WO2022121507A1 - 一种针对非对称伺服液压位置跟踪***的低复杂控制方法 - Google Patents
一种针对非对称伺服液压位置跟踪***的低复杂控制方法 Download PDFInfo
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- the invention relates to the field of servo hydraulic position control, in particular to a low-complexity control method for an asymmetric servo hydraulic position tracking system.
- Servo hydraulic systems have the advantages of excellent load efficiency, small power ratio, and fast response speed, so they are widely used in modern industries (such as active suspension systems, hydraulic excavators, manipulators).
- the servo hydraulic system includes two kinds of hydraulic actuators, the symmetrical hydraulic actuator with double rod and the asymmetric hydraulic actuator with single rod.
- active suspension control research the areas of the two oil chambers are often considered equal, and a symmetrical hydraulic actuator is used.
- asymmetric servo hydraulic systems due to the existence of the piston rod, the effective areas of the rod cavity and the rodless cavity of the hydraulic cylinder are not equal, and the symmetrical hydraulic actuator that can achieve the same performance is often larger than the asymmetric hydraulic actuator. It is used in a few special occasions, and widely used in industry is asymmetric hydraulic actuators. Therefore, it is unreasonable to place symmetrical hydraulic actuators in the vehicle suspension system with great space limitations.
- the asymmetric servo hydraulic system is a complex nonlinear system, and it involves various uncertainties, such as load changes, parameter uncertainties, and unknown nonlinearities, which will lead to modeling and design control. Therefore, for asymmetric servo-hydraulic systems, high-precision position control is facing a huge challenge.
- the parameter uncertainties mainly include leakage coefficient, oil film viscosity and viscous friction coefficient
- the unknown nonlinearity mainly includes spool dead zone and external disturbance, which hinder the development of high-performance controllers.
- many control techniques have been developed in the past ten years, such as neural network adaptation, fuzzy logic control, robust adaptive control, and backstepping adaptive control.
- Bechlioulis CP, Rovithakis GA, et al. initially proposed novel controller design methods that can guarantee tracking error transient performance.
- the transient and steady-state performance of tracking error is specified by introducing a specified performance function, and the original system with constraints is equivalent to an unlimited system by introducing error transformation.
- This idea is further applied to high-order nonlinear fault-tolerant control systems, hydraulic servo systems, and suspension systems.
- the control schemes are all combined with adaptive control methods to deal with unknown dynamics in the system.
- the servo hydraulic system and its position control method have the following shortcomings: 1.
- the single-rod nonlinear servo hydraulic system is a typical complex nonlinear system, which involves load changes, parameter uncertainty and unknown Because of the nonlinearity and other problems, there is a huge gap between the establishment of the theoretical model and the actual system, which leads to the difficulty and complexity of designing the controller; 2.
- Most of the current servo-hydraulic position control methods are based on backstep control adaptive However, these control methods have a high degree of dependence on the model, and in the process of backstepping design of high-order systems, a large amount of calculation will be generated, and the online learning of uncertain parameters is not conducive to actual experiments.
- the present invention discloses a low-complexity control method for an asymmetric servo-hydraulic position tracking system, including the following steps: S1: establishing a servo-hydraulic system model of a single-exit rod; S2: according to the single-exit rod S3: According to the controller of the servo hydraulic system with a single rod and the model of the servo hydraulic system with a single rod, it is proved that the single output rod The stability of the servo-hydraulic system of the rod.
- the process of establishing the model expression of the servo-hydraulic system of the single rod is as follows: establish the dynamic model of the hydraulic cylinder according to Newton's second law:
- f(t) represents various disturbances
- x and m represent the position and mass of the load respectively
- B is the viscous damping coefficient
- K is the equivalent spring stiffness of the load, when the load is an inertial load
- K 0
- P 1 , P 2 are the pressures of the large and small chambers of the hydraulic cylinder
- a 1 , A 2 are the effective areas of the pistons of the large and small chambers
- the load pressure dynamics is expressed by the following formula:
- C t is the leakage coefficient inside the hydraulic cylinder, and C e is the external leakage coefficient of the hydraulic cylinder.
- ⁇ e is the elastic modulus of oil;
- Q 1 is the hydraulic oil flow rate with rod cavity,
- Q 2 is the hydraulic oil flow rate without rod cavity;
- P s is the oil supply pressure of the hydraulic system
- P r is the oil return pressure of the hydraulic system
- C d is the flow coefficient of the orifice
- w is the area gradient of the spool valve
- ⁇ is the oil density
- x v is the spool of the servo valve
- ⁇ is the time constant of the servo valve dynamics model, and u(t) is the current input; considering the spool displacement ⁇ (x v ) with an unknown dead zone, its expression is as follows:
- the parameters m r and m l represent the left and right slopes of the dead zone characteristic curve, and the parameters br and b l represent the breakpoints of the input nonlinearity;
- ⁇ 1 , ⁇ 2 , ⁇ 3 are virtual control variables
- x 1r is the command signal of the hydraulic position tracking system
- z 1 is the position tracking error
- the controller of the servo hydraulic system is:
- the standardized error vector has a maximum solution in the non-empty open set ⁇ ⁇ in the time period t ⁇ [0, ⁇ max ): the non-empty open set ⁇ ⁇ , select the performance function
- ⁇ i satisfy: ⁇ i (0)>min ⁇ -i , ⁇ - i ⁇
- , i 1...4, we can get:
- V 1 V 01 +A 1 x
- V 2 V 02 -A 2 x
- a safety margin is reserved, that is, according to the physical structure, the hydraulic cylinder can fluctuate up to 12 cm up and down near the neutral position, and the amplitude of the command signal is less than or equal to 10 cm to ensure h 1 h 2 h 3 is bounded, that is, there are three positive numbers respectively make
- the present invention provides a low-complexity control method for an asymmetric servo-hydraulic position tracking system, which can solve various uncertainties in the hydraulic system (eg, unknown friction effects, variable parameters, etc.). Determined and load changes) and unknown nonlinear problems (such as spool dead zone, external disturbances), the design of the controller does not rely on an accurate mathematical model, only the state signal that can be measured, the calculation of the control rate is consistent with the existing in Compared with the algorithm developed on the basis of backstepping adaptation, the calculation process is simple, the amount of calculation is small, it is convenient for real-time control, and it is easier to realize engineering; the invention can ensure the convergence speed and steady-state accuracy of tracking error; finally, the experimental results show that, Compared with the traditional pid control method, the position tracking effect of the present invention has higher steady-state precision and smaller tracking displacement phase lag.
