Synthesis of robust PID Control systems using stability feeler and partial model matching

Matsuda, Tadasuke; Nakamura, Yukinori

doi:10.1002/tee.23071

Cited by 2 publications

(21 citation statements)

References 18 publications

(20 reference statements)

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“…Therefore, the traditional PID linear controller with fixed parameters cannot adapt to the complex nonlinear feed servo system, which often leads to poor parameter tuning, poor control performance, and poor adaptability to operating conditions [19]. An APID method for precision contour machining is studied.…”

Section: Discussionmentioning

confidence: 99%

Simulation of Cutting Error of Cradle CNC Machine Tool Utilizing Three-Loop Pid Control Model

2021

IJOMAM

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The purpose of this work is to study the error of the three-loop PID (Packet Identifier) control model of cradle CNC (Computer Numerical Control) machine tool in the cutting process through simulation. Here, the milling and hobbing process are controlled through the vertical feed servo system of the cradle CNC machine tool. At the same time, the model is established in the ADAMS (Automatic Dynamic Analysis of Mechanical Systems) and MATLAB (Matrix Laboratory) software, including the servo motor, the complete control system, and the mechanical operation system. Then, the parameters of the three-loop PID are re-tuned. The gain parameters are adjusted from small to large, and the integral time constant is adjusted from large to small following the general experience of the external load. The steady-state value without vibration overshoot is set as the optimal value. Finally, the cradle CNC machine tool and the hobbing model are constructed, and the milling and hobbing are simulated through experiment. The pitch deviation and accumulation deviation of the simulated gear are measured through the VGMC (Virtual Gear Measurement Centre). The simulation experiment shows that the initial values set through the PID controller can shorten the system instability that arose from random values and shorten the intelligent algorithm and optimization time. Therefore, the error of the cradle CNC machine tool is significantly smaller than that of the ordinary CNC machine tool in the gear cutting process when controlled by a servo drive system with more accuracy, rapidity, and stability. It provides a more effective method to reduce the error in future precision machining. This can improve the accuracy requirements for products in the machining of CNC machine tools in China and lays a foundation for future intelligent control research.

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Section: Discussionmentioning

confidence: 99%

Simulation of Cutting Error of Cradle CNC Machine Tool Utilizing Three-Loop Pid Control Model

2021

IJOMAM

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“…Therefore, in Ref. [20],

{\overset{p}{true}}_{i}

is assumed to be the nominal value of

p_{i}

defined as

{\overset{p}{true}}_{i} = \frac{p_{i \min} + p_{i \max}}{2} false(i = 0, 1, 2, \dots, n false)

and replace

p_{i} false(i = 0, 1, 2, 3 false)

in (7) with

{\overset{p}{true}}_{i} false(i = 0, 1, 2, 3 false)

to determine the parameters of the controller. The replaced equation is as follows:

\begin{matrix} \frac{{\overset{p}{true}}_{3}}{{\overset{p}{true}}_{0}} goodbreak- σ m_{2} \frac{{\overset{p}{true}}_{2}}{{\overset{p}{true}}_{0}} goodbreak+ σ^{2} ((), {m_{2}}^{2} goodbreak- m_{3}) \frac{{\overset{p}{true}}_{1}}{{\overset{p}{true}}_{0}} \\ goodbreak+ σ^{3} ((), 2 m_{2} m_{3} goodbreak- {m_{2}}^{3} goodbreak- m_{4}) goodbreak= 0 . \end{matrix}

The first step of the method in Ref.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The replaced equation is as follows:

\begin{matrix} \frac{{\overset{p}{true}}_{3}}{{\overset{p}{true}}_{0}} goodbreak- σ m_{2} \frac{{\overset{p}{true}}_{2}}{{\overset{p}{true}}_{0}} goodbreak+ σ^{2} ((), {m_{2}}^{2} goodbreak- m_{3}) \frac{{\overset{p}{true}}_{1}}{{\overset{p}{true}}_{0}} \\ goodbreak+ σ^{3} ((), 2 m_{2} m_{3} goodbreak- {m_{2}}^{3} goodbreak- m_{4}) goodbreak= 0 . \end{matrix}

