<p>Dual hydraulic cylinder systems often suffer from degraded tracking and synchronization consistency under strong nonlinearities, inter-cylinder parameter mismatch, and external disturbances. This paper presents an SARPID framework that integrates an anti-windup PID baseline, a Deep Q-Network optimized Safety–Advantage Residual (SAR) compensation, and an inter-cylinder coupling correction under input constraints to mitigate saturation and overly aggressive actuation. A high-fidelity MATLAB simulation platform is established based on a high-order nonlinear plant model, and the proposed method is benchmarked against PID, PID + MPC, and an ESO-SMC controller. In the reported disturbed condition, SARPID reduces the maximum synchronization error from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$1.5071$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.5071</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$0.21765\,\textrm{mm}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.21765</mn> <mspace width="0.166667em" /> <mtext>mm</mtext> </mrow> </math></EquationSource> </InlineEquation>, and the RMS synchronization error from <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$1.0238$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.0238</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$0.019866\,\textrm{mm}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.019866</mn> <mspace width="0.166667em" /> <mtext>mm</mtext> </mrow> </math></EquationSource> </InlineEquation>. The synchronization-error variance decreases from <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$1.0483$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.0483</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$0.000395\,\mathrm {mm^2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.000395</mn> <mspace width="0.166667em" /> <msup> <mi mathvariant="normal">mm</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. The reported comparisons also show that the SARPID control-voltage responses contain less high-frequency content. Using a <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\mathrm {V\cdot s}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">V</mi> <mo>·</mo> <mi mathvariant="normal">s</mi> </mrow> </math></EquationSource> </InlineEquation>-based control-effort index, SARPID yields <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$0.73\,\mathrm {V\cdot s}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.73</mn> <mspace width="0.166667em" /> <mrow> <mi mathvariant="normal">V</mi> <mo>·</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation> under disturbances, compared with <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$5.53\,\mathrm {V\cdot s}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>5.53</mn> <mspace width="0.166667em" /> <mrow> <mi mathvariant="normal">V</mi> <mo>·</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation> for PID and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$5.01\,\mathrm {V\cdot s}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>5.01</mn> <mspace width="0.166667em" /> <mrow> <mi mathvariant="normal">V</mi> <mo>·</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation> for PID+MPC. These results are consistent with improved synchronization consistency under the modeled nonlinearities, parameter mismatch, and external disturbances.</p>

High-precision synchronization of dual hydraulic cylinder systems via SARPID control with disturbance-rejection enhancement

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发表日期：

2026年2月2日

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Haoren Zhou,
Jinsheng Zhang,
Heng Zhang,
Yao Sun

摘要

Dual hydraulic cylinder systems often suffer from degraded tracking and synchronization consistency under strong nonlinearities, inter-cylinder parameter mismatch, and external disturbances. This paper presents an SARPID framework that integrates an anti-windup PID baseline, a Deep Q-Network optimized Safety–Advantage Residual (SAR) compensation, and an inter-cylinder coupling correction under input constraints to mitigate saturation and overly aggressive actuation. A high-fidelity MATLAB simulation platform is established based on a high-order nonlinear plant model, and the proposed method is benchmarked against PID, PID + MPC, and an ESO-SMC controller. In the reported disturbed condition, SARPID reduces the maximum synchronization error from $1.5071$ $1.5071$ to $0.21765\,\textrm{mm}$ $0.21765 mm$ , and the RMS synchronization error from $1.0238$ $1.0238$ to $0.019866\,\textrm{mm}$ $0.019866 mm$ . The synchronization-error variance decreases from $1.0483$ $1.0483$ to $0.000395\,\mathrm {mm^2}$ $0.000395 {mm}^{2}$ . The reported comparisons also show that the SARPID control-voltage responses contain less high-frequency content. Using a $\mathrm {V\cdot s}$ $V \cdot s$ -based control-effort index, SARPID yields $0.73\,\mathrm {V\cdot s}$ $0.73 V \cdot s$ under disturbances, compared with $5.53\,\mathrm {V\cdot s}$ $5.53 V \cdot s$ for PID and $5.01\,\mathrm {V\cdot s}$ $5.01 V \cdot s$ for PID+MPC. These results are consistent with improved synchronization consistency under the modeled nonlinearities, parameter mismatch, and external disturbances.