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In this note, constant reference tracking using integral control for negative-imaginary (NI) systems preceded by hysteresis nonlinearity is addressed. The hysteresis nonlinearity is considered to be slope-restricted, though no specific modeling framework is exploited. It is effectively shown that integral tracking controllers are guaranteed to exist when a stable NI system with sign-definite dc-gain is preceded by such hysteresis nonlinearities. When the dc-gain is negative-definite, under positive feedback configuration with positive slope-restricted hysteresis, it is established that the integral controller gain can be any positive diagonal matrix. The development of the proposed model-independent inversion-free scheme is carried out in general state-space setting and is applicable for multiple-input multiple-output systems with decoupled hysteresis nonlinearities. Effectiveness of the results is illustrated with examples.

This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov–Krasovskii (LK) functional to derive delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus ensure global asymptotic stability in presence of any time-delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

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Lanthanum-132/135 is an emerging theranostic pair of radiometals that might find widespread application in nuclear medicine. The present study describes the production of 132/135La in a low energy linear accelerator via natBa (p, n) 132/135La reaction. A robust and efficient method has been optimized for separation of no-carrier-added (NCA) 132/135La from the bulk irradiated target by electrodeposition of 132/135La on platinum anode. Near quantitative electrodeposition yield of 132/135La could be obtained when a potential of 6 V was applied for 20 min in an electrolyte solution (containing Ba and La) maintained at pH ∼ 3. After electrochemical separation, 132/135La could be obtained with > 99.99 % radionuclidic purity in a form suitable for radiopharmaceutical preparation. As a proof of concept, 132/135La-complex of a tumor avid peptide conjugate, namely, DOTA-E-[c(RGDfK)]2 was formulated with > 98 % yield and the radiolabeled complex maintained its integrity under physiological conditions over a prolonged period of time. Overall, this study amply demonstrates that electrochemical separation is a viable strategy for obtaining 132/135La for theranostic radiopharmaceutical preparation.

In this paper, absolute stability condition is investigated when a hysteresis nonlinearity is connected to a linear subsystem via positive feedback in Lur'e system framework. In particular, the non...

This paper presents a full-order dynamic anti-windup compensation design scheme for stable LTI systems using a Riccati inequality based approach. The scheme utilizes the Weston-Postlethwaite’s generalized anti-windup configuration and applies right coprime factorization of the plant transfer function matrix to obtain a linear conditioning scheme. The proposed anti-windup scheme ensures the internal stability of the closed-loop control system in presence of actuator saturation and also reduces the performance degradation caused by the saturation phenomena. The Riccati inequality based approach offers a simple and straightforward anti-windup compensator design method which is independent of the design of nominal controller. The effectiveness of the proposed technique is demonstrated through a MIMO example.

In this paper, a static state feedback robust controller design method for linear systems with parametric uncertainty is presented. The closed-loop stability analysis is carried out in the sense of Lyapunov and the controller design parameters with constraints are formulated in linear matrix inequality (LMI) framework. A less conservative robust stability result is obtained by introducing a new set of sufficient conditions developed which contains the information of minimum eigenvalue of the perturbation matrices. The control effort is also reduced by imposing additional constraints in the designed framework. The proposed design technique is illustrated by considering several numerical examples that show the superiority of the proposed technique over the existing methods.

This paper presents a design of stabilizing dynamic feedback control law for steering steady-states of biochemical reaction networks. The design is carried out on a structurally similar reduced linear system model, obtained at the neighborhood of equilibrium point of the nonlinear system. The biochemical reaction network is modeled as a quasi-polynomial system with a translation into the positive orthant retaining all qualitative behaviors of the original system. The control law design is formulated as a bilinear matrix inequality (BMI) problem and an iterative algorithm is presented to find the controller gains. Two examples are illustrated to show the effectiveness of the proposed method.

This paper presents the stabilization problem of linear discrete-time systems with time-varying delay using a new Lyapunov-Krasovskii (LK) functional. A tighter estimate of the forward difference of LK functional is obtained by invoking the summation inequality and reciprocally convex combination lemma. A delay-dependent condition for the existence of state-feedback controller is derived in linear matrix inequality (LMI) framework which ensures asymptotic stability in the sense of Lyapunov. The effectiveness of the proposed results is demonstrated through numerical examples.

This paper presents an observer-based controller design method for linear systems with interval time-varying state-delay. In this work, using a new Lyapunov-Krasovskii (LK) functional, a less conservative stabilisation criterion is derived. The Wirtinger's inequality and reciprocally convex combination lemma are exploited to develop a computationally tractable method by representing the design constraints in linear matrix inequality (LMI) framework. Numerical examples are given to demonstrate the superiority of the proposed results over the existing method.

