A case study on the universal compensation-improvement mechanism: A robust PID filter-shaped optimal PI tracker for systems with/without disturbances

Tsai, Jason Sheng Hong; Wang, Hsuan Han; Guo, Shu‐Mei; Shieh, Leang-San; Canelon, Jose I.

doi:10.1016/j.jfranklin.2018.03.006

Cited by 6 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar to the case of a strictly proper system (i.e., no Du c (t) term) [14], the definition of net EID of an input-output feedthrough system with both mismatched input and output disturbances is analogous to the definition given in [4]. Definition 1.…”

Section: Property Of the Eid Estimatormentioning

confidence: 99%

“…Based on the proof of the existence of EID for strictly proper systems [14], an EID is developed in Section 3 of this paper as an extension to the case of proper continuous-time systems. Given a controllable and observable proper system with all stable zeros and unknown mismatched independent input disturbances d i (t) = G i d i (t) and output disturbances d o (t) = G o d o (t), an EID d e (t) exists that enters the plant through the control input channel B and the input-output direct feedthrough term D, such that the two systems-one with {d i (t) and d o (t)} and the other with the matched disturbances {Bd e (t) and Dd e (t)}-share the same outputs but differ in their states [15,16].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

Tsai

Chen

et al. 2020

Applied Sciences

Self Cite

View full text Add to dashboard Cite

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

show abstract

Section: Property Of the Eid Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

Tsai

Chen

et al. 2020

Applied Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…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. Moreover, the disturbance observer and functional observer are developed to measure the external disturbance [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…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. Moreover, the disturbance observer and functional observer are developed to measure the external disturbance [13][14][15]. However, the proposed design approaches [13,14] cannot be directly applied to the systems with a direct feed-through term and unknown nonlinear perturbation; hence, the PID controller is worth being developed, especially if the controlled system is with nonlinear perturbations and direct feed-through term.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the disturbance observer and functional observer are developed to measure the external disturbance [13][14][15]. However, the proposed design approaches [13,14] cannot be directly applied to the systems with a direct feed-through term and unknown nonlinear perturbation; hence, the PID controller is worth being developed, especially if the controlled system is with nonlinear perturbations and direct feed-through term. With the design of the PI-type controller, the controlled system has the augmented structure, and this structure may result in an uncontrollable augmented controlled system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Lyapunov stability analysis of a robust model reference adaptive PI controller for systems with matched and unmatched dynamics

Evald

Hollweg

Tambara

et al. 2022

Journal of the Franklin Institute

View full text Add to dashboard Cite

A case study on the universal compensation-improvement mechanism: A robust PID filter-shaped optimal PI tracker for systems with/without disturbances

Cited by 6 publications

References 23 publications

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

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

Lyapunov stability analysis of a robust model reference adaptive PI controller for systems with matched and unmatched dynamics

Contact Info

Product

Resources

About