# Adaptive Sliding Mode Control Based on Disturbance Observer for Placement Pressure Control System

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## Abstract

**:**

## 1. Introduction

## 2. Calculation Model of Placement Pressure

## 3. Establishing Mathematical Model of Placement Pressure Control System

_{pn}is placement pressure, $\tau $ is the angle between winding tension and screw load,$\text{}{J}_{\mathrm{s}}$, $\text{}{c}_{\mathrm{s}}$ and ${F}_{\mathrm{G}}$ are screw moment of inertia, screw damping coefficient and screw load, respectively.

## 4. DOB-Based ASMC

#### 4.1. Design of Sliding Mode Controller

#### 4.2. Design of Disturbance Observer

#### 4.3. Design of Gain Adaptive Law

## 5. Simulation Analysis and Experimental Verification

#### 5.1. Simulation Analysis

_{1}(t) = 300 N) is used for positioning control, and relevant parameters of placement pressure control system are shown in Table 1. The simulation results of step response are shown in Figure 8, Figure 9 and Figure 10. Figure 8 and Figure 9 are the step response simulation results of PID and SMC, respectively. The control error of PID step response and SMC step response are 12.58 N and 6.28 N, respectively. The SMC algorithm has strong robustness and can effectively reduce the control error compared with the PID algorithm. However, it can be seen in Figure 9 that the sliding mode control has large high-frequency chattering, which will affect the system structure and damage the sensor. In order to reduce the high frequency chattering of the control input, the ASMC-DOB control algorithm is proposed. Figure 10 shows that the control error is 3.46 N. Compared PID and SMC, the control error of the design ASMC-DOB is reduced by 72.5%, and 41.3%, respectively.

