Journal of Optimization Theory and Applications

, Volume 59, Issue 2, pp 183–207 | Cite as

Dynamically similar control systems and a globally minimum gain control technique: IMSC

Contributed Papers


The concept of dynamically similar control systems is introduced. The necessary and sufficient conditions to minimize a quadratic modal gain measure are given for dynamically similar closed-loop control systems. The globally minimum modal gain is obtained when the independent modal space control (IMSC) is used. Corollaries of the results for the control of infinite-dimensional structural distributed parameter systems (DPS) are given. Based on the results, a modal interaction parameter (MIP) is defined for all control systems. The minimum value of MIP is zero and uniquely corresponds to the IMSC. A nonzero value of MIP corresponds to all other coupled control (CC) designs and implies suboptimality relative to the IMSC design. The relative optimality of the real-space gain matrices of the IMSC and the CC designs depends on the actuator locations for the IMSC. Based on this, a real-space interaction parameter (RIP) is defined. A positive value of RIP renders IMSC optimal in its real-space gain matrix. The MIP and RIP are indications of suboptimality of a particular control technique and can be used to tune-up the control design via actuator locations. Actuator distribution criteria are suggested for both CC and IMSC designs, based on the values of MIP and RIP, respectively.

Key Words

Distributed parameter system control modal control control gain optimization 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • H. Öz
    • 1
  1. 1.Department of Aeronautical and Astronautical EngineeringOhio State UniversityColumbus

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