Fundamental limitations due to jω-axis zeros in SISO systems

Goodwin, Graham C.; Woodyatt, A. R.; Middleton, Richard H.; Shim, Jaehoon

doi:10.1016/s0005-1098(98)00224-6

Cited by 42 publications

(14 citation statements)

References 12 publications

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“…It was also shown that these formulae in closed form can be used to determine the zeros that result in minimum transient time. Jung et al [5] and Goodwin et al [6] found some limitations on transient response in terms of poles and zeros of the system. An interesting result was also reported by Leon de la Barra [7] who has shown that there are some relations between the nonminimum phase zeros and the case of undershooting [3].…”

Section: Introductionmentioning

confidence: 99%

A New PID Tuning Method Based on Transient Response Control

Hamamcı¹

2014

Balkan Journal of Electrical and Computer Engineering

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Section: Introductionmentioning

confidence: 99%

A New PID Tuning Method Based on Transient Response Control

Hamamcı¹

2014

Balkan Journal of Electrical and Computer Engineering

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“…He then considered the case of a single degree of freedom oscillator and extended the results to SISO systems with many modes and to MIMO systems. When considering a flexible axis under PID control a root locus study shows that the closed-loop bandwidth is limited by the open-loop anti-resonance and that there exists a maximum closed-loop damping ratio that depends on the inertia ratio whatever the values of the control parameters [8].Therefore classical tuning of PID controllers using pole-placement or optimization criteria based on a periodic and minimum-phase models are not applicable to flexible mechanical structures. However in a number of specific cases the adequate PID parameters can be found with optimization techniques for determining speed loop PID parameters by minimizing an ITAE criterion or assuming the existence of multiple roots [18].…”

Section: Introductionmentioning

confidence: 99%

Active vibration control of a piezoelectric beam using PID controller: Experimental study

Rahman

Alam

2012

Lat. Am. j. solids struct.

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Vibration suppression of smart beams using the piezoelectric patch structure is presented in the present work. The smart system consists of a beam as the host structure and piezoceramic patches as the actuation and sensing elements. An experimental set-up has been developed to obtain the active vibration suppression of smart beam. The set-up consists of a smart cantilever beam, the data acquisition system and a LabView based controller. Experiments are performed for different beam specimen. The coupled efficient layerwise (zigzag) theory is used for theoretical finite element modeling. The finite element model is free of shear locking. The beam element has two nodes with four mechanical and a variable number of electric degrees of freedom at each node. In the thickness direction, the electric field is approximated as piecewise linear across an arbitrary number of sub-layers in the piezoelectric layers. Cubic Hermite interpolation is used for the deflection, and linear interpolation is used for the axial displacement and the shear rotation. Undamped Natural Frequencies are obtained by solving the Eigen Value problem using Subspace Iteration method for cantilever beam. A state space model characterizing the dynamics of the physical system is developed from experimental results using PID approach for the purpose of control law design. The experimental results obtained by using the active vibration control system have demonstrated the validity and efficiency of PID controller. Experiments are conducted to compare the controlling of various cantilever beams of different sizes. It shows that the present actuator and sensor based control method is effective and the LabView control plots for various beams can be used as a benchmark for analytical work. The results are compared with ABAQUS software and 1D Finite element formulation based on zigzag theory.

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“…However, there are few solutions to that problem despite its importance in control system. Fundamental limitations in system response due to zeros of the closed-loop system are presented in [4]. In [5], an approach for synthesizing compensators for non-overshooting response was studied.…”

Section: Introductionmentioning

confidence: 99%

A new approach for transient response control via characteristic ratio assignment method

Kang¹,

Rho

Kim

2011

Int. J. Control Autom. Syst.

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This paper proposes a new direct approach to control the transient response of a LTI system. The characteristic of a repeated-pole system is first studied. It can be shown that the step response of this kind of system has no overshoot. µ-scaled characteristic ratios, β i = µα i , i =1, n, and τ are introduced, where α i is the principal characteristic ratio and τ is the generalized time constant. It is shown that two parameters, µ and τ, are used to successfully control the overshoot and the transient time of all minimum phase LTI systems. The result shows that the proposed method is comparable to the method proposed by Bhattacharyya [1], but more luminous and simple in approach.

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Fundamental limitations due to jω-axis zeros in SISO systems

Cited by 42 publications

References 12 publications

A New PID Tuning Method Based on Transient Response Control

A New PID Tuning Method Based on Transient Response Control

Active vibration control of a piezoelectric beam using PID controller: Experimental study

A new approach for transient response control via characteristic ratio assignment method

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