液压位置控制伺服系统外文翻译.doc

液压位置控制伺服系统外文翻译 液压位置控制伺服系统一 绪论 在控制系统的研究中液压位置控制伺服系统被广泛的应用,因为当工作点的状态发生变化时他的输出动态特性是非线性的。但是这种非线性的动态特性使得调节装置的设计变的比较困难。例如:在位置控制液压伺服系统的设计中若按照PID这种传统的控制方法来设计,那么将使得控制参数的调节变的比较困难。如果在设计中使液压伺服系统线性化,那么许多重要的动态信息或许会被丢失或忽略。所以液压伺服控制系统设计中选择一个适合非线性的控制方法就显得特别的重要了。在这篇的论文中,将对带柔性负载液压伺服系统滑模态控制的应用进行讨论。 滑模态控制 3-7 是一个有力的非线性控制方法,它能够为非线性系统提供鲁棒性能。在这个方法中通常利用系统的工作点对预期轨迹进行跟踪。在整流输出的滑模块控制系统中将会在矢量空间的预期子空间中形成一个滑模是一个众所周知的事实.在外部干扰和结构参数未知的设备表面,这个滑模块有着非常有用的不变特性。最近出版了一些研究用滑模块控制的液压动力系统的论文。但大多数的都只有讨论刚性负载的液压位置控制伺服系统。却很少有人讨论用滑模块控制的更复杂得像带柔性负载的液压位置控制伺服系统。在一些研究中华模块被用作起重机起重臂的简化模型,它由两个滑块和一个弹簧连接而成。基本的控制问题已经有Viersma开始讨论研究了,一些适合于滑块控制的应用场合将在后面的论文中提出。在这些研究中人们利用一个最佳的二次线性方程的几何模型来使工作点附近的线段线性化,因此要在现实中获得比较理想的鲁棒性能比较困难。在这篇论文中我们将利用实时实验来演示和讨论一个适合解决柔性负载液压位置控制伺服系统的滑模块控制方法。在第二段中我们将给出柔性负载的液压位置控制伺服系统的数学模型以及综述暂且存在的一些问题。根据控制目的,我们将在第三段中讲述一些为这个模型所设计的滑模块的一些细节。第四段中我们将对由实时实验获得有用的仿真图形进行分析。最后我们在第五段中给出结论。二 问题的阐述2.1数学模型的建立 首先我们建立描述柔性负载液压位置控制伺服系统的结构之间关系的数学模型。系统的数学模型的建立来源于力平衡方程,其方程如下: 其中液压腔中腔1和腔2的连续性方程(3)、(4)中的参数、的确定如下: 其中C是常数,C的计算公式如下: 系统中还使用了没有动力学的快速阀,其特性的描述如下: 利用下面替代关系进行变换: 那么我们可以得到描述这个模型的状态矢量方程: 其中 我们定义负载压降如下: 所以系统的状态矢量为现在我们规定这个模型的控制问题要求如下,系统得参数位置情况下,在预先给定一个有限的输入量,滑模块控制设计的工作状态矢量能够跟踪渴望得到状态矢量,这个过程也可以通过数学模型来表达: 为跟踪预期轨迹的系统的阶跃响应的上升时间。 (18)三 滑模块控制系统的设计 在这一段中我们将要设计一个系统的参考模型并要定义一个交换表面。首先我们利用Lyapunov稳定性理论可以获得一个等价的控制规律,然后我们再得出整个滑模块控制系统的控制规律。3.1 设计预期轨迹 这个模型的控制系统的方块图如Fig. 2.所示。定义系统误差如下: 其中i1,4.我们可以利用参考输入我们可以得到活塞位置的预期轨迹,相应的预期最大速度可以通过对进行求导得到。我们可以建立一个如下的参考模型来获得柔性负载的预期位置轨迹及其速率轨迹。 其中s为拉普拉斯变换因子,通过解放成(12)可以得到。为了得到零误差的稳定状态,根据方程(9)-(14)、(16)、(19)和(20),可以得到动态误差系统的空间矢量方程如下: 3.2 设计转换表面 特地为这个模型设计了一个转换表面,起作用使为了同时对系统的所有状态的预期轨迹进行跟踪,其数学表达如下: 并定义e为 其中()为有利因子。 3.3 滑模块控制器其拉普拉斯表达式为:V为正数,根据拉普拉斯稳定性判据可以得到 这是建立滑模块控制系统的必要条件,将方程(23)-(27)以及(29)带入(31)可以得到 所以我们可以通过方程(32)得到在没有外部干扰的情况下的模型的所谓等价控制规律如下: 因此整个滑模块模型的控制规律可以假设为: 其中K为开关的增益,是用来保证在转换表面形成一个滑模块,是滑模块控制系统中的一个非常重要的参数。控制规律方程由等价控制和转换控制两部分组成。为了减少输入信号的失真,我们用因子函数(35)代替输入信号函数(34),这个函数的特性描述如下: 在S里是分界层的厚度,在动力学的书瞬态阶段,S可能在分界层之内或之外,然而只要满足拉普拉斯稳定性判别定理,S的取值仍然在这个层的范围内。在设计滑模块控制的过程中,选择适合的参数(例如K、N和阀的增益)就非常重要了。因为系统是非线性的,所以这些参数的值没有规律来确定,一些参数的确定是通过反复的实验来确定或错误的选择。四 仿真和试验4.1 试验环境 图Fig. 3是滑模块试验的实验装置模型,该实验装置可以在Lappeenranta工业大学的机械自动化实验室实现。 改实验装置使用的伺服阀是4661超级伺服阀,气缸的规格为32/22/1000。为了校核系统的刚度,该系统的结构参数(可以)可以在下列范围内变化。 1的变化范围为78-194 kg。 2的变化范围为22-220 kg。 3弹簧的刚度 k 为 67314 N/ m 或 136607 N/m 。 因为系统的阻尼在这个装置中不是很重要,所以可以忽略不计。为了获得系统状态的各种测量值,可以直接通过传感器来测定。可以通过计算机来对求导来获得,也可以通过对系统的实时数模转换来实现。取样频率在这一个程序中是 200赫兹 。 这个控制程序是以远程终端为平台的C/C+语言。控制信号的电压通过放大器转换成电流。4.2开环回路 在进行实时试验过程之前,我们要检验一下第二端中建立的模型的精确性。当我们提供10伏特的电压作为伺服阀的输入时,则负载,以及腔一腔二压力的阶跃响应特性曲线如下所示:仿真和试验数据结果显示该数学模型 4.3 闭环回路 为了保证所给控制器的精确性,我们首先进行仿真。通过仿真我们可以确定控制系统的性能。在第三节的提到的参考系统的参数我们把它定义为阻尼比()和固有频率()通过选择适当的控制参数,(78 kg, m222 kg, k67,314 N/m, 145bar, ,),前面括号中所给的为柔性负载伺服系统的各个参数。在初始状态、时间间隔为0.005s情况下通过普通的Runge-Kutta方法进行仿真,图Figure 5为用滑模块控制的柔性负载液压控制伺服系统来跟踪阀有限电压输入时参考阶跃响应仿真的特性曲线: 在Fig. 5中,虚线所示的负载轨迹和活塞的轨迹都向我们事先设计好的实线轨迹渐进,图中给出负载的压力随时间变化以及伺服阀的电压随时间变化的特性曲线。参考的正弦响应特性曲线的仿真结果如图Fig. 6所示。 通过仿真对控制器进行调整后,我们在实际中对该控制系统进行测试。实时实验室在相同的条件下进行测量。为了获得控制系统的鲁棒性能,我们将系统的各个结构参数像4,1那样调整然后进行试验。情况A所给的控制系统设计中的各个参数(78 kg, 22kg and k67,314 N/m)定义为名义参数。当相应的结构参数由情形A变成情形B(78 kg, 22 kg and k67,314 N/m),活塞位置的参考轨迹为阶跃响应轨迹。