#### 5.2. Experimental Verification

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Su, J.M.; Zhou, S.J.; Li, R.H.; Xiao, Z.C.; Cui, H. A review of carbon car bon composites for engineering applications. New Carbon Mater.
**2015**, 30, 106–114. [Google Scholar] - Jalali, M.; Moliere, T.; Michaud, A.; Wuthrich, R. Multidisciplinary characterization of new shield with metallic nanoparticles or composite aircrafts. Compos. Part B Eng.
**2013**, 50, 309–317. [Google Scholar] [CrossRef] - Kim, D.; Centea, T.; Nutt, S.R. Out-time effects on cure kinetics and viscosity for an out of autoclave prepreg Modelling and monitoring. Compos. Sci. Technol.
**2014**, 100, 63–69. [Google Scholar] [CrossRef] - Centea, T.; Grunenfelder, L.K.; Nutt, S.R. A review of out of autoclave prepregs—Material properties, process phenomena, and manufacturing considerations. Compos. Part A Appl. Sci. Manuf.
**2015**, 70, 132–154. [Google Scholar] [CrossRef] - Deng, B.; Shi, Y.Y.; Yu, T.; Kang, C.; Zhao, P.B. Multi-response parameter interval sensitivity and optimization for the composite tape winding process. Materials
**2018**, 11, 220. [Google Scholar] [CrossRef] [Green Version] - Tobalina-Baldeon, D.; Sanz-Adan, F.; Martinez-Calvo, M.A.; Santamaría-Pena, J. Dynamic tensile stress-compressive stress behavior of thermoplastic matrix composite materials reinforced with continuous fiber for automotive damping and anti-vibration structural elements. Materials
**2020**, 13, 5. [Google Scholar] [CrossRef] [Green Version] - Lee, E.; Cho, C.H.; Hwang, S.H.; Kim, M.G.; Han, J.W.; Lee, H.; Lee, J.H. Improving the vertical thermal conductivity of carbon fiber-reinforced epoxy composites by forming layer-by-layer contact of inorganic crystal. Materials
**2019**, 12, 3092. [Google Scholar] [CrossRef] [Green Version] - Deng, B.; Shi, Y.Y. Modeling and optimizing the composite prepreg tape winding process based on grey relational analysis coupled with BP neural network and bat algorithm. Nanoscale Res. Lett.
**2019**, 14. [Google Scholar] [CrossRef] [Green Version] - Kang, C.; Shi, Y.Y.; He, X.D.; Yu, T.; Deng, B.; Zhang, H.J.; Sun, P.C.; Zhang, W.B. Multi-response optimization of T300/epoxy prepreg tape-wound cylinder by grey relational analysis coupled with the response surface method. Mater. Res. Express
**2017**, 4. [Google Scholar] [CrossRef] - Yu, T.; Shi, Y.Y.; He, X.D.; Kang, C.; Deng, B.; Song, S.B. Optimization of parameter ranges for composite tape winding process based on sensitivity analysis. Appl. Compos. Mater.
**2017**, 24, 821–836. [Google Scholar] [CrossRef] - Simorgh, A.; Razminia, A.; Shiryaev, V.I. System identification and control design of a nonlinear continuously stirred tank reactor. Math. Comput. Simul.
**2020**, 173, 16–31. [Google Scholar] [CrossRef] - Pereira, R.D.O.; Veronesi, M.; Visioli, A.; Normey-Rico, J.E.; Torrico, B.C. Implementation and test of a new autotuning method for PID controllers of TITO processes. Control Eng. Pract.
**2017**, 58, 171–185. [Google Scholar] [CrossRef] - Karami, M.; Tavakolpour-Saleh, A.R.; Norouzi, A. Optimal nonlinear PID control of a micro-robot equipped with vibratory actuator using ant colony algorithm: Simulation and experiment. J. Intell. Robot. Syst.
**2020**. [Google Scholar] [CrossRef] - Weng, Y.P.; Gao, X.W. Data-driven sliding mode control of unknown MIMO nonlinear discrete-time systems with moving PID sliding surface. J. Frankl. Inst. Eng. Appl. Math.
**2017**, 354, 6463–6502. [Google Scholar] [CrossRef] - Sharifi, S.; Ahmadyan, S.; Ebrahimi, S. Designing of incorporating fuzzy-sliding mode controller based on strategy moving sliding surface for two-link robot manipulator. J. Frankl. Inst. Eng. Appl. Math.
**2012**, 9, 3475–3480. [Google Scholar] - Boiko, I.M. Chattering in sliding mode control systems with boundary layer approximation ofdiscontinuous control. Int. J. Syst. Sci.
**2013**, 44, 1–8. [Google Scholar] [CrossRef] - Shtessel, Y.; Edwards, C.; Fridman, L.; Levant, A. Sliding Mode Control and Observation; Springer: New York, NY, USA, 2014; pp. 163–166. [Google Scholar]
- El-Sousy, F.F.M. Adaptive dynamic sliding-mode control system using recurrent RBFN for high-performance induction motor servo drive. IEEE Trans. Ind. Inform.
