development by presenting a performance evaluation of balancing bicopter control in roll attitude. It aims to determine the best controller structure for the balancing bicopter. The controller types evaluated are based on Ziegler-Nichols tuning method; they are proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers. Root locus plot of the closed-loop balancing bicopter system is used to decide the tuning approach. This work considers a difference in pulse-width-modulation (PWM) signal between the left and right rotors as the signal control and bicopter angle in roll movement as the output. Parameters tuned by the method are Kp, Ti, and Td which is based on the ideal PID structure. The performance test utilizes rising time, settling time, maximum overshoot, and steady-state error to determine the most preferred controller. The result shows that PI-controller has the best performance among the other candidates, especially in maximum overshoot and settling time. It reaches 8.34 seconds in settling time and 3.71% in maximum overshoot. Despite not being the best in rising time and resembling PID-controller performances in steady-state error criteria, PI-controller remains the most preferred structure considering the closeness of the response to the desired value.

Assessment of environmental data quality and its effect on modelling error of full-scale plants with a closed-loop mass balancing

Environmental plants are notorious for poor data quality and sensor reliability due to the hostile environment in which the measurement equipment has to function, where the measurements and flow rate equipment in plants must be mutually consistent. The aim of this study is to detect any error in the measured data in an environmental plant and reconcile the data with some gross errors by using a closed data reconciliation of mass balance and the Lagrange multiplier method. A data reconciliation method based on closed-loop mass balance is suggested in order to reduce or remove error within data and obtain reliable process data. The proposed method is applied to a full-scale plant to detect the gross error in measured data, investigate the effects of erroneous data on modelling errors and compare the modelling performances of the faulty data and reconciled data. The results show that the proposed method can efficiently detect any gross error in data, estimate the error-free data by a reconciliation method and enhance the modelling accuracy by using reconciled data. This study provides a simple way to incorporate prior knowledge of plant modelling of a closed-loop mass balancing to identify any gross error and reconcile the faulty measurements.

Closed-loop balancing for a class of non-linear singularly perturbed systems

The aim of this article is to investigate the closed-loop balancing reduction method for a class of non-linear singularly perturbed systems. We show that the well-known two-stage strategy involved commonly within the singular perturbation theory can be used to derive an approximate closed-loop balancing. The proposed two-stage method avoids the difficult task of solving high dimensional and ill conditioned non-linear Hamilton–Jacobi equation due to the presence of the small perturbation parameter.

On the structure of energy functions of singularly perturbed bilinear systems

Two balanced model reduction schemes for bilinear systems have been proposed in the literature. The first schema is based on the algebraic controllability and observability matrices Gramians. The second is based on the notion of the controllability and observability energy functions already introduced for nonlinear systems. The aim of this paper is to present some interesting structures of the energy functions and algebraic Gramians of bilinear singularly perturbed systems. These results permit to avoid the ill conditioning and the high dimensionality in the computation of the energy functions of bilinear singularly perturbed systems. In the second part of the paper, closed-loop balancing is considered and similar development leads to the so-called past and future energy functions. Copyright © 2005 John Wiley & Sons, Ltd.

On-line hemodiafiltration in critical care.

On-line products of substitution fluid permits virtually unlimited fluid volume exchange during continuous hemodiafiltration (CHDF) to critical care. In on-line hemodiafiltration (HDF), endotoxin free dialysate obtained using pyrogen cut filters is infused into the blood circuit, and HDF is automatically performed using the closed-loop balancing system of the dialysis machine. On-line CHDF is the application of this on-line HDF to continuous renal replacement therapy in the critical care field. We performed on-line CHDF on 376 acute renal failure patients during a 5 year period, and the mean survival rate was 62.5%. We concluded that the on-line CHDF system is safe and effective at maintaining acute renal failure patients.

Iterative model and controller reduction using closed-loop balancing, with application to a compact disc mechanism

The standard configuration for model-based control design is reformulated into a twin feedback configuration with the model and controller written in separate feedback loops. Closed-loop balanced reduction is developed in this framework. A scheme with alternating model reduction, optimal control synthesis and controller reduction steps is designed to find high-performance low-order controllers. CD-player tracking controllers with orders below 10 have been found starting from a 120th-order model. Copyright © 1999 John Wiley & Sons. Ltd.

CONTROLLER REDUCTION FOR NONLINEAR PLANTS—AN L 2 APPROACH

SUMMARY This paper extends the H = balanced truncation approach of Mustafa—Glover for linear plants to input aƒne nonlinear plants. Nonlinear H = balanced truncation is used to obtain a reduced order controller. Conditions which ensure that this controller stabilizes the full order plant are derived. This is done by relating the model reduction problem to a robust stabilization problem with unstructured perturbation. In addition an upper bound on the performance of the closed loop system, with respect to the ‚ 2 gain, is obtained. When specialized to linear plants this bound reduces to Mustafa—Glover’s result. ( 1997 by John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control, Vol. 7, 475—505 (1997) When modern controller design algorithms are applied to high order plants the resulting controller may have order high enough to create problems with its implementation. The controller reduction problem is concerned with reducing the order of the controller so as to maintain the stability of the control system and preserve the control system performance. Early research on this problem revealed that reducing the order of a full order stabilizing controller using open loop model reduction techniques was not suƒcient to preserve closed loop stability. Moreover this drawback was also encountered when the low order controller was obtained by designing it to control a reduced order approximation of the plant. Recently in References 1 and 2 this diƒculty has been overcome, in the linear case, by using H = closed loop balancing,2 to reduce the order of the plant. The controller obtained for this reduced order plant will then be of low order and still achieve both stability and an H = bound when used with the reduced order plant. The preservation of stability when this controller is used with the full order plant is then obtained by resorting to robust stability theory.3 This is done by viewing the change in the plant resulting from replacing the reduced order plant by the full order plant as an H = bounded unstructured uncertainty. The nonlinear balancing method and its use in model reduction was introduced in Reference 4 asymptotically stable plants and extended to unstable plants in Reference 5—7. The plant/controller reduction procedure based on nonlinear H = balancing was studied in References 6 and 7. Properties of the H = singular value functions and some properties of the reduced order „his paper was recommended for publication by editor I. Postlethwaite

Closed-loop balanced realizations of LTI discrete-time systems

The problem of closed-loop balancing discrete LTI models is addressed. It is shown that results similar to those known for the continuous case can be extended to the discrete case. A new cross-Riccati equation is introduced which allows the direct balancing of MIMO symmetric discrete systems avoiding the solution of the two traditional Riccati equations for Kalman filtering and LQG control. Moreover, some suitable properties of such a cross-Riccati equation are shown. Finally, a method for obtaining discrete approximated models, based on the introduced equation, which appears to be suitable for approximating LQG controllers, is shown.

Closed-loop balancing and singular perturbation: a new result

A new procedure for deriving approximated models and LQG reduced-order compensators for a linear plant is presented. Two examples show the improvements of the proposed method with respect to other classical procedures.