Mathematical Problems in Engineering

Volume 2016, Article ID 3936810, 12 pages

http://dx.doi.org/10.1155/2016/3936810

## Compound Control Strategy for MDF Continuous Hot Pressing Electrohydraulic Servo System with Uncertainties and Input Saturation

^{1}School of Electro-Mechanical Engineering, Northeast Forestry University, Harbin 150040, China^{2}School of Information and Computer Engineering, Northeast Forestry University, Harbin 150036, China

Received 27 June 2016; Revised 17 October 2016; Accepted 10 November 2016

Academic Editor: Francisco Gordillo

Copyright © 2016 Zhu Liang-kuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A compound control strategy is investigated for Medium Density Fiberboard (MDF) continuous hot pressing electrohydraulic servo system (EHSS) with uncertainties and input saturation. Firstly, a hyperbolic tangent function is applied to approximate saturation nonlinearity in the system. And thus the mathematical model is continuous and differentiable. Subsequently, the slab thickness tracking controller is constructed by using a dynamic surface control (DSC) method, which introduces first-order low-pass filters to calculate derivatives of virtual control input in each step. Compared with the conventional backstepping controller, complexity of the design procedure is alleviated obviously. Moreover, a composite disturbance of uncertainties and input saturation is estimated by a nonlinear disturbance observer for compensation of the control law. Finally, an appropriate Lyapunov function is chosen to prove that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the tracking error converges to zero asymptotically. Numerical simulation results are also exhibited to authenticate and validate the benefits of the proposed control scheme.

#### 1. Introduction

With the increasing contradiction between supply and demand of timber resource, Medium Density Fiberboard (MDF) plays a significant role in the wood based panel market, owing to its favorable physical characteristics and excellent mechanical properties [1]. At present, continuous hot pressing electrohydraulic servo system (EHSS) is widely used to produce MDF. Hot pressing, as a core process of producing MDF, determines its final density, thickness, shape, and so on [2]. Particularly, gauge thickness is the key to obtain the high-quality MDF. Therefore, precise thickness control should be investigated for the MDF continuous hot pressing EHSS.

Unfortunately, both uncertainties and input saturation, which are inherent in the MDF continuous hot pressing EHSS, have a great influence on the control performance, degrading the precision of slab thickness. On one hand, uncertainties lie in system parameter perturbations and external disturbances. Due to the existence of temperature and pressure, some system parameters such as oil bulk modulus and oil liquid density may vary violently as the time goes by [3]. Simultaneously, external disturbances, consisting of steam pressure in the slab and environmental factors, have an undesirable impact on the EHSS. On the other hand, input saturation is one of inevitable nonlinearities from the actuator limitation [4]. Once the control input exceeds the upper voltage, the actuator action is invariable. Then, the electrohydraulic servo valve fails to supply the sufficient oil to the hydraulic cylinder. It will deteriorate the transient performance and accuracy of the EHSS severely. What is worse, it probably leads to instability. Accordingly, actuator saturation is not only a practical phenomenon, but also a theoretical problem when a precise control law is designed.

For the uncertainties in the EHSS, sliding mode control (SMC) attracted considerable attention [5–8], owing to its insensitiveness to the parameter perturbations and external disturbances during the sliding motion. However, chattering problem emerged in the system when the discontinuous sliding mode is applied, resulting in the extra power consumption and unmodeled high-frequency dynamics. Reference [5] introduced a varying boundary layer into the SMC to suppress the chattering. Combining adaptive law with SMC, [6] removed the assumption that bounds of uncertainties should be known and chattering phenomenon. By virtue of the universal approximation, fuzzy self-tuning mechanism [7] and adaptive Radial Basis Function (RBF) neural network [8] were brought into the SMC. Moreover, since the EHSS is always treated as a three-order or high integral cascade system, backstepping technique [9–11], known as a systematic and recursive design methodology with the flexibility, was widely utilized.

Nevertheless, the aforementioned literatures ignored the effect of input saturation in the EHSS. To handle the saturation constraints, a number of approaches have been presented and employed into different fields so far. In [12], an antiwindup method was proposed for a class of linear systems subject to actuator saturation. Reference [13] developed an adaptive model predictive controller (MPC) for nonlinear system in presence of saturation. By means of command filters, a constrained backstepping strategy is applied for flight control [14]. Although the abovementioned researches coped with the saturation problem in various systems, rigorous proof and general design procedures could not be guaranteed. Recently, Wen et al. introduced a smooth function to approximate the input saturation and an auxiliary system with the Nussbaum function to compensate for the effect arising from saturation nonlinearity in [15]. It argued that the transient performance depended on some certain design parameters in an explicit way. Thereafter, [16] constructed an adaptive neural network (ANN) controller by Gaussian error function to represent the input saturation. It ensure that the tracking error could converge to a small neighborhood around an origin.

