State‐space Digital Pid Controller Design for Multivariable Analog Systems With Multiple Time Delays

Madsen, Jennifer; Shieh, Leang-San; Guo, Shu‐Mei

doi:10.1111/j.1934-6093.2006.tb00266.x

Cited by 21 publications

(8 citation statements)

References 25 publications

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“…The Laplace transform method and the final-value theorem are employed to design the tracking controller [11,12]. To shape the tracking performance, the literature in [13,14] designed the augmented state for PID filter then the controlled system is transformed to the augmented controlled system with a direct feed-through term.…”

Section: Introductionmentioning

confidence: 99%

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

et al. 2019

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A robust linear quadratic analog tracker (LQAT) consisting of proportional-integral-derivative (PID) controller, sliding mode control (SMC), and perturbation estimator is proposed for a class of nonlinear systems with unknown nonlinear perturbation and direct feed-through term. Since the derivative type (D-type) controller is very sensitive to the state varying, a new D-type controller design algorithm is developed to avoid an unreasonable large value of the controller gain. Moreover, the boundary of D-type controller is discussed. To cope with the unknown perturbation effect, SMC is utilized. Based on the fast response of SMC controlled systems, the proposed perturbation estimator can estimate unknown nonlinear perturbation and improve the tracking performance. Furthermore, in order to tune the PID controller gains in the designed tracker, the nonlinear perturbation is eliminated by the SMC-based perturbation estimator first, then a hybrid Taguchi real coded DNA (HTRDNA) algorithm is newly proposed for the PID controller optimization. Compared with traditional DNA, a new HTRDNA is developed to improve the convergence performance and effectiveness. Numerical simulations are given to demonstrate the performance of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

et al. 2019

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“…Most of the parameters are systematically tuned using state‐feedback and state‐feedforward LQR approach. An extension for multiple time delays is presented in .…”

Section: Introductionmentioning

confidence: 99%

Wind Turbine Multivariable Optimal Control Based on Incremental State Model

Adánez

Al‐Hadithi

Jiménez

2017

Asian Journal of Control

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The multivariable optimal control of a wind turbine by an approach based on incremental state model is proposed. The advantages of incremental state model in comparison with the non incremental one are that the control action cancels steady state errors and incremental state solves the problem of computing the target state, choosing zero as an objective. Linear Quadratic Regulator (LQR) and optimal state observer are applied. The effectiveness of the proposed control method, over the non incremental one, is examined by applying the linear controllers to the nonlinear wind turbine model. The results show that incremental LQR control presents good transient response and zero steady state errors, even in presence of disturbances, nonlinearities and modelling errors.

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“…This work was supported also by the development project of key laboratory of Liaoning Province. systems, the problem is relatively simple and general and effective techniques have been proposed mainly based on the Routh-Hurwitz criterion, such as, the Ziegler-Nichols method in [3], generalization of the Hermite-Biehler Theorem in [4], the Astrom-Hagglund method in [5], and also some new summary results in [6][7][8][9][10][11]. However, as inherent phenomena, time delays are encountered in a variety of interconnected real systems or processes, which makes the problem much more complex.…”

Section: Introductionmentioning

confidence: 99%

The τ Decomposition Method for PID Controllers of First Order Delayed Unstable Processes

Cai¹,

Zhang²,

Yang³

et al. 2014

Asian Journal of Control

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The stabilization of first‐order delayed (FOD) unstable processes with proportional–integral–derivative (PID) controllers is considered, and all the feasible PID controllers are determined. Different from the existing results which are based on the D‐partition technique and partitioning complex's real and imaginary parts, a novel procedure enlightened by the τ decomposition method is proposed to characterize the space of controller parameters. Generally speaking, the parameter space is mainly divided into four regions: delay independent stable region, delay independent unstable region, delay interval dependent stable region, and delay interval dependent unstable region. The depiction of the space partition boundaries and the determination of stable intervals become the main problems. In our work, these boundaries are related to the existence of the purely imaginary roots (PIRs) of the systems' characteristic equation, and the determination of stable intervals refers to the number and value of the PIRs. Thus, the key points are the number and calculation of PIRs. According to our discussion, analytical results on both topics are obtained in explicit form. Finally, vivid numerical simulations are given to illustrate the results.

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State‐space Digital Pid Controller Design for Multivariable Analog Systems With Multiple Time Delays

Cited by 21 publications

References 25 publications

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

Wind Turbine Multivariable Optimal Control Based on Incremental State Model

The τ Decomposition Method for PID Controllers of First Order Delayed Unstable Processes

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