The first step of the method in Ref. [20] is to calculate the positive and minimum value of

σ

satisfying (9) and then use the following equations:

c_{0} = \frac{{\overset{true^}{p}}_{0}}{σ},

c_{1} = \frac{{\overset{p}{true}}_{0} ({\overset{p}{true}}_{1} / {\overset{p}{true}}_{0} - σ m_{2})}{σ},

c_{2} = \frac{{\overset{p}{true}}_{0} \{{\overset{p}{true}}_{2} / {\overset{p}{true}}_{0} - σ m_{2} {\overset{p}{true}}_{1} / {\overset{p}{true}}_{0} + σ^{2} ({m_{2}}^{2} - m_{3})\}}{}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…In this case, the characteristic polynomial family of the closed‐loop system is represented as follows:

\begin{array}{l} scriptP (s) & goodbreak= false{\frac{{\overset{p}{true}}_{0}}{σ} goodbreak+ ((), p_{0} goodbreak+ \frac{{\overset{p}{true}}_{1}}{σ} goodbreak- m_{2} {\overset{true^}{p}}_{0}) s \\ goodbreak+ ({}, p_{1} goodbreak+ \frac{p_{2}}{σ} goodbreak- m_{2} {\overset{true^}{p}}_{1} goodbreak+ σ ((), {m_{2}}^{2} goodbreak- m_{3}) {\overset{true^}{p}}_{0}) s^{2} \\ goodbreak+ p_{2} s^{3} goodbreak+ \dots goodbreak+ p_{n} s^{n + 1} \\ | p_{i} \in ([] p_{i \min}, p_{i \max}), σ \in ([] σ_{\min}, σ_{\max}) false} . \end{array}

In Ref. [20], another characteristic polynomial family is defined, in order to check robust stability of the closed‐loop system by using the edge theorem [21] and the stability feeler [22]. The coefficients of

s

in (13) are replaced by new independent variables, and their variation‐ranges are defined as the ranges which the original coefficients can take.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The method in Ref. [20] sets up an interval of the time constant of the reference model and analyzes robust stability of the closed‐loop system. If the closed‐loop system is not robustly stable, the interval of the time constant is reset and robust stability is analyzed again.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reduction of Conservativeness of Robust PID Control System Design Method: An Approach Using the Mapping Theorem and the Cremer–Leonhard–Mikhailov Criterion

Terui

Matsuda

Nakamura

2023

IEEJ Transactions Elec Engng

Self Cite

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This paper gives a novel method to design less-conservative robust PID control systems. The partial model matching method is a design method for PID control systems. That is a method to design a control system that matches a reference model as closely as possible. This method does not guarantee robust stability of a PID control system because it is assumed that there are no uncertainties on the coefficients of the lower-order terms of the plant. Therefore, in our previous work, a robust design method based on the partial model matching method was proposed. However, the drawback of this conventional method is that the results of stability analysis are conservative. In this paper, we aim to reduce the conservativeness caused by the conventional method. To achieve this goal, we use a robust stability analysis method based on the Cremer-Leonhard-Mikhailov criterion and the mapping theorem. Moreover, we also propose a new method to update the value of a design parameter. A numerical example shown in this paper implies that the conservativeness is reduced by the proposed method.

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Synthesis of robust PID Control systems using stability feeler and partial model matching

Cited by 2 publications

References 18 publications

Simulation of Cutting Error of Cradle CNC Machine Tool Utilizing Three-Loop Pid Control Model

Simulation of Cutting Error of Cradle CNC Machine Tool Utilizing Three-Loop Pid Control Model

Reduction of Conservativeness of Robust PID Control System Design Method: An Approach Using the Mapping Theorem and the Cremer–Leonhard–Mikhailov Criterion

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