- uncertainties in the hydraulic system eg, unknown friction effects, variable parameters, etc.
- unknown nonlinear problems such as spool dead zone, external disturbances
- the degree of control displacement hysteresis is basically unchanged, the tracking error always converges within the specified boundary, and the amplitude is basically not attenuated.
- the displacement tracking error of the pid algorithm is larger, and the control algorithm of the present invention can still ensure that the tracking error converges within the specified boundary, the degree after the phase is small, and the amplitude is basically not attenuated.
- Fig. 1 is a kind of low-complexity control method flow chart for the asymmetric servo hydraulic position tracking system of the present invention:
- Figure 2 is a model block diagram of a servo hydraulic system with a single rod
- Figure 3(a) is the structure composition diagram I of the experimental platform
- Figure 3(b) is the structural composition diagram II of the experimental platform
- Figure 3(c) is the structural composition diagram III of the experimental platform
- Figure 3(d) is the structural composition diagram IV of the experimental platform
- Fig. 4 is the error convergence simulation curve graph under the action of the controller of the present invention.
- Fig. 5 is the simulation curve diagram of tracking error convergence under disturbance action
- Fig. 6 is the simulation curve diagram of error convergence under the action of unknown spool dead zone
- Fig. 7 is a simulation curve diagram of spool displacement under the action of unknown spool dead zone
- FIG. 8 is a simulation graph showing the comparison of error convergence between the control method of the present invention and the adaptive backstepping control mode (SPPFBSA) with unknown dead zone of the spool that satisfies the specified performance;
- SPPFBSA adaptive backstepping control mode
- Fig. 9 is a statistical diagram of control method of the present invention and SPPFBSA simulation calculation time and error adjustment time;
- FIG. 1 is a flowchart of a low-complexity control method for an asymmetrical servo hydraulic position tracking system of the present invention: a low-complexity control method for an asymmetrical servo-hydraulic positional tracking system, comprising the following steps: S1: establish a Servo hydraulic system model; Figure 2 is a block diagram of the servo hydraulic system model with a single output rod; S2: According to the servo hydraulic system model of a single output rod, the controller of the single output rod servo hydraulic system is designed with a low-complex control strategy; S3: According to the controller of the single-rod servo-hydraulic system and the model of the single-rod servo-hydraulic system, the stability of the single-rod servo-hydraulic system is proved.
- P s is the oil supply pressure of the hydraulic system
- P r is the oil return pressure of the hydraulic system
- C d is the flow coefficient of the orifice
- w is the area gradient of the spool valve
- ⁇ is the oil density
- x v is the spool displacement of the servo valve ;
- the indeterminate parameter leakage coefficient Ct is bounded, that is make
- the uncertain parameter leakage coefficient C e is bounded, that is, make
- the uncertain parameter oil elastic modulus ⁇ e is bounded, namely make
- the spool displacement x v of the servo valve is actually controlled by the voltage or current input u to obtain the required corresponding force.
- the dynamic characteristics of the servo valve are as follows:
- ⁇ is the time constant of the servo valve dynamics model and u(t) is the current input.
- the parameters m r and m l represent the left and right slopes of the dead zone characteristic curve, and the parameters br and b l represent the breakpoints of the input nonlinearity;
- the servo valve is a key mechanical component in the electro-hydraulic actuator.
- the current or voltage controls the displacement of the spool of the servo valve, and then controls the hydraulic oil to be drawn in or out of the oil chamber, and finally the actuator performs the corresponding movement; obviously, in the servo valve
- In the hydraulic position tracking system there must be a nonlinear problem of the dead zone of the spool. Therefore, it is necessary to consider the adverse effects of this problem to obtain better system performance; in addition, considering that it is difficult to obtain an accurate slope of the dead zone model in practical applications and interval points, so a robust and strong novel control strategy is proposed to solve this problem;
- ⁇ 1 , ⁇ 2 , ⁇ 3 are the virtual control quantities obtained in the subsequent proof process
- x 1r is the command signal of the hydraulic position tracking system
- z 1 is the position tracking error
- four positive smooth decreasing functions is selected as the specified performance function
- the virtual control function is selected as follows:
- the controller of the servo hydraulic system is:
- the virtual controller and the controller of the servo hydraulic system can ensure that the closed-loop signal is bounded as follows:
- V 1 V 01 + A 1 x
- V 2 V 02 -A 2 x
- h 1 h 2 h 3 bounded, that is, there are three positive numbers respectively.
