Alexander Lanzon

The University of Manchester, Manchester, England, United Kingdom

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Publications (118)99.74 Total impact

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    ABSTRACT: In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These “mixed” systems are already fairly well characterised in the continuous-time domain, but the widespread adoption of digital controllers makes it necessary to verify whether commonly used discretisation procedures preserve the characteristic of “mixedness”. First, we analyse the effects of classical discretisation methods on the “mixed” property using Nyquist methods. A frequency domain feedback stability result is then presented. Finally, we develop a spectral-based characterisation of “mixed” discrete-time systems which provides a practical computational test that can also be applied to the MIMO case. Several examples validate the developed theory.
    European Journal of Control 09/2014; · 1.25 Impact Factor
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    ABSTRACT: Given a linear time-invariant plant, the search for a suitable multiplier over the class of Zames–Falb multipliers is a challenging problem which has been studied for several decades. Recently, a new linear matrix inequality search has been proposed over rational and causal Zames–Falb multipliers. This letter analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers. The addition of a Popov multiplier to the anticausal Zames–Falb multiplier is implemented by analogy with the causal search. As a result, a search over a noncausal subset of Zames–Falb multipliers is obtained. A comparison between all the search methods proposed in the literature is given.
    Systems & Control Letters 08/2014; 70:17–22. · 1.67 Impact Factor
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    ABSTRACT: This paper proposes a two degree of freedom control using a combined feedforward/feedback architecture for MIMO nanopositioning stages. The proposed control system provides higher bandwidth and better performance compared with a single degree of freedom feedback controller. The paper proposes a systematic synthesis methodology to design the controller based on closed loop performance. The results are verified via simulation and hardware experiment.
    2014 European Control Conference (ECC); 06/2014
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    Joaquin Carrasco, William P. Heath, Alexander Lanzon
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    ABSTRACT: Recent results in equivalence between classes of multipliers for slope-restricted nonlinearities are extended to multipliers for bounded and monotone nonlinearities. This extension requires a slightly modified version of the Zames–Falb theorem and a more general definition of phase-substitution. The results in this paper resolve apparent contradictions in the literature on classes of multipliers for bounded and monotone nonlinearities.
    Systems & Control Letters 04/2014; 66:65–71. · 1.67 Impact Factor
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    Ian R. Petersen, Alexander Lanzon
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    ABSTRACT: This paper presents a survey of recent results on the theory of negative imaginary systems. This theory can be applied to the robust control of large flexible structures with colocated force actuators and position sensors.
    01/2014;
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    ABSTRACT: The negative imaginary (NI) property is exhibited by many systems such as flexible structures with force actuators and position sensors and can be used to prove the robust stability of flexible structure control systems. In this paper, we derive methods to check for the NI and strict negative imaginary (SNI) properties in both the single-input single-output as well as multi-input multi-output cases. The proposed methods are based on spectral conditions on a corresponding Hamiltonian matrix obtained for a given system transfer function matrix. Under certain conditions, a given transfer function matrix satisfies the NI property if and only if the corresponding Hamiltonian matrix has no pure imaginary eigenvalues with odd multiplicity. It is also shown that a given transfer function matrix satisfies the SNI property if and only if the corresponding Hamiltonian matrix has no eigenvalues on the imaginary axis, except at the origin. The results of this paper are applied to check the NI property in two nanopositioning applications.
    IEEE/ASME Transactions on Mechatronics 01/2014; 19(3):895-903. · 3.14 Impact Factor
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    Alexander Lanzon, Alessandro Freddi, Sauro Longhi
    AIAA Journal of Guidance, Control and Dynamics. 01/2014; 37(2):580-591.
  • Joaquin Carrasco, William P. Heath, Alexander Lanzon
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    ABSTRACT: Different classes of multipliers have been proposed in the literature for obtaining stability criteria using passivity theory, integral quadratic constraint (IQC) theory or Lyapunov theory. Some of these classes of multipliers can be applied with slope-restricted nonlinearities. In this paper the concept of phase-containment is defined and it is shown that several classes are phase-contained within the class of Zames–Falb multipliers. There are two main consequences: firstly it follows that the class of Zames–Falb multipliers remains, to date, the widest class of available multipliers for slope-restricted nonlinearities; secondly further restrictions may be avoided when exploiting the parametrization of the other classes of multipliers.
    Automatica. 06/2013; 49(6):1732–1740.
  • M. Osinuga, S. Patra, A. Lanzon
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    ABSTRACT: In this paper, an algorithm that gives the best achievable performance bound on a given control problem is proposed using the 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. Copyright © 2012 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 05/2013; 23(8). · 1.90 Impact Factor
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    ABSTRACT: Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, a necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary (SNI). These general stability results captures all previous NI stability results which have been developed. The stability conditions in this paper are given purely in terms of properties of the plant and controller transfer function matrices, although the proofs rely on state space techniques. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented.
    IEEE Transactions on Automatic Control 05/2013; · 2.72 Impact Factor
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    ABSTRACT: Characterisations of “mixed” systems are presented in a discrete-time setting. First, a feedback stability result based on the Nyquist stability theorem is presented. Second, an eigenvalue-based characterisation of “mixed” systems based on their state-space data is derived. The results are analogous to previous results presented for the continuous-time case and provide a foundation for further study concerning the discretisation of “mixed” systems.
    Control Conference (ECC), 2013 European; 01/2013
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    ABSTRACT: Flexible structures with collocated force actuators and position sensors lead to negative imaginary dynamics. However, in some cases, the mathematical models obtained for these systems, for example, using system identification methods may not yield a negative imaginary system. This paper provides two methods for enforcing negative imaginary dynamics on such mathematical models, given that it is known that the underlying dynamics ought to belong to this system class. The first method is based on a study of the spectral properties of Hamiltonian matrices. A test for checking the negativity of the imaginary part of a corresponding transfer function matrix is first developed. If an associated Hamiltonian matrix has pure imaginary axis eigenvalues, the mathematical model loses the negative imaginary property in some frequency bands. In such cases, a first-order perturbation method is proposed for iteratively collapsing the frequency bands whose negative imaginary property is violated and finally displacing the eigenvalues of the Hamiltonian matrix away from the imaginary axis, thus restoring the negative imaginary dynamics. In the second method, direct spectral properties of the imaginary part of a transfer function are used to identify the frequency bands where the negative imaginary properties are violated. A pointwise-in-frequency scheme is then proposed to restore the negative imaginary system properties in the mathematical model.
    International Journal of Control 01/2013; 86(7). · 1.01 Impact Factor
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    ABSTRACT: 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.
    Systems & Control Letters 12/2012; 61(12):1269–1276. · 1.67 Impact Factor
  • Sourav Patra, Alexander Lanzon
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    ABSTRACT: 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.
    Automatica 10/2012; 48(10):2710–2716. · 2.92 Impact Factor
  • J Carrasco, WP Heath, G Li, A Lanzon
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    ABSTRACT: The above technical note presents a novel convex search within the Zames-Falb multiplier class. The aim of this correspondence is to correct the misuse of a relaxation on one condition in the search. This relaxation leads to nontrivial numerical errors in all six examples discussed in the technical note. Correct application of the conditions still gives an improvement over absolute stability criteria in the literature for at least one example, but some of the claims for lack of conservativeness in the above technical note should be moderated.
    IEEE Transactions on Automatic Control 09/2012; 57(9):2422-2428. · 2.72 Impact Factor
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    ABSTRACT: A robust Kalman conjecture is defined for the robust Lur’e problem. Specifically, it is conjectured that the nonlinearity’s slope interval for which robust absolute stability is guaranteed corresponds to the robust interval of the uncertain plant. We verify this robust Kalman conjecture for first-order plants perturbed by various norm-bounded unstructured uncertainties. The analysis classifies the appropriate stability multipliers required for verification in these cases. Robust control of Lur’e-type nonlinear systems satisfying this novel conjecture can therefore be designed using linear robust control methods.
    7th IFAC Symposium on Robust Control Design; 06/2012
  • M. Osinuga, S. Patra, A. Lanzon
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    ABSTRACT: This paper proposes a state-space solution to weight optimization problem in ℋ∞ℋ∞ 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.
    Automatica 03/2012; 48(3):505–513. · 2.92 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Given a linear time-invariant plant, the search of a suitable multiplier over the class of Zames-Falb multiplier is a challenging problem which has been studied for several decades. Recently, a new linear matrix inequality search has been proposed over rational and causal Zames-Falb multipliers. This paper analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
  • M.K. Mohamed, A. Lanzon
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    ABSTRACT: Tri-rotor UAVs are more efficient compared to quadrotors in regard to the size and power requirement, yet, tri-rotor UAVs are more challenging in terms of control and stability. In this paper, we propose the design and control of a novel tri-rotor UAV. The proposed platform is designed to achieve six degree of freedom using a thrust vectoring technique with the highest level of flexibility, manoeuvrability and minimum requirement of power. The proposed tri-rotor has a triangular shape of three arms where at the end of each arm, a fixed pitch propeller is driven by a DC motor. A tilting mechanism is employed to tilt the motor-propeller assembly and produce thrust in the desired direction. The three propellers can be tilted independently to achieve full authority of torque and force vectoring. A feedback linearization associated with ℋ∞ loop shaping design is used to synthesize a controller for the system. The results are verified via simulation.
    Control (CONTROL), 2012 UKACC International Conference on; 01/2012
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    ABSTRACT: In this paper, a stabilization procedure that forces an uncertain system to be stable and satisfy the negative imaginary property is presented. The controller synthesis procedure is based on the negative imaginary lemma. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.
    Innovative Engineering Systems (ICIES), 2012 First International Conference on; 01/2012