实验结果和仿真的对照如图Fig. 7所示。 图中所示的实线为参考轨迹,点画线为情形A的轨迹,虚线为情形B的轨迹。当活塞的参考轨迹用正弦响应特性曲线来表示时,其实验结果和仿真的对照如图Fig.8所示: 当结构参数超出了名义结构参数的范围时,特性曲线中将出现超调量和稳态误差。由于刚性负载和柔性负载的挠度不同,当结构参数由名义参数开始变化时,在响应的开始时柔性负载系统的震动非常小,而且很快就消失了,所以它不影响柔性负载液压位置控制系统的稳定性。因此结构参数未知的柔性负载液压位置控制系统在跟踪事先决定的参考轨迹时弊刚性负载系统有更好的鲁棒性能。从仿真和实验结果我们可以看出所给定的滑模块控制对柔性负载液压位置控制伺服系统是有效的。五 结论 我们建立了一个适合于柔性负载液压控制的伺服系统的滑模块控制体系。鲁棒控制方法来源于Lyapunov判据。从这些实验演示可以看出滑模块控制器在维持设计的伺服系统的动态特性在同一水平有着非常好的鲁棒性能。从仿真和实验结果可以看出通过改进方法我们可以获得很好的阶跃响应和正弦响应特性。应该指出的是这种方法可以推广到一般情况,例如多个刚性和柔性负载的情况。结果很有用的,而且在未来在相似的方案方面的进一步的研究将会是被运用。 HYDRAULIC POSITION SERVOS HPSIntroduction Hydraulic position servos HPS are widely used in the control system studies because it has a nonlinear dynamic behavior when the operating point of state changes 1. The nonlinear dynamic property makes the control design difficult. For example, it is not easy to tune the control parameters when designing the control system of HPS with classic control methods such as PID 2. Some important dynamic information may also be lost if the hydraulic servo system is linearized during the design. So it is important to select a nonlinear control method particularly suitable for hydraulic servo systems. In the present paper, a sliding mode control is discussed incapplication to HPS with a flexible load. Sliding mode control 3-7 is a powerful nonlinear control method capable of providing robust performance for nonlinear dynamic system. In the method the desired is tracked by the operating point of the system. It is a well-known fact that sliding mode control with switching output will result in a sliding mode on a predefined subspace of state space. This mode has useful invariance properties in the face of uncertainties of plant such as external disturbances and structural parameters, and therefore is a candidate for tracking control of uncertain nonlinear system. Some papers dealing with sliding mode control of fluid power systems 2, 5, 7 are recently published. Most of them only consider hydraulic position servo with a rigid load. So far few papers deal with sliding mode control of the more complex model which is similar to the HPS with a flexible load. This model in some studies is used as a simplified model of a crane boom. It contains two masses connected with a spring. The basic control problem is discussed by Viersma 1. Some applications of adaptive control in this area have been presented in 8, 9. In these studies a math- ematical model with linear quadratic LQ optimization is linearized in the vicinity of an operating point, so it is not easy to obtain robust performance in practice. The present paper discusses the sliding mode control method suitable for solving the control problem of HPS with a flexible load. Results on simulation and experiment in real time are shown. In Section 2, the mathematical model of HPS with a flexible load is presented, and a statement of problems is briefly given. According to the control goal, sliding mode control design for this model is discussed in detail in Section 3. In Section 4, a series of simulations are