- ⁇ :R+ ⁇ ⁇ ⁇ R n is a continuous function vector
- ⁇ ⁇ ⁇ R n is a non-empty open set
- Definition 1 A solution ⁇ (t) of the initial value problem (50), without proper right extension, the solution is the largest;
- the initial value theorem is as follows: For the initial value problem (12), if ⁇ (t, ⁇ ) satisfies: (1) when t>0, ⁇ (t, ⁇ ) satisfies the local Lipschitz condition for ⁇ ; (2) for ⁇ (t) ⁇ ⁇ , ⁇ (t, ⁇ ) is piecewise continuous; (3) For ⁇ (t) ⁇ ⁇ , ⁇ (t, ⁇ ) is locally integrable with respect to t; then in the time period t ⁇ [ 0, ⁇ max ), there is a solution to the initial value problem (50) ⁇ (t) ⁇ ⁇ , where ⁇ max >0.
- the initial value proposal is as follows: Assuming the initial value theorem holds; for the maximum solution ⁇ (t) on the time period [0, ⁇ max ) and the set When ⁇ max ⁇ , there exists a time constant t 1 ⁇ [0, ⁇ max ) such that
- the experimental platform is built, and the experimental software program is debugged.
- the experimental platform is mainly divided into two parts: software design and hardware circuit connection;
- Fig. 3 (a) is the structural composition diagram I of the experimental platform;
- Fig. 3(b) is the structural composition of the experimental platform II;
- Fig. 3(c) is the structural composition of the experimental platform III;
- Fig. 3(d) is the structural composition of the experimental platform IV;
- the hardware of the experimental platform is mainly divided into three parts, the first part is
- the actuator mainly includes a hydraulic source system (such as accumulator, hydraulic pump, etc.), a servo valve and a single-rod hydraulic cylinder actuator.
- the experimental platform of the present invention adopts a three-position five-way servo valve, and its model is FD234-01K004VSX2A .
- the second part is the signal acquisition mechanism.
- the hardware of the signal acquisition mechanism is mainly the signal conversion board and the A/D board.
- the function of the signal conversion board is to convert the voltage and current signals to each other. Specifically, the sensor signal 4-20ma current signal is converted into 1-5v voltage signal, convert the voltage signal of ⁇ 5v to the current signal of ⁇ 10ma, the A/D board used in the experiment platform of the present invention is ADT882, its function is to realize the mutual conversion of analog continuous signal and digital discrete signal .
- the third part is the control mechanism.
- the core of the control mechanism is the industrial control computer.
- the experimental platform of the present invention adopts the industrial computer pc104, and its function realizes the construction of the software platform and the realization of the control algorithm.
- the hardware line connection mainly refers to the connection between each sensor signal line and the servo valve control current signal line and the signal conversion board, and the connection between the signal conversion board and the ADT882 board.
- the software design environment is VC++6.0, window operating system, the software program mainly includes writing interface functions, configuring A/D board, setting interrupt program to complete signal acquisition, control quantity calculation and output;
- the initial value of the boundary ⁇ i0 should be as large as possible, the upper bound of the error convergence rate hi should be as small as possible, and the upper bound of the steady-state residual set of the convergence error should be as large as possible;
- the second step adjust the virtual control rate gains k 1 , k 2 , k 3 , k 4 , when the control rate gain ki is adjusted to an appropriate value;
- the third step slowly and appropriately reduce the initial value of the boundary ⁇ i0 , increase the upper bound hi of the error convergence rate, and reduce the steady-state residual error of the convergence error Set the upper bound value ⁇ i ⁇ until the desired control effect is achieved.
- Fig. 4 is the simulation curve diagram of error convergence under the action of the controller of the present invention, as can be seen from Fig. 4, the controller of the present invention can ensure the convergence speed and control accuracy of the displacement tracking error;
- the controller of the present invention has a strong inhibitory effect on strong disturbances, and can still ensure the transient and steady-state performance of the convergence error.
- Figure 6 is the simulation curve of error convergence under the action of unknown spool dead zone
- Figure 7 is the simulation curve of spool displacement under the action of unknown spool dead zone
- Figures 6 and 7 verify the low-complexity control scheme proposed in this paper It has better robustness to deal with unknown spool dead zone problem.
- the unknown dead zone nonlinearity of the valve core is added to the system model.
- Fig. 8 is a comparative simulation graph of error convergence between the control method of the present invention and the adaptive backstepping control method (SPPFBSA) with unknown dead zone of the spool that meets the specified performance
- Fig. 9 is the simulation calculation time and error of the control method of the present invention and SPPFBSA Adjustment time statistics chart; it can be seen from Figure 8 that both controllers can ensure the convergence speed and steady-state accuracy of the displacement tracking error, but as can be seen from Figure 9, in the simulation running time, the controller of the present invention and Compared with the SPPFBSA controller, it is reduced by 91.7%, and the error convergence adjustment time is reduced by 95.5%. Because the controller design of the invention has low dependence on the model, compared with the algorithm developed on the basis of backstepping self-adaptation, the calculation amount is small, and online learning is not required, so it is convenient for real-time control and engineering realization.
- the displacement tracking curve obtained by the controller of the present invention has almost only a small phase lag during the upward process of the cylinder, Compared with the ascending process of the cylinder block, when the cylinder block descends, the phase lag degree of the displacement tracking curve is larger, but the control effect of the controller of the present invention is in the whole process of the displacement tracking, the displacement tracking curve is higher than the pid displacement tracking curve. The degree of phase lag is small.