Publication Stats

549 Citations
99.74 Total Impact Points

Institutions

  • 2007–2014
    • The University of Manchester
      • School of Electrical and Electronic Engineering
      Manchester, England, United Kingdom
    • Catholic University of Louvain
      Walloon Region, Belgium
  • 2009–2011
    • University of New South Wales
      • School of Engineering and Information Technology
      Kensington, New South Wales, Australia
  • 2010
    • University of Science and Technology of China
      Luchow, Anhui Sheng, China
  • 2004–2009
    • National ICT Australia Ltd
      Sydney, New South Wales, Australia
    • Delft University Of Technology
      • Delft Center for Systems and Control (DCSC)
      Delft, South Holland, Netherlands
  • 2008
    • Universität Bremen
      • Center of Applied Space Technology and Microgravity
      Bremen, Bremen, Germany
  • 2003–2007
    • Australian National University
      • Research School of Engineering
      Canberra, Australian Capital Territory, Australia
    • University of Melbourne
      • Department of Electrical and Electronic Engineering
      Melbourne, Victoria, Australia
  • 1999–2005
    • University of Cambridge
      • Department of Engineering
      Cambridge, ENG, United Kingdom
  • 2001–2002
    • Georgia Institute of Technology
      • School of Aerospace Engineering
      Atlanta, GA, United States