In this paper, two control allocation algorithms have been proposed for overactuated systems. The algorithms are developed by formulating constrained control allocation problem into an equivalent fixed point framework. The first algorithm follows sequential solving method while the other one involves a zero finding technique by the Newton method. In order to consider limiting constraints, the saturation function has been taken into account that leads to a nonsmooth zero finding problem and the proposed method guarantees superlinear convergence. The second algorithm is easy to implement and faster than the algorithm developed based on the sequential solving technique. To demonstrate the effectiveness of the proposed algorithms, a detail simulation study has been carried out, in which one example considers both the actuator rate and amplitude constraints.

A robust synthesis technique is devised for synergism and saturation systems, commonly known as S-systems, for steering steady-states of the anaerobic fermentation pathway (AFP) of Saccharomyces cerevisae. The stability, steady-state error and robustness aspects are analyzed. The synthesis problem is framed in a computationally efficient convex optimization framework. The linear matrix inequalities are formulated for minimization of steady-state error, improvement of robustness and utilization of minimum control inputs ensuring the stability of the synthetic AFP.

This paper deals with absolute stability of a Lur'e system with positive feedback where the linear subsystem exhibits negative-imaginary frequency response and the nonlinearity connected in feedback is time-invariant, memoryless and slope-restricted. The proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative-imaginary class. Along with that, positive definiteness of a symmetric matrix needs to be ensured, where the symmetric matrix is obtained by subtracting the dc-gain matrix of the linear subsystem from a strictly positive diagonal matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities. The stability criterion is proved using a Lur'e-Postnikov-type Lyapunov function. Numerical examples are presented to demonstrate the proposed results.

This paper presents a static state feedback controller design for uncertain linear systems with varying time delay. A less conservative stability criterion is derived invoking a new Lyapunov-Krasovskii (LK) functional. The reciprocally convex combination lemma and Wirtinger’s inequality are exploited to develop a computationally tractable method where the design constraints are formulated in linear matrix inequality (LMI) framework. Numerical examples are given to demonstrate the superiority of the proposed results over the existing methods.

A large signal voltage stability index is proposed in this study. Although the study focuses on a wind farm connected system, the index can predict instability of any power system. The index gives an idea about the stability margin of the power system under a given operating condition and can be used to predict emergency situations following a large disturbance such as line outage. The proposed index can be used effectively for systems with static as well as dynamic loads. The proposed index is verified in standard test systems. Matrix perturbation theory is used to verify the viability of the index.

Flight control systems are often equipped with reconfigurable control allocation schemes to redistribute control commands in the event of actuator failures. In this brief, a reconfiguration scheme is proposed and is based on the direct allocation method. An iterative algorithm is developed and uses the same lookup tables prepared offline for normal operations, thereby saving a considerable amount of computation time and process memory. To elucidate the effectiveness of the method, the proposed allocation algorithm is applied to a satellite launch vehicle model. Simulation results show satisfactory performance of the method in the presence of multiple actuator failures.

This paper presents a full-order state observer-based scheme that transforms a causal, LTI, minimally realized system into a strongly strict negative-imaginary system by defining an auxiliary output based on the observed states. The auxiliary output is used for closed-loop control with positive feedback invoking the internal stability condition of negative-imaginary theory. A set of LMI conditions is derived that determines the value of a design parameter μ required for the proposed scheme to transform a given system with a minimal state-space realization into a strongly strict negative-imaginary system. The proposed scheme is applicable for both stable/unstable and square/non-square systems. In this paper, the framework is further explored for robustness analysis of uncertain systems and numerical examples are given to elucidate effectiveness of the proposed results.

Biochemical networks normally operate in the neighborhood of one of its multiple steady states. It may reach from one steady state to other within a finite time span. In this paper, a closed-loop control scheme is proposed to steer states of the glycolysis and glycogenolysis (GG) pathway from one of its steady states to other. The GG pathway is modeled in the synergism and saturation system formalism, known as S-system. This S-system model is linearized into the controllable Brunovsky canonical form using a feedback linearization technique. For closed-loop control, the linear-quadratic regulator (LQR) and the linear-quadratic gaussian (LQG) regulator are invoked to design a controller for tracking prespecified steady states. In the feedback linearization technique, a global diffeomorphism function is proposed that facilitates in achieving the regulation requirement. The robustness of the regulated GG pathway is studied considering input perturbation and with measurement noise.