It is supposed to point out that tackling both uncertainties and saturation for the EHSS is more challenge than taking one single problem into consideration with some specified control approach. There are still some common problems as follows: (1) When the SMC or backstepping method is used to design the controller, they need to calculate the high-order derivatives of reference signals and virtual control in each subsystems which may aggravate the calculation burden. It is unconducive to implement in practice. (2) As mentioned above, some researchers introduced an auxiliary system [15] and adaptive neural network [16] to eliminate the saturation effects, causing complexity of the designed controller.

Note that the main task is simplifying the design procedure from two aspects. One is alleviating the calculation burden. In particular, the existing backstepping technique in the EHSS gives rise to “explosion of differential terms” obviously, due to its repeated derivatives of virtual control inputs and signal references. The complexity grows drastically as the order increases. Therefore, a dynamic surface control (DSC) strategy was presented by Swaroop et al. in [17], applying several first-order low-pass filters to calculate the derivatives of virtual control inputs. Then, the burdensome calculation is avoided effectively.

The other is reducing the complexity of controller as possible. Although control algorithm with adaptive law, artificial-intelligence based method, and auxiliary systems might get perfect robustness and antisaturation properties, they also introduced quantities of extra parameters, such as adaptive law parameters and NN weights [18]. Such parameters will further aggravate the complexity of the controller, especially in presence of uncertainties and input saturation. Hence, nonlinear disturbance observer- (NDO-) based control strategy is popular because of its simple formation and less design parameters [19]. Some scholars view the model uncertainties, external disturbances, and saturation nonlinearities as a composite disturbance term and adopt a NDO to estimate and compensate it appropriately. References [20–24] suggested that NDO-based controllers have advantages on the robustness and compensation of saturation without many design parameters.

Except for the problem of uncertainties and input saturation, there are also some other factors which will have an impact on the MDF slab thickness, like unreliable communication links [25], input delay [26], sensor fault, and limited communication capacity [27].

Inspired by the work mentioned above, a compound control strategy is investigated for the MDF continuous hot pressing electrohydraulic servo system (EHSS) with uncertainties and input saturation. The controller chooses the DSC approach to realize the tracking control and the NDO to compensate the composite disturbance term, consisting of uncertainties and saturation nonlinearities. The control motivation is used to cancel the influence which aroused the composite disturbance and guarantees a precise thickness control performance with lower calculation burden.

The contribution can be summarized as follows:(1)Due to the existence of input saturation in the system, the MDF slab thickness tracking control performance is impacted. A hyperbolic tangent function is introduced into the MDF continuous hot pressing EHSS system mathematic model to approximate the saturation nonlinearities. And thus a continuous differentiable model is obtained to ensure that the DSC approach can be applied.(2)With the help of two first-order low-pass filters, the derivatives of virtual control inputs are obtained. Compared with conventional backstepping controller, the complexity of design in the DSC method is alleviated. Meanwhile, the burdensome calculation is avoided which is conducive to the engineering implement.(3)We develop a NDO to estimate the composite disturbance term of uncertainties and saturation nonlinearity. It effectively compensates for the designed control law and guarantees the MDF slab thickness precision.

The organization of the rest paper is as follows. The description of hot pressing process and the EHSS model is given in Section 2. In Section 3, a compound controller is established with the DSC technique and the NDO. The stability analysis is presented in Section 4. Simulation results are performed to demonstrate the effectiveness of the proposed strategy in Section 5. Finally, the paper is concluded in Section 6.

#### 2. Process and System Description

##### 2.1. Hot Pressing Process

Hot pressing is an essential process of the flat pressing way to produce MDF. Namely, high temperature and high pressure are supplied to MDF slab after preloading process. The chemical components of fiber are degraded in the presence of high temperature. Then, the fiber activity is excited. At the same time, bonding force is formed among the fiber. The aim of high pressure is to suppress the rebounded force inside and discharge the steam. Hence, the fiber can interweave tightly [28]. In addition, the MDF slab is pressed to the specified thickness under the pressure.

Particularly, gauge thickness is the key to obtain the high-quality MDF. Slab thickness is determined in a fixing-thickness phase, which is mainly about the final MDF figuration. With temperature and pressure in a reasonable range, discharging the left steam in the slab is the main task to avoid the defects such as surface bubbling and lamination. Nevertheless, due to the existence of steam pressure, thickness deviation is prone to appear. In the thicker area, steam cannot be discharged under the same pressure. Therefore, precise gauge control of MDF slab thickness is particularly significant at the fixing-thickness stage to cancel the deviation immediately.

##### 2.2. The Hot Pressing EHSS System

Configuration of the continuous hot pressing machine is depicted in Figure 1. A MDF slab is carried into an inlet by steel conveyor belts whose driving force is supplied from a couple of driven rolling wheels. Then, it reaches on a pair of steel platens, accomplishing the hot pressing process. The pressure is provided by hundreds of hydraulic cylinders and the temperature is transferred by the heated oil in the cylinder [28].