- the control effect of the controller of the present invention is that the phase lag degree is basically unchanged during the cylinder body ascending process, and the phase lag degree is getting smaller and smaller during the cylinder body descending process, and the amplitude is basically not attenuated.
- the pid tracking error becomes larger and larger, while the tracking error of the controller of the present invention is basically unchanged and converges within the specified performance boundary.
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Abstract
一种针对非对称伺服液压位置跟踪***的低复杂控制方法,该方法包括以下步骤:建立单出杆的伺服液压***模型(步骤1);根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器(步骤2);根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性(步骤3)。该方法可以解决液压***中存在的各种不确定性问题和未知的非线性问题,控制器的设计不依赖精确的数学模型,只需要能够测量的状态信号。
Description
本发明涉及伺服液压位置控制领域,尤其涉及一种针对非对称伺服液压位置跟踪***的低复杂控制方法。
伺服液压***具有出色的负载效率,较小的功率比,响应速度快等优点,因此,在现代工业中,它们被广泛应用(例如主动悬挂***,液压挖掘机,机械手)。伺服液压***包括两种液压执行机构,双出杆对称液压执行机构和单出杆非对称液压执行机构。在主动悬挂控制研究中常常将两个油腔面积视为相等,使用对称液压执行机构。对于非对称伺服液压***,由于活塞杆的存在导致液压缸的有杆腔和无杆腔的有效面积不等,能够实现相同性能的对称液压执行机构往往比非对称液压执行机构体积要大,一般应用于少数特殊场合,工业上广泛应用的则是非对称液压执行机构。因此,在空间局限性很大的汽车悬挂***中放置对称液压执行机构是不合理的。
然而,非对称伺服液压***是一个复杂的非线性***,同时它涉及了各种各样的不确定性,例如,负载变化,参数不确定以及未知的非线性,这将导致建立模型和设计控制器的困难性和复杂性,因此,对于非对称伺服液压***,高精度的位置控制正在面临巨大的挑战。其中,参数不确定主要包括泄露系数,油膜粘度和粘滞摩擦系数,未知的非线性主要包括阀芯死区和外部扰动,这些因素阻碍了高性能控制器的发展。为了满足位置跟踪***的操作性能,在过去的十几年里已经发展了许多控制技术,例如神经网络自适应,模糊逻辑控制,鲁棒自适应控制,反步自适应控制。在这些控制方式中,自适应控制,由于它的在线学习能力,可以处理参数不确定问题,鲁棒自适应控制可以处理未知扰动问题。尽管上述基于自适应控制的算法可以获得很好的仿真结果,但是,一个关键的问题是,这些算法具有沉重的计算负担,需要很长时间才能达到收敛,所以,在液压***中,应用基于自适应的上述控制算法是困难的。此外,伺服液压***现有的控制方法大多数是在反步控制的基础上进行开发的。众所周知,在高阶***的反步设计过程中,由于虚拟控制函数反复求导,将导致计算***问题。因此,寻找设计对***依赖程度低,计算负担轻的,没有函数逼近功能的新颖的控制策略是很有必要的。
另外,在伺服液压位置跟踪***中,从实际的应用角度来看,上述方法中如果存在潜在的不好的瞬态响应(超调过大,收敛缓慢),这将可能导致跟踪性能恶化,发生危险甚至造成硬件的损坏。Bechlioulis CP,Rovithakis GA等人最初提出了能够保证跟踪误差瞬态性能的新颖的控制器设计方法。该方法通过引入规定性能函数,规定跟踪误差瞬态和稳态性能,通过引入误差变换,将原始的带有限制的***等效成没有限制的***。这个思想进一步的被应用到高阶非线性容错控制***,液压伺服***,悬架***。然而,使用规定性能函数的上述文献中,控制方案都与自适应控制方式相结合处理***中未知动力学问题。
综上所述,伺服液压***及其位置控制方法存在以下不足之处:一、单出杆非线性伺服液压***是一种典型的复杂非线性***,它涉及了负载变化,参数不确定以及未知的 非线性等问题,以至于建立理论模型与实际***之间存在巨大差距,导致设计控制器的困难性和复杂性;二、目前存在的伺服液压位置控制方式大多数是在反步控制自适应基础上进行开发的,然而这些控制方式对模型的依赖程度较高,并且在高阶***的反步设计过程中,会产生较大的计算量,对不确定参数的在线学习,不利于实际试验中实时控制;三、从实际的应用角度来看,在伺服液压位置跟踪***中,如果存在潜在的不好的瞬态响应(超调过大,收敛缓慢),这将可能导致跟踪性能恶化,发生危险甚至造成硬件的损坏。
发明内容