**2013**, 9, 1922–1936. [Google Scholar] [CrossRef] - Velasco, J.; Barambones, O.; Calvo, I.; Zubia, J.; de Ocariz, I.S.; Chouza, A. Sliding mode control with dynamical correction for time-delay piezoelectric actuator systems. Materials
**2020**, 13, 132. [Google Scholar] [CrossRef] [Green Version] - Paolo, M.; Nils, W.; Udo, B.; Horst, H. A robust sliding mode control of a hybrid hydraulic piezo actuator for camless internal combustion engines. In Proceedings of the 2011 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Budapest, Hungary, 3–7 July 2011; pp. 499–504. [Google Scholar]
- Zhao, Y.; Qiao, W.; Wu, L. An adaptive quasi-sliding-mode rotor position observerbased sensorless control for interior permanent magnet synchronous machines. IEEE Trans. Power Electron.
**2013**, 28, 5618–5629. [Google Scholar] [CrossRef] - Huang, C.F.; Liao, T.L.; Chen, C.Y.; Yan, J.J. The design of quasi-sliding mode control for a permanent magnet synchronous motor with unmatched uncertainties. Comput. Math. Appl.
**2012**, 64, 1036–1043. [Google Scholar] [CrossRef] [Green Version] - Wang, A.; Jia, X.; Dong, S. A new exponential reaching law of sliding mode control to improve performance of permanent magnet synchronous motor. IEEE Trans. Magn.
**2013**, 49, 2409–2412. [Google Scholar] [CrossRef] - Cheng, C.; Liu, S.Y.; Wu, H.Z.; Zhang, Y. Neural network-based direct adaptive robust control of unknown MIMO nonlinear systems using state observer. Int. J. Adapt. Control Signal Process.
**2020**, 34, 1–14. [Google Scholar] [CrossRef] - He, J.; Luo, M.Z.; Zhang, Q.Q.; Zhao, J.H.; Xu, L.S. Adaptive fuzzy sliding mode controller with nonlinear observer for redundant manipulators handling varying external force. J. Bionic Eng.
**2016**, 13, 600–611. [Google Scholar] [CrossRef] - Wu, H.M.; Karkoub, M. Hierarchical fuzzy sliding-mode adaptive control for the trajectory tracking of differential-driven mobile robots. Int. J. Fuzzy Syst.
**2019**, 21, 33–49. [Google Scholar] [CrossRef] - Dong, L.; Tang, W.C. Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances. ISA Trans.
**2014**, 53, 110–116. [Google Scholar] [CrossRef] - Yang, J.; Li, S.H.; Yu, X.H. Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans. Ind. Electron.
**2013**, 60. [Google Scholar] [CrossRef] - Wen, T.; Xiang, B.; Wang, Z.Y.; Zhang, S.L. Speed control of segmented PMLSM based on improved SMC and speed compensation Model. Energies
**2020**, 13, 981. [Google Scholar] [CrossRef] [Green Version] - Paciornik, S.; d’Almeida, J. Digital microscopy and image analysis applied to composite materials characterization. ISA Trans.
**2010**, 15, 172–181. [Google Scholar] [CrossRef] [Green Version] - Fedulov, B.N.; Antonov, F.K.; Safonov, A.A.; Ushakov, A.E.; Lomov, S.V. Influence of fibre misalignment and voids on composite laminate strength. J. Compos. Mater.
**2015**, 49, 2887–2896. [Google Scholar] [CrossRef] - Croft, K.; Lessard, L.; Pasini, D.; Hojjati, M.; Chen, J.H.; Yousefpour, A. Experimental study of the effect of automated fiber placement induced defects on performance of composite laminates. Compos. Part A Appl. Sci. Manuf.
**2011**, 42, 484–491. [Google Scholar] [CrossRef] [Green Version] - Okuya, T.; Nakada, M.; Miyano, Y. Reliable test method for tensile strength in longitudinal direction of unidirectional carbon fiber-reinforced plastics. J. Reinf. Plast. Compos.
**2013**, 32, 1579–1585. [Google Scholar] [CrossRef] - Deng, B.; Shi, Y.Y. Modeling and simulation of voids in composite tape winding process based on domain superposition technique. Appl. Compos. Mater.
**2018**, 25, 1219–1236. [Google Scholar] [CrossRef] - Devanathan, S.; Koch, P.N. Comparison of meta-modeling approaches for optimization. J. Compos. Mater.
**2012**, 827–835. [Google Scholar] [CrossRef] - Standardization Administration of the People’s Republic of China. Test Method for Mechanical Properties of Ring of Filament-Winding Reinforced Plastics; Standardization Administration of the People’s Republic of China: Beijing, China, 2008. [Google Scholar]
- Paciornik, S.; D’Almeida, J.R.M. Measurement of void content and distribution in composite materials through digital microscopy. J. Compos. Mater.
**2009**, 43, 101–112. [Google Scholar] [CrossRef] - Zhu, H.Y.; Wu, B.C.; Li, D.H.; Zhang, D.X.; Chen, Y.Y. Influence of voids on the tensile performance of carbon/epoxy fabric laminates. J. Mater. Sci. Technol.
**2011**, 27, 69–73. [Google Scholar] [CrossRef] - Nikishkov, Y.; Airoldi, L.; Makeev, A. Measurement of voids in composites by X-ray computed tomography. Compos. Sci. Technol.
**2013**, 89, 89–97. [Google Scholar] [CrossRef] - Standardization Administration of the People’s Republic of China. Carbon fiber reinforced plastics Determination void content and fiber volume content; Standardization Administration of the People’s Republic of China: Beijing, China, 2008. [Google Scholar]

