Search

This paper exploits the decentralized integral controllability (DIC) of stable negative-imaginary (NI) systems with non-singular DC-gain matrix to develop a constant input tracking framework with failure tolerance property in the event of sensor and/or actuator faults. By virtue of the DIC property of NI systems, it is shown that a positive feedback interconnection of two NI systems, of which one is a decentralized integrator system with non-negative gains and the other one is a stable NI system having negative definite DC-gain matrix, is internally stable. This is in contrast to the existing results where, for internal stability, at least one of the systems needs to be strictly negative-imaginary (SNI). Further it is shown that, in a positive feedback interconnection, stable NI systems with negative definite DC-gain matrix exhibit integral controllability (IC) property for any positive value of the integral gain k , which is a distinct property of stable NI systems having negative definite DC-gain matrix since the existing notion of IC for LTI systems offers only a finite range of k . Using the DIC property and the eigenvalue loci technique, some new results and research directions for the NI systems have also been presented in this paper.

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 addresses the problem of dynamic output feedback controller synthesis in LMI framework for LTI generalized plants with negative-imaginary uncertainties. The proposed technique transforms the controller synthesized nominal closed-loop system into a strongly strict negative-imaginary system and exploits the DC loop gain condition pertaining to negative-imaginary theory to establish internal stability in presence of negative-imaginary uncertainties. Apart from making the closed-loop system robustly stable, the designed output feedback controller also facilitates multi-objective performance of the closed-loop system such as minimizing the H 2 and H ∞ norms, reducing the peak overshoot, increasing the decay rate, optimizing the settling time, etc. Illustrative examples have been studied to demonstrate the usefulness of the proposed control scheme. A thorough μ -analysis subjected to ‘mixed’ two-block perturbations is included in the examples to show that the designed controller can also facilitate a certain level of robust H ∞ performance in presence of stable NI/SNI uncertainties.

In robust iterative identification and control redesign techniques, a stabilizing controller connected in a closed loop is normally replaced by an alternative attractive stabilizing controller to improve robustness and performance of the closed-loop system. In this paper, novel test methods are proposed to check whether a new stabilizing controller improves performance or not when the existing controller is replaced by this new controller in the closed loop. The proposed tests are based on closed-loop data and no plant model, and can be used for both the SISO and MIMO linear time-invariant systems. 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. These assumptions are common in iterative identification and control redesign techniques. The performance improvement test methods proposed in this paper build on the experimental set-up proposed in Dehghani, Lecchini, Lanzon, and Anderson (2009) which was used to only check whether controllers ensure internal stability of a feedback interconnection or not. In this paper, new test methods are proposed to ascertain robust performance improvement that cannot be obtained from test results of Dehghani et al. (2009). A numerical example is illustrated to show effectiveness of the proposed test methods.

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.

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.