根据现有技术存在的问题,本发明公开了一种针对非对称伺服液压位置跟踪***的低复杂控制方法,包括以下步骤:S1:建立单出杆的伺服液压***模型;S2:根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器;S3:根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性。
进一步地,其特征还在于:所述建立单出杆的伺服液压***模型表达式的过程如下:根据牛顿第二定律建立液压缸体的动力学模型:
其中:f(t)表示各种干扰,x和m分别表示负载的位置和质量,B是粘性阻尼系数,K是负载的等效弹簧刚度,当负载是惯性负载时,K=0,F=A
1*P
1-A
2*P
2是液压作动器输出的主动力,其中P
1,P
2是液压缸大小腔压力,A
1,A
2是大小腔活塞的有效面积;采用三位五通伺服阀,负载压力动力学通过如下公式表示:
式中:V
1,V
2分别为有杆腔和无杆腔容积,V
1=V
01+A
1x,V
2=V
02-A
2x,V
01和V
02分别为活塞处于初始位置时,无杆腔和有杆腔容积,C
t为液压缸内部的泄露系数,C
e为液压缸的外泄露系数。β
e为油液弹性模量;Q
1是有杆腔液压油流量,Q
2是无杆腔液压油流量;
P
s为液压***供油压力,P
r为液压***回油压力,C
d为节流口的流量系数,w是滑阀面积梯度,ρ是油液密度,x
v是伺服阀的阀芯;通过电压或电流输入u来控制伺服阀的阀芯位移x
v,进而获得所需要的对应的力,伺服阀的动态特性如下所示:
τ是伺服阀动力学模型的时间常数,u(t)是电流输入;考虑了存在未知死区的阀芯位移Γ(x
v),其表达式如下:
参数m
r和m
l代表死区特性曲线的左右斜率,参数b
r和b
l代表输入非线性的断点;阀芯死区表示为Γ(x
v)=m(t)x
v+d(t),m(t),d(t)表达式如下所示:
由于m
r,m
l,b
r,b
l有界,故d(t)有界,记d(t)上界为
定义状态变量如下:x
1=x,
x
3=P
1,x
4=P
2,x
5=x
v,获得具有未知阀芯死区位置跟踪***的状态方程如下:
进一步地:所述根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器的过程如下:定义误差变量:
z
1=x
1-x
r z
2=x
2-α
1 z
3=F-α
2 z
4=x
5-α
3 (17)
其中,α
1,α
2,α
3是虚拟控制量,x
1r是液压位置跟踪***的指令信号,F(F=A
1x
3-A
2x
4)是作动器输出的主动力,z
1是位置跟踪误差,z
i i=2...4是控制误差,四个正的光滑递减函数
选做规定性能函数,定义标准化误差ζ
i,对z
i i=1...4做误差转换,转换后的误差
如下:
选取虚拟控制器如下:
伺服液压***的控制器为:
进一步地,所述根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性的过程如下:S3-1:利用初值定理,证明标准化误差向量在时间段t∈[0,τ
max)时,在非空开集合Ω
ζ中存在最大解;S3-2:当标准化误差向量在时间段t∈[0,τ
max)上,在非空开集合Ω
ζ中存在最大解时,虚拟控制器以及伺服液压***的控制器,对于t∈[0,τ
max)能保证闭环信号有界;S3-3:利用初值提议证明当S3-2中的τ
max=+∞时,所有闭环信号有界仍是正确的。
进一步地,所述利用初值定理,证明标准化误差向量在时间段t∈[0,τ
max)时,在非空开集合Ω
ζ中存在最大解:非空的开集合Ω
ζ,选择性能函数ρ
i时,满足:ρ
i(0)>min{δ
-i,δ
-
i}|z
i(0)|,i=1...4由此可得:|ζ
i(0)|<min{δ
-i,δ
-
i},i=1...4,因此,标准化误差向量ζ(0)∈Ω
ζ;由于期望的追踪轨迹x
r,性能函数ρ
i(t),i=1...4,中间控制信号α
i,i=1...3和控制率u是连续光滑可导的,阀芯死区位置跟踪***的状态方程中的动力学变量是连续可导的函数,故式标准化误差向量中函数L(t,ζ)关于时间t是分段连续的,且在开集合Ω
ζ中,ζ满足利普希茨条件;初值定理中的条件都满足,所以在时间段[0,τ
max)中,标准化误差向量存在唯一的最大解ζ(t)∈Ω
ζ,对于
都能保证ζ
i(t)∈Ω
ζ,i=1...4。
进一步地,所述当标准化误差向量在时间段t∈[0,τ
max)上,在非空开集合Ω
ζ中存在最大解时,虚拟控制器以及伺服液压***的控制器,对于t∈[0,τ
max)能保证闭环信号有界的的过程如下:S3-2-1:根据式(18)求出
对时间的导数
△
1(t)=r
1k
1 (32)
(33)和(34)符合不等式引理形式,由不等式引理可知,因为a
1有界,即
|a
1|<A
1,0<△
1(t)<r
M1k
1,所以
因为
有界,可得-δ
-1ρ
1(t)<z
1<δ
-
1ρ
1(t),所以对于
跟踪误差z
1在规定的边界内衰减;保证在时间段t∈[0,τ
max)跟踪误差z
1在规定性能边界中收敛,因为指令是有界正弦信号,所以状态变量x
1是有界的;
进一步可得:
(38)和(39)符合不等式引理形式,由不等式引理可知,因为a
2有界即
使得|a
2|<A
2,
所以
由于
有界,可得-δ
-2ρ
2(t)<z
2<δ
-
2ρ
2(t),所以对于
保证控制误差z
2有界和状态变量x
2有界;