Negative-imaginary systems have important engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators. This paper proposes a new Negative-Imaginary Lemma for generalized negative-imaginary systems, where the minimality assumption is relaxed. The proposed lemma facilitates both analysis and synthesis for negative-imaginary systems. Invoking this result, a systematic robust static state-feedback synthesis method is proposed in an LMI framework for systems with strictly negative-imaginary uncertainty (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure) assuming all states are available for state feedback. Two numerical examples are given to show the usefulness of the proposed results.

In this paper, a new iterative algorithm is developed using control theoretic approach to find the minimum norm solution of underdetermined problems. The minimum norm solution is obtained by applying the H∞ optimization technique. The accuracy and convergence rate of the proposed algorithm are ensured using the framework of linear feedback control theory. The performances of the proposed method, the QR decomposition method, and the least square minimal residue (LSMR) method are compared numerically. The number of iterations in the proposed algorithm is comparable with the LSMR method. Finally, the developed algorithm is applied to the control allocation problem and its effectiveness is demonstrated through a detailed simulation study.

In this paper strict negative-imaginariness is defined in input-output sense, which is different from the notion of existing strictly negative-imaginary systems. The class of output strictly negative-imaginary systems is characterized in state-space with respect to a non-negative parameter δ. The newly defined class of output strictly negative-imaginary systems forms an intersection with the existing class of strictly negative-imaginary systems. Further, a time-domain definition is also provided to classify strict and non-strict negative-imaginary systems in dissipative framework which is applicable to both linear and nonlinear cases. Several numerical examples are given to show the usefulness of the key results.

In this paper, an algorithm that gives the best achievable performance bound on a given control problem is proposed using the H ? loop-shaping design framework. In view of standard design requirements, the robust performance is maximized at low and high frequencies while keeping the robust stability margin above a specified level, and the robust stability margin is directly improved at mid frequencies (around crossover). The proposed frequency-dependent optimization problem is cast in an LMI framework. The resulting solution algorithm simultaneously synthesizes loop-shaping weights and a stabilizing controller that achieve the maximum performance for a given level of robust stability margin corresponding to sufficient gain and phase margins of the closed-loop system. � 2012 John Wiley & Sons, Ltd.

This paper proposes a state-space solution to weight optimization problem in @?"~ loop-shaping control. A pointwise-in-frequency weight optimization framework is transformed into convex optimization searches that are independent of frequency. The introduced optimization problem therefore avoids gridding of the frequency space and consequently, the inaccuracies attributed to fitting transfer functions to magnitude data. In this optimization problem, the order of the weight is specified 'a priori', thus facilitating the synthesis of low-order controllers, which is desirable from an implementation perspective. The proposed solution algorithm simultaneously synthesizes a robust stabilizing controller and a loop-shaping weight (pre-compensator) that maximize the robust stability margin subject to constraints on the performance and the singular values of the weight. Three numerical examples are given to illustrate the effectiveness of the technique.

In this paper, an economic parameterization for positive parahermitian matrix functions is introduced and applied to the μ -analysis framework wherein we propose a new state-space optimization problem for finding the required D -scales. Among the four state-space matrices to be used to realize the optimal D -scale, A and B are chosen via a Laguerre parameterization whereas the other two state-space matrices, C and D are obtained by spectral factorization after solving a convex optimization problem formulated in an LMI framework. The obtained D -scale satisfies the commuting property with the uncertainty structure. The proposed economic parameterization yields advantages in terms of less computational time and less number of decision variables and also, the proposed state-space optimization framework gives a frequency independent solution algorithm in state-space variables for the required D -scales. Two numerical examples are used to demonstrate the effectiveness of the proposed algorithm.

SUMMARY This paper presents readily applicable distance measures, robust stability margins and associated robust stability and robust performance theorems for three commonly used uncertainty structures (additive, input/output multiplicative, output/input inverse multiplicative). Besides providing robust stability results for a larger uncertainty class than previously reported (ℛℒ∞ instead of ℛℋ∞), this paper also states robust performance theorems for the above uncertainty structures. In contrast to previous methods for robust performance analysis, they only require the computation of two infinity norms for every uncertain plant considered. The theorems in this paper enable practising engineers to choose the most suitable uncertainty structure for a family of uncertain plants, as illustrated through a physically motivated numerical example. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, novel test methods are proposed to check whether a new stabilizing controller improves robust performance or not when the existing controller is replaced by this new controller in the closed-loop. For the proposed tests, the plant dynamics is assumed to be unknown whereas the existing and new controller transfer function matrices are known to the designer. The proposed tests are based on closed-loop data and can be used for both the SISO and MIMO systems. The test methods in this paper build on the experimental set-up of Dehghani et al. (2009), however, the proposed results in this paper for robust performance improvement test cannot be obtained from the test results of Dehghani et al. (2009).

