Open‐Closed‐Loop PD Iterative Learning Control with a Variable Forgetting Factor for a Two‐Wheeled Self‐Balancing Mobile Robot

Dong, Jian; He, Bin; Zhang, Chenghong; Li, Gang

doi:10.1155/2019/5705126

Cited by 8 publications

(8 citation statements)

References 27 publications

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“…In this section, an input disturbance observer (a proposal in [29]) is presented and applied for system (14). By using the Euler method, we have an approximate discrete-time model of system (14) as follows:…”

Section: Compound Disturbance Observermentioning

confidence: 99%

“…eir nature is an unstable, underactuated, and nonlinear system, so it is very difficult to control them. ere have been many controllers designed for TWIRs such as backstepping [3,4], sliding mode control [5][6][7], nonlinear control [8][9][10][11], PID control [12,13], PD controller with iterative learning [14], fractional PID [15], fuzzy control [16,17], model predictive control [18], and nonlinear disturbance observer-based control [19].…”

Section: Introductionmentioning

confidence: 99%

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Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

Tran

Nguyen

2020

Journal of Control Science and Engineering

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In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

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Section: Compound Disturbance Observermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

Tran

Nguyen

2020

Journal of Control Science and Engineering

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“…However, they focused only on algorithm convergence, and an in-depth analysis of the forgetting factor effect on system output characteristics was not performed. In recent years, ILCs with forgetting factor, without enough supporting theory, have been applied to several engineering domains (Cao et al, 2015; Dong et al, 2019; Lan et al, 2017; Lin et al, 2019). Most reports indicated that the forgetting factor prevented the accumulation of initial resetting errors and interference.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

Dai

Gong

et al. 2021

Transactions of the Institute of Measurement and Control

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Iterative learning control with forgetting factor (ILCFF) is widely used in control engineering. However, choosing the optimal parameters of ILCFF to improve system-output characteristics has been a challenging issue for controller designers. This paper proposes an iterative learning control (ILC) algorithm that involves a variable forgetting factor based on optimal gains for a class of discrete linear time-invariant systems with aperiodic disturbances. The convergence of the algorithm is analyzed, and the necessary and sufficient condition for its convergence is derived in terms of proportional–integral–derivative coefficients. A design method based on optimal gains is established to determine the algorithm coefficients and to accelerate system convergence. Furthermore, the influence of the forgetting factor on both the system-output error and the scope of the proposed algorithm is analyzed. Additionally, the most suitable system type for the application of the forgetting factor is determined. The effectiveness of the algorithm is verified by performing a theoretical analysis and a case-based simulation. The proposed iteration-varying optimal forgetting-factor-based ILC algorithm undergoes fast convergence with a small system-output error. The findings disrupt the conventional view that the use of the forgetting factor increases system-output error. In fact, in a system with small trajectory and increased disturbances, the error induced by the forgetting factor may be smaller than that of the traditional optimal ILC algorithm.

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“…Here, the feedback controller is directly incorporated in the learning scheme, by adding the control action to the learning signal. Several instances of these algorithms have been proposed over the years, as for example including integral actions [20], a time-variable forgetting factor [21], or its extension to networked systems [22].…”

Section: Introductionmentioning

confidence: 99%

PI^σ - PI^σ Continuous Iterative Learning Control for Nonlinear Systems with Arbitrary Relative Degree

Cenceschi

Angelini

Santina

et al. 2021

2021 European Control Conference (ECC)

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Online-Offline Iterative Learning Control provides an effective and robust solution to learn precise trajectory tracking when dealing with repetitive tasks. Yet, these algorithms were developed under the assumption that the relative degree between input and output is one. This prevents applications in many practically meaningful situations -e.g. mechanical systems control. To overcome this issue, this manuscript proposes a PI σ -PI σ algorithm fusing information from the whole visible dynamics. We provide sufficient convergence conditions when the controlled system has a generic constant relative degree, and it is possibly subject to measurement delay. The controller is validated on several simulation scenarios, including learning to swing-up a soft pendulum.

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Open‐Closed‐Loop PD Iterative Learning Control with a Variable Forgetting Factor for a Two‐Wheeled Self‐Balancing Mobile Robot

Cited by 8 publications

References 27 publications

Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

PI^σ - PI^σ Continuous Iterative Learning Control for Nonlinear Systems with Arbitrary Relative Degree

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Open‐Closed‐Loop PD Iterative Learning Control with a Variable Forgetting Factor for a Two‐Wheeled Self‐Balancing Mobile Robot

Cited by 8 publications

References 27 publications

Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

PIσ - PIσ Continuous Iterative Learning Control for Nonlinear Systems with Arbitrary Relative Degree

Contact Info

Product

Resources

About

PI^σ - PI^σ Continuous Iterative Learning Control for Nonlinear Systems with Arbitrary Relative Degree