将式(10),(24),(11)和(21)带入(40)中得:
其中V
1=V
01+A
1x,V
2=V
02-A
2x;
(43)和(44)符合不等式引理形式,由不等式引理可知,因为a
3有界,即
使得|a
3|<A
3,
所以
由于
有界,可得-δ
-3ρ
3(t)<z
3<δ
-
3ρ
3(t),所以对于
保证控制误差z
3有界和主动力u
a有界,从状态方程的数学表达式上看,状态变量x
3和x
4是有界的,并且它们都小于液压源P
s的压力值;
(48)和(49)符合不等式引理形式,由不等式引理可知,因为a
4有界,即
使得|a
4|<A
4,
所以
由于
有界,可得-δ
-4ρ
4(t)<z
4<δ
-
4ρ
4(t),所以对于
保证控制误差z
4有界和状态变量x
5有界。
进一步地,所述利用初值提议证明当S3-2中的τ
max=+∞时,所有闭环信号有界仍是正确的过程如下:
假设τ
max<+∞,初值提议中强调存在一个时间常数t
1∈[0,τ
max)使得
造成矛盾,得出的假设是τ
max=+∞,对于任何t∈[0,+∞),所有闭环***信号是有界的,并且能够保证跟踪误差在规定边界内收敛。
由于采用了上述技术方案,本发明提供的一种针对非对称伺服液压位置跟踪***的低复杂控制方法,可以解决液压***中存在的各种不确定性问题(如,未知的摩擦效应,参数不确定以及负载变化)和未知的非线性问题(例如阀芯死区,外部扰动),控制器的设计不依赖精确的数学模型,只需要能够测量的状态信号,控制率的计算与现有的在反步自适应基础上开发的算法相比,计算过程简单,计算量很小,便于实时控制,更加容易工程实现;本发明可以保证跟踪误差的收敛速度和稳态精度;最后,实验结果表明,本发明的位置跟踪效果与传统的pid控制方法相比,稳态精度更高,跟踪位移相位滞后程度更小。当期望轨迹信号频率提高时,pid算法控制得到的实际跟踪位移相位滞后程度越大,幅值衰减越厉害,位移跟踪误差越大,本发明的控制算法在期望轨迹信号频率提高时,得到的实际控制位移滞后程度基本不变,跟踪误差始终在规定边界内收敛,幅值基本没有衰减。当期望信号频率不变,幅值变大时,pid算法的位移跟踪误差越大,本发明控制算法,仍然可以保证跟踪误差在规定边界内收敛,相位之后程度很小,幅值基本没有衰减。
为了更清楚地说明本申请实施例或现有技术中的技术方案,下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图仅仅是本申请中记载的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。
图1是本发明一种针对非对称伺服液压位置跟踪***的低复杂控制方法流程图:
图2是单出杆的伺服液压***模型框图;
图3(a)是实验平台结构组成图Ⅰ;
图3(b)是实验平台结构组成图Ⅱ;
图3(c)是实验平台结构组成图Ⅲ;
图3(d)是实验平台结构组成图Ⅳ;
图4是本发明控制器作用下的误差收敛仿真曲线图;
图5是扰动作用下的跟踪误差收敛仿真曲线图;
图6是具有未知阀芯死区作用下的误差收敛仿真曲线图;
图7是具有未知阀芯死区作用下的阀芯位移仿真曲线图;
图8是本发明控制方法与满足规定性能的具有阀芯未知死区的自适应反步控制方式(SPPFBSA)的误差收敛对比仿真曲线图;
图9是本发明控制方法与SPPFBSA仿真计算时间与误差调节时间统计图;
图10是指令信号为TS=3s:x
r=100sin((2*pi*t)/3)mm,本发明控制方法与pid对比位移跟踪实验图;
图11是指令信号为TS=3s:x
r=100sin((2*pi*t)/3)mm,本发明控制方法的跟踪误差实验图;
图12是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;
图13是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法的跟踪误差实验图;
图14是指令信号为TS=1s:x
r=50sin(2*pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;
图15是指令信号为TS=1s:x
r=50sin(2*pi*t)mm,本发明控制方法的跟踪误差实验图;
图16是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;
图17是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法的跟踪误差实验图;
图18是指令信号为TS=2s:x
r=80sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;
图19是指令信号为TS=2s:x
r=80sin(pi*t)mm,本发明控制方法的跟踪误差实验图;
图20是指令信号为TS=2s:x
r=60sin(pi*t)mm,本发明控制方法与pid对比位移 跟踪实验图;
图21是指令信号为TS=2s:x
r=60sin(pi*t)mm,本发明控制方法的跟踪误差实验图。
为使本发明的技术方案和优点更加清楚,下面结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚完整的描述:
下面结合附图对本发明具体实施方式做进一步说明:
