Robust Static Output Feedback H 2 / H ∞ Control Synthesis with Pole Placement Constraints: An LMI Approach

  • Published: 05 August 2020
  • Volume 19 , pages 241–254, ( 2021 )

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  • Hadi Behrouz 1 ,
  • Iman Mohammadzaman   ORCID: orcid.org/0000-0002-9346-6541 1 &
  • Ali Mohammadi 1  

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This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H 2 , and H ∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.

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Faculty of Electrical and Computer Engineering, Malek Ashtar University of Technology, Tehran, Iran

Hadi Behrouz, Iman Mohammadzaman & Ali Mohammadi

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Hadi Behrouz was born in Marvdasht, Fars, Iran in 1989. He received his M.S. degree in control engineering from the Shiraz University of Technology, Shiraz, Iran, in 2013. He is currently pursuing a Ph.D. degree in control engineering at Malek Ashtar University of Technology, Tehran, Iran. His research interests include robust and multi objective control and LMI optimization.

Iman Mohammadzaman received his Ph.D. degree in control engineering from Tarbiat Modares University, Tehran, Iran, in 2011. Since 2013, he has been an Assistant Professor with the Faculty of Electrical and Computer Engineering, Malek Ashtar University of Technology, Tehran, Iran. His research interests include robust control, nonlinear control, and convex optimization.

Ali Mohammadi received his Ph.D. degree in control engineering from Sharif University of Technology, Tehran, Iran, in 2003. Since 2003, he has been an Assistant Professor with the Faculty of Electrical and Computer Engineering Department, Malek Ashtar University of Technology, Tehran, Iran. His research interests include estimation, signal processing and control of LPV systems.

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Behrouz, H., Mohammadzaman, I. & Mohammadi, A. Robust Static Output Feedback H 2 / H ∞ Control Synthesis with Pole Placement Constraints: An LMI Approach. Int. J. Control Autom. Syst. 19 , 241–254 (2021). https://doi.org/10.1007/s12555-019-0290-3

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Received : 28 April 2019

Revised : 25 February 2020

Accepted : 01 April 2020

Published : 05 August 2020

Issue Date : January 2021

DOI : https://doi.org/10.1007/s12555-019-0290-3

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Pole Placement by Static Output Feedback

  • Mathematics and Statistics

Research output : Contribution to journal › Article › peer-review

T1 - Pole Placement by Static Output Feedback

AU - Wang, Xiaochang

M3 - Article

JO - J. of Math. Sys. Estim. Control

JF - J. of Math. Sys. Estim. Control

IMAGES

  1. Pole placement with output feedback

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  2. Figure 1 from Robust pole placement by static output feedback

    pole placement static output feedback

  3. 5: Closed-loop interconnection of mode M(s) with static output feedback

    pole placement static output feedback

  4. Pole placement with output feedback

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  5. Full state feedback control-pole placement and LQR.

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  6. Simulation block diagram of the simple pole placement state feedback

    pole placement static output feedback

VIDEO

  1. The Concept of Pole Placement in Classical and Modern Control, 30/3/2016

  2. L19 Numerical example on pole placement

  3. POLE PLACEMENT DAN LQR

  4. POLE PLACEMENT DAN LQR

  5. Pole Placement Control in State Space

  6. Pole placement by state feedback method

COMMENTS

  1. PDF Pole Placement by Static Output Feedback for Generic Linear Systems

    The pole placement problem is formulated as follows: Given a system S =(A;B;C),andasetofpointsfs 1;:::;s ngin C (listed with multiplicities) symmetric with respect to the real axis, nd a real matrix Ksuch that the zeros of ' Kare exactly s 1;:::;s n. For a xed system S, we de ne the (real) pole placement map (1.4) ˜ S:Mat R(m p) !Poly R (n);˜

  2. Pole Placement by Static Output Feedback for Generic Linear Systems

    Pole Placement by Static Output Feedback for Generic Linear Systems Authors: A. Eremenko and A. Gabrielov Authors Info & Affiliations https://doi.org/10.1137/S0363012901391913 Get Access BibTeX Tools Abstract We consider linear systems with m inputs, p outputs, and McMillan degree n such that n = mp.

  3. Partial Pole Placement using Static Output Feedback

    Partial Pole Placement using Static Output Feedback - ScienceDirect IFAC-PapersOnLine Volume 53, Issue 2, 2020, Pages 4527-4533 Partial Pole Placement using Static Output Feedback Manuel Pusch ⁎ , Julian Theis ⁎⁎ , Daniel Ossmann ⁎⁎⁎ Add to Mendeley https://doi.org/10.1016/j.ifacol.2020.12.470 Get rights and content

  4. PDF Partial Pole Placement using Static Output Feedback

    In general, the optimization problem for arbitrary pole placement using static output feedback is non-convex and its complexity increases with the number of inputs and outputs. To tackle this issue, control methods have been developed which facilitate controller design by decoupling and placing each pole of interest individually.