This paper proposes a design framework that maximizes the robust performance of a closed-loop system via weight optimization in ℋ ∞ loop-shaping control. In line with design objectives, frequency-dependent optimization problems are formulated in LMI framework to maximize robust performance at low and high frequencies, and directly improve the robust stability margin at mid frequencies. The philosophy of the work thus gives the best robust performance that can be achieved on a particular problem once a level of robust stability margin is demanded. Loop-shaping weights and controller are simultaneously synthesized from the proposed algorithm.

Smooth variation in the magnitude response of weights facilitates ℋ ∞ loop-shaping design, as it prevents the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, when the shaped plant is formed based on closed-loop design specifications. For accurate fitting of transfer functions to magnitude data, smooth weights also allow low-order transfer functions to be used when such smooth variations in their magnitude responses are computed point-wise in frequency. In this paper, smoothness constraints for weights, expressed as gradient constraints on a log scale in dB/decade, which is intuitive from a design perspective, are imposed in a weight optimization framework for ℋ ∞ loop-shaping control. This work builds on [A. Lanzon, Weight optimization in ℋ ∞ loop-shaping, Automatica 41 (1) (2005) 1201–1208], where additional constraints are formulated in linear matrix inequality (LMI) form to cast a complete weight optimization framework. The resulting algorithm thus maximizes the robust stability margin and simultaneously synthesizes smooth weights along with a stabilizing controller. A numerical example is given to elucidate the efficacy of the smoothness constraints in ℋ ∞ loop-shaping control.

Real parametric uncertainty is common in many applications. In this study, the authors analyse the robust stability of feedback loops of single-input single-output systems with negative imaginary frequency response subject to real parametric uncertainty. A recent result on the stability of such feedback loops is specialised to this case, resulting in a very simple stability condition dependent only on the steady-state parameters of the systems. The structured singular value for this system type is also obtained, and it is shown that it yields related but more constrained, easily computable stability guarantees. In a numerical example, the robust stability of a control loop for a DC machine subject to real parametric uncertainty is analysed.

This article addresses a robust controller design technique for an uncertain linear time invariant plant with input saturation constraint. The uncertainty of the plant is presented in a normalised coprime factorisation framework, which is a general description of the unstructured uncertainty of the system. For controller synthesis, the H∞ loop-shaping method adopted is new to the actuator saturation control problem. In the presence of input saturation, the H∞ loop-shaping framework has been transformed into an equivalent Lur'e-type system, and then Popov absolute stability criteria are applied to ensure closed-loop stability against unstructured uncertainty and saturation nonlinearity of the system. For the synthesising controller, a sequence of design steps has been addressed by formulating the design constraints in a bilinear matrix inequality framework. To show the effectiveness of the proposed method, a numerical example has been demonstrated.

This technical note provides a reformulation of closed-loop systems that have negative imaginary frequency response into closed-loop systems that have bounded gain, so that theory and results from H∞ control can be borrowed to enable controller synthesis for the former class of systems. Systems with negative imaginary frequency response (negative-imaginary systems for short) arise for example in structures with collocated position sensors and force actuators, and finding a systematic controller synthesis treatment for such systems has important applications in, for example, lightly damped large space structure problems. The key result in this technical note assists by reformulating such systems into a bounded-real framework. This technical note also addresses a controller synthesis problem in an H∞ optimal control framework for a generalized plant with an invariant zero at the origin in its (1,2) element which is due to the reformulation of the closed-loop system from a negative-imaginary system to a bounded-real framework. An example demonstrates the feasibility of the reformulation given herein.

In this paper, an attempt has been made to address on the design of pre-compensator to obtain the solution of H∞ loop-shaping control problem. Two different design techniques have been proposed where the first one is based on singular value decomposition (SVD) technique along with the matrix perturbation approach; the other one is focused in linear matrix inequality (LMI) framework leading to minimize the condition number of the pre-compensator that, in turn, reduces loop deterioration. A numerical example has been considered to illustrate the effectiveness of the proposed method.

This paper attempts to develop an alternate but simple technique for designing a static output feedback H"~ loop shaping controller from four-block H"~ framework. Sufficient conditions are established for the existence of a static H"~ loop shaping controller. These conditions are in LMI form, and are different from those obtained in [Prempain, E. (2004). Static H"~ loop shaping control. Control 2004. UK: University of Bath; Prempain, E., & Postlethwaite, I. (2004). Static H"~ loop shaping control of fly-by-wire helicopter. In Conference on decision and control (pp. 1188-1195); Prempain, E., & Postlethwaite, I. (2005). Static H"~ loop shaping control of fly-by-wire helicopter. Automatica, 41, 1517-1528] using normalized coprime factorization approach. Numerical examples are considered to illustrate the results of this paper.