图1是本发明一种针对非对称伺服液压位置跟踪***的低复杂控制方法流程图:一种针对非对称伺服液压位置跟踪***的低复杂控制方法,包括以下步骤:S1:建立单出杆的伺服液压***模型;图2是单出杆的伺服液压***模型框图;S2:根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器;S3:根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性。
所述建立单出杆的伺服液压***模型表达式的过程如下:
首先,根据牛顿第二定律建立液压缸体的动力学模型:
力学方程(1)中额外项f(t)表示各种干扰(例如,未建模的摩擦效应,未建模的动力学,外部扰动等),x和m分别表示负载的位置和质量,B是粘性阻尼系数,K是负载的等效弹簧刚度,负载主要是惯性负载,因此,K=0;F=A
1*P
1-A
2*P
2是液压作动器输出的主动力,其中P
1,P
2是液压缸大小腔压力,可以利用压力传感器测量出来,A
1,A
2是大小腔活塞的有效面积。
式中V
1,V
2分别为有杆腔和无杆腔容积(V
1=V
01+A
1x,V
2=V
02-A
2x),V
01和V
02分别为活塞处于初始位置时,无杆腔和有杆腔容积,C
t为液压缸内部的泄露系数,C
e为液压缸的外泄露系数,β
e为油液弹性模量,Q
1是无杆腔供(回)油流量,Q
2是有杆腔回(供)油流量,Q
1和Q
2计算公式如下:
P
s为液压***供油压力,P
r为液压***回油压力,C
d为节流口的流量系数,w是滑阀面积梯度,ρ是油液密度,x
v是伺服阀的阀芯位移;
在液压作动器操作中,实际是通过电压或电流输入u来控制伺服阀的阀芯位移x
v,进而获得所需要的对应的力,伺服阀的动态特性如下所示:
τ是伺服阀动力学模型的时间常数,u(t)是电流输入。
本文考虑了存在未知死区的阀芯位移Γ(x
v),其表达式如下:
参数m
r和m
l代表死区特性曲线的左右斜率,参数b
r和b
l代表输入非线性的断点;
假设3:参数m
r,m
l,b
r,b
l是未知的正数且m
r=m
l,在本文中,斜率上界是m
max,b
r的上界是
b
l的上界是
阀芯死区可以表示为Γ(x
v)=m(t)x
v+d(t),
m(t),
d(
t)表达式如下所示:
众所周知,伺服阀在电液执行器中是关键的机械部件,电流或电压控制伺服阀的阀芯位移,进而控制油腔抽入或抽出液压油,最后执行器执行相应的运动;显然,在伺服液压位置跟踪***中必然存在阀芯死区非线性的问题,因此,有必要考虑这种问题的不利影响以获得更好的***性能;此外,考虑到实际应用中难以获得死区模型精确的斜率以及间隔点,因此提出了一种鲁棒很强的新颖控制策略来解决这一问题;
所述根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器的过程如下:定义误差变量:
z
1=x
1-x
r z
2=x
2-α
1 z
3=F-α
2 z
4=x
5-α
3 (17)
其中,α
1,α
2,α
3是后续证明过程中获得的虚拟控制量,x
1r是液压位置跟踪***的指令信号,F(F=A
1x
3-A
2x
4)是作动器输出的主动力;z
1是位置跟踪误差,z
i i=2...4是控制误差;为了解决跟踪误差的瞬态和稳态问题且顺利选取虚拟控制量,四个正的光滑递减函数
被选做规定性能函数;定义标准化误差ζ
i,对z
i i=1...4做误差转换,转换后的误差
如下:
选取虚拟控制函数如下:
伺服液压***的控制器为:
进一步地,所述根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性的过程如下:S3-1:利用初值定理,证明标准化误差向量在时间段t∈[0,τ
max)时,在非空开集合Ω
ζ中存在最大解;S3-2:当标准化误差向量在时间段t∈[0,τ
max)上,在非空开集合Ω
ζ中存在最大解时,虚拟控制器以及伺服液压***的控制器,对于t∈[0,τ
max)能保证闭环信号有界;S3-3:利用初值提议证明当S3-2中的τ
max=+∞时,所有闭环信号有界仍是正确的。为了顺利完成控制器稳定性证明,提出一项引理,并且证明该引理的正确性;
证明:
基于位置误差,误差变量(17)与标准化误差ζ
i(18)的关系,x
1,x
2,F,x
5可以重新写成:x
1=ζ
1ρ
1+x
r x
2=ζ
2ρ
2+α
1 F=ζ
3ρ
3+α
2 x
5=ζ
4ρ
4+α
3 (24)
对(18)中的ζ
i(i=1...4)直接求导,可以得到:
通过定义标准化误差向量ζ=[ζ
1,ζ
2,ζ
3,ζ
4]
T,(25)-(28)能够写成如下形式:
进一步地,利用初值定理,证明标准化误差向量在时间段t∈[0,τ
max)时,在非空开 集合Ω
ζ中存在最大解的过程如下:Ω
ζ是非空的开集合,选择性能函数ρ
i时满足ρ
i(0)>min{δ
-i,δ
-
i}|z
i(0)|,i=1...4由此可以推导出|ζ
i(0)|<min{δ
-i,δ
-
i},i=1...4,因此,对于式(29)ζ(0)∈Ω
ζ;此外,由于期望的追踪轨迹x
r,性能函数ρ
i(t),i=1...4,中间控制信号α
i,i=1...3和控制率u是连续光滑可导的,阀芯死区位置跟踪***的状态方程中的动力学变量是连续可导的函数,故式标准化误差向量中函数L(t,ζ)关于时间t是分段连续的,且在开集合Ω
ζ中,ζ满足利普希茨条件;不等式引理中的条件都满足,所以在时间段[0,τ
max)中,标准化误差向量存在唯一的最大解ζ(t)∈Ω
ζ,对于
都能保证ζ