**Figure 7.**Block diagram of adaptive sliding mode control strategy based on disturbance observer (ASMC-DOB).

**Figure 8.**Step response of PID (simulation). (

**a**) Control error and tracking response; (

**b**) Control input.

**Figure 9.**Step response of SMC (simulation). (

**a**) Control error and tracking response; (

**b**) Control input.

**Figure 10.**Step response of ASMC (simulation). (

**a**) Control error and tracking response (

**b**) Control input.

**Figure 11.**Step response of PID (experiment). (

**a**) Control error and tracking response (

**b**) Control input.

**Figure 12.**Step response of SMC (experiment). (

**a**) Control error and tracking response (

**b**) Control input.

**Figure 13.**Step response of ASMC (Experiment). (

**a**) Control error and tracking response (

**b**) Control input.

Parameter | Value | Description | Parameter | Value | Description |
---|---|---|---|---|---|

${R}_{\mathrm{s}}\left(\mathsf{\Omega}\right)$ | 7 | Motor resistance | $p$ | 3 | Pole pairs of motor |

$\varphi $ | 20 | Magnetic flux | $\phi $ | 3 | Pole arc coefficient |

${c}_{\mathrm{m}}$ | 0.12 | Motor damping coefficient | ${c}_{\mathrm{s}}$ | 0.11 | Screw damping coefficient |

$\chi $ | 45° | Dovetail groove slope angle | ${J}_{\mathrm{m}}(\mathrm{kg}\xb7{\mathrm{m}}^{2})$ | 0.03 | Motor moment of inertia |

$\mu $ | 0.15 | Friction coefficient | $m(\mathrm{kg})$ | 5 | Worktable mass |

$d(\mathrm{mm})$ | 16 | Screw diameter | $H\left(\mathrm{mm}\right)$ | 8 | Screw lead |

Response | PID | SMC | ASMC | ||
---|---|---|---|---|---|

Step | Simulation | Control error | 12.58 | 6.82 | 3.46 |

Chattering extent | Small | Large | Smaller | ||

Experiment | Control error | 13.92 | 7.34 | 4.28 | |

Chattering extent | Small | Large | Smaller |

Type | PID | SMC | ASMC |
---|---|---|---|

E_{1} E_{2} E_{3} | F_{1} F_{2} F_{3} | G_{1} G_{2} G_{3} | |

Void content (%) | 1.2 1.32 1.28 | 0.98 1.02 1.18 | 0.22 0.32 0.38 |

_{1}—the first position of specimen E; F

_{1}—the first position of specimen F; G

_{1}—the first position of specimen G.

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**MDPI and ACS Style**

Hong, Q.; Shi, Y.; Chen, Z.
Adaptive Sliding Mode Control Based on Disturbance Observer for Placement Pressure Control System. *Symmetry* **2020**, *12*, 1057.
https://doi.org/10.3390/sym12061057

**AMA Style**

Hong Q, Shi Y, Chen Z.
Adaptive Sliding Mode Control Based on Disturbance Observer for Placement Pressure Control System. *Symmetry*. 2020; 12(6):1057.
https://doi.org/10.3390/sym12061057

**Chicago/Turabian Style**

Hong, Qi, Yaoyao Shi, and Zhen Chen.
2020. "Adaptive Sliding Mode Control Based on Disturbance Observer for Placement Pressure Control System" *Symmetry* 12, no. 6: 1057.
https://doi.org/10.3390/sym12061057