  5. Generalized pole placement via static output feedback: A methodology

    This paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form: given nsubsets of the complex plane, find a static output feedback that places in each of these subsets a pole of the closed-loop system.

  6. Pole Placement Via Output Feedback: a Methodology Based on Projections

    This paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form: given n subsets of the complex plane, find a static output feedback that places in each of these subsets a pole of the closed loop system.

  7. [PDF] Pole Placement by Static Output Feedback for Generic Linear

    A sufficient rank condition for arbitrary pole assignability by static output feedback of m-input, p-output linear systems of McMillan degree n<mp is given and an effective computational method to compute the feedback laws assigning any self-conjugate set of closed-loop poles is given. Expand

  8. PDF Static Output Feedback Pole Placement via a Trust Region Approach

    Simple modifications allow the approaches to be applied to problems for which the entries of K are constrained, for example, pole placement by decentralized control, in which case K must be block diagonal. The approaches can be used for either continuous time or discrete time systems.

  9. Static Output Feedback Pole Placement via a Trust Region Approach

    This technical note presents two closely related algorithms for the problem of pole placement via static output feedback. The algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles. Extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm ...

  10. Robust static output feedback design with pole placement constraints

    A necessary and sufficient condition for static output feedback (SOF) controller design for linear systems with polytopic uncertainties is derived in the form of the linear matrix inequalities ... which guarantees a minimum bound on the H 2 performance level in addition to the pole placement constraints. One of the advantages of the new method ...

  11. Robust pole placement by static output feedback

    This paper tackles the problem of pole placement by static output feedback. The considered systems are LTI and subject to both polytopic and norm-bounded uncertainties i.e. the uncertain closed-loop state matrix can be written A/sub o/ = A + BK/sub o/C + JEL. Matrices A,B,C, J and L belong to polytopes of matrices whereas E is unknown. K/sub o/ is the matrix associated with the static output ...

  12. Partial Pole Placement using Static Output Feedback

    In this paper, a novel control approach is presented for placing either a single pole or a conjugate complex pole pair at a predefined location using rank-one static output feedback. Rank-one feedback can be interpreted as blending inputs and outputs to define a single input and single output loop with a desirable root locus along which the ...

  13. PDF Robust Static Output Feedback H2=H¥ Control Synthesis with Pole Place

    Abstract: This paper studies the robust static output feedback (SOF) problem considering pole placement con-straints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems.

  14. Pole placement via static output feedback is NP-hard

    Pole placement via static output feedback is NP-hard. Abstract: This note proves that the problem of pole placement via static output feedback for linear time-invariant systems is NP-hard. Published in: IEEE Transactions on Automatic Control ( Volume: 49 , Issue: 5 , May 2004 )

  15. [Pdf] Pole Placement Via Output Feedback: a Methodology Based on

    Abstract This paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form: given n subsets of the complex plane, find a static output feedback that places in each of these subsets a pole of the closed loop system. The algorithm presented is iterative in nature and is based on alternating projection ideas.

  16. Output feedback pole placement with dynamic compensators

    Output feedback pole placement with dynamic compensators J. Rosenthal, Xiaochang A. Wang Published in IEEE Transactions on… 1 June 1996 Engineering TLDR The authors establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system by dynamic compensators of degree at most q. Expand View via Publisher

  17. Decentralized Local Pole-Placement Control Design using Static Output

    Abstract: This paper proposes Pole- placement control design procedures using static output feedback. The pole-placement problem is posed as a multilinear design problem. To guarantee that a real solution exists to the multilinear pole-placement equation, the concept of placing the closed-loop poles locally about the open loop poles is introduced.

  18. Static output feedback—A survey

    POLE PLACEMENT WITH STATIC OUTPUT FEEDBACK Here, it desired to select the gain K to place the poles (or the eigenvalues) in the closed-loop system (3) at desired locations. However, in a historical Static output feedback: a survey context a pole is said to be assignable (by output feedback) if K may be selected such that (3) has a pole ...

  19. Pole Placement by Static Output Feedback

    TY - JOUR. T1 - Pole Placement by Static Output Feedback. AU - Wang, Xiaochang. PY - 1992. Y1 - 1992. M3 - Article. SP - 205. EP - 218. JO - J. of Math. Sys. Estim.

  20. Pole placement by parametric output feedback

    Output feedback Eigenstructure assignment 1. Introduction Besides optimal control the pole placement approach is one of the most popular design methods in linear control theory.