i(t)∈Ω
ζ,i=1...4;
进一步地,所述当标准化误差向量在时间段t∈[0,τ
max)上,在非空开集合Ω
ζ中存在最大解时,虚拟控制器以及伺服液压***的控制器,对于t∈[0,τ
max)能保证闭环信号有界的过程如下:
将式(10),(24)和(19)带入(30)中得:
选取李雅普诺夫函数:
(33)和(34)符合不等式引理形式,由不等式引理可知,因为a
1有界(
|a
1|<A
1),0<△
1(t)<r
M1k
1,所以
因为
有界,由(13)和(14)可得-δ
-1ρ
1(t)<z
1<δ
-
1ρ
1(t),所以对于
跟踪误差z
1在规定的边界内衰减;所以能够保证在时间段t∈[0,τ
max)跟踪误差z
1在规定性能边界中收敛,因为指令是有界正弦信号,所以状态变量x
1是有界的;S3-2-2:根据式(18)求出
对时间的导数
(38)和(39)符合不等式引理形式,由不等式引理可知,因为a
2有界
使得|a
2|<A
2,
所以
由于
有界,由(13)和(14)可得-δ
-2ρ
2(t)<z
2<δ
-
2ρ
2(t),所以对于
能够保证控制误差z
2有界和状态变量x
2有界;
记:△
3(t)=r
3m(t)k
3h
1 (42)
其中:
其中:V
1=V
01+ A
1x,V
2=V
02-A
2x;在实际问题中,考虑作动器的安全运行,留出安全裕度(即根据物理结构,液压缸在中位附近上下最大可波动12厘米,所给指令信号,一般不超过10厘米。),这样我们可以保证h
1h
2h
3有界,即分别存在三个正数
使得
考虑到
且α
1,
ρ
i是有界的,m(t)为阀芯死区的未知斜率,m(t)是有界的(即
),由极值定理可知a
3有界;由(41)和(42)得:
(43)和(44)符合不等式引理形式,由不等式引理可知,因为a
3有界
使得|a
3|<A
3,
所以
由于
有界,由(13)和(14)可得-δ
-3ρ
3(t)<z
3<δ
-
3ρ
3(t),所以对于
能够保证控制误差z
3有界和主动力u
a有界,从数学模型中H
1和H
2的数学表达式上看,状态变量x
3和x
4是有界的,并且它们都小于液压源P
s的压力值;
将式(10),(24)和(22)带入(45)中得:
记:
(48)和(49)符合不等式引理形式,由不等式引理可知,因为a
4有界
使得| a
4|<A
4,
所以
由于
有界,由(13)和(14)可得-δ
-4ρ
4(t)<z
4<δ
-
4ρ
4(t),所以对于
我们能够保证控制误差z
4有界和状态变量x
5有界。
进一步地,所述利用初值提议证明当S3-2中的τ
max=+∞时,所有闭环信号有界仍是正确的过程如下:从上证明中可知,
是有界的,即
从式(23)可知
这是非空集合;很明显
因此,假设τ
max<+∞,初值提议中强调存在一个时间常数t
1∈[0,τ
max)使得
很明显造成矛盾。所以我们得出正确的假设是τ
max=+∞,因此,对于任何t∈[0,+∞),所有闭环***信号是有界的,并且能够保证跟踪误差在规定边界内收敛。
考虑初始值问题:ζ(t)=ν(t,ζ),ζ(0)=ζ
0∈Ω
ζ (50)
其中ν:R+×Ω
ζ→R
n是连续函数向量,并且Ω
ζ∈R
n是非空的开集合。
定义1:初值问题(50)的一个解ζ(t),没有适当的右扩展,则该解最大;
初值定理如下:对于初值问题(12),如果ν(t,ζ)满足:(1)在t>0时,关于ζ,ν(t,ζ)满足局部Lipschitz条件;(2)对于ζ(t)∈Ω
ζ,ν(t,ζ)满足分段连续;(3)对于ζ(t)∈Ω
ζ,ν(t,ζ)关于t满足局部可积;那么在时间段t∈[0,τ
max)上,初值问题(50)存在一个解ζ(t)∈Ω
ζ,其中τ
max>0。初值提议如下:假设初值定理成立;对在时间段[0,τ
max)上的最大解ζ(t)并且集合
当τ
max<∞时,存在时间常数t
1∈[0,τ
max),使得
为了验证本发明控制器设计的正确性,搭建实验平台,进行实验软件程序调试,搭建实验平台主要分为软件设计和硬件线路连接两部分;图3(a)是实验平台结构组成图Ⅰ;图3(b)是实验平台结构组成图Ⅱ;图3(c)是实验平台结构组成图Ⅲ;图3(d)是实验平台结构组成图Ⅳ;实验平台的硬件主要分成三部分,第一部分是执行机构,主要包括液压源***(如蓄能器,液压泵等),伺服阀和单出杆的液压缸作动器,本发明实验平台采用三位五通伺服阀,其型号为FD234-01K004VSX2A。第二部分是信号采集机构,信号采集机构硬件主要是信号转换板和A/D板卡,信号转换板的功能是电压电流信号相互转换,具体来说,将传感器信号4-20ma电流信号转换成1-5v电压信号,将±5v的电压信号转换到±10ma的电流信号,本发明实验平台采用的A/D板卡是ADT882,其功能是实现模拟量连续信号与数字量离散信号的相互转换。第三部分是控制机构,控制机构的核心是工业控制计算机,本发明实验平台采用工控机pc104,其功能实现软件平台的搭建以及控制算法的实现。硬件线路连接主要 指,各个传感器信号线以及伺服阀控制电流信号线与信号转换板的连接,信号转换板与ADT882板卡的连接。软件设计环境是VC++6.0,window操作***,软件程序主要包括编写界面函数,配置A/D板卡,设置中断程序完成信号采集,控制量计算以及输出;
进一步地,调试实验,优化参数,直到实验结果达到预期的控制效果;第一步:调节本发明算法中规定边界的边界初值ρ
i0,误差收敛速率的上界h
i以及收敛误差稳态残差集上界值ρ
i