available, these are also followed by experiments in real time. Conclusions constitute Section 5.2. Problem statemen2.1. Mathematical model The mathematical model of HPS with a flexible load see Fig. 1 describing the relationship between the components 1 is firstly presented. The mathematical model of this system is derived by using force balances as follows where Q, and QZ in eqn 3 and eqn 4 are the continuity equations for the chamber 1 and chamber 2 of the cylinder, its mathematical description is as where c, is constant value, which is determined by The fast valve without dynamics is applied in the system. The description of this valve is below Using the notation as state variables. So state space equations of this model are described as follows where We define load pressure as So state vector of the system is xx , x2,x5T. Now we state the control problem of this model as follows. Sliding mode controller has to be designed such that theoperating state vector xx , x2,x5T track asymptotically a desired state vector xdxid, xzd,:5dT which is predetermined with a finite control input i in the presence of parameter uncertainty of the system. The processes are also math- ematically described as where to0 is the rise time of step response of systems to track the desired trajectories.Design for slide mode control system In this section, a reference model of the system is designed and switching surfaces are defined. With Lyapunov stability theory, we can obtain equivalent control law at first, then overall sliding mode control law of this system.3.1. Design for desired trajectory The control system block diagram of the model is shown as Fig. 2. The states error of system is defined as where i1,4. The desired trajectory of piston position x3d is previously available to use as reference input of control system. The corresponding desired velocity xM is achieved by differential for x3d. We can obtain the desired trajectory of the flexible load position x,d and its velocity x,d by designing a reference model as follows where s is Laplace operator. x5d is obtained by solving eqn 12. To achieve zero steady state error, according to eqns 9一14, eqns 16, 19 and 20, the state-space equations of the error dynamic system are derived as follows3.2. Design for switching surface In order to achieve all of states of system to track the desired trajectories at the same time, the function of switching surface is specially defined for this model as follows where a is defined as where w; i1,5 are weighted gains3.3. Sliding mode controller Lyapunov function is designed as which is positive. The Lyapunov stability criterion is described as follows which constitutes the attractive condition for the sliding mode control. Substitute eqns 29 and 23一27 into eqn 31 given So we can get the so-called equivalent control law of the model from eqn 32 under the circumstances of undisturbed system as follows Therefore the overall sliding mode control law is proposed as follows where K expresses the switching gain which is used to guarantee a sliding regime onthe switching surface St, it is an important parameter in sliding mode control. The control law 34 is composed of two components which are described by the equivalent control and the switch control, respectively. In order to reduce the degree of the chattering of the control input signal, a saturation function sat S is replaced instead of the sign function sgn S of the eqn 34. The property of the function is described as where0 is the boundary layer width in S. During transient phase of the dynamics, S may move in and out this boundary. However, once the Lyanpunov stability criterion is satisfied, S remains entrapped in this layer. In the process of design for sliding mode control, it is very important to choose the suitable control parameters such as N, K,and weighting gains. Because of system nonlinear, there is no regular method to determine these values. Some appropriate control parameters have to be selected by trial and error. 4. Simulations and experiments4.1. Experimental environment In Fig. 3 the experimental system installation of the model, which is available at the Laboratory of Machine Automation in Lappeenranta University of Technology, is presented. In this installation, the servo valve used is Ultra Hydraulics 4661 servo valve. The dimensions of the cylinder are 32/22/1000. To verify robustness of control system, the structural parameters of the model such as m, m2 and k are easy to be changed as follows: 1 The range of m, is from 78-194 kg. 2 The range of m2 is from 22-220 kg. 3 The stiffness of spring k is 67,314 N/m or 136,607 N/m. The structural damping is neglected here because it is not important in this model. In order to acquire measurement of system states, xP, x1 and p1 p2 are directly measured by position and pressure transducers, respectivelyare differential from with computer, which is also implementation of the digital control of system in real time. The sampling frequency is 200 Hz in this process. The control program is C/C+language program which is generated by RTW 10. Data acquisition is implemented with commercially available computer board CIO-DAS16 including 12- bit ADC and DAC cards. Control signal voltage is converted from voltage V into current i by an amplifier.4.2. Opened loop Firstly, we verify the validation of mathematical model in Section 2 before going in for real time experiment of control process. When applying step response as input to servo-valve with amplitude 10 V. The step responses of load position x, piston position xP, pressure in chamber one p, and pressure in chamber one p2 are shown in Fig. 4. The simulated and experimental results show that the mathematical model of opened loop can represent practical rig accurately.4.3. Closed loop To ensure the validity of the proposed controller, simulations were firstly carried out. Simulation had been done in order to determine the performance of control system. The parameters of reference model, which were described in Chapter 3, were taken as damping ratio b0.7 and natural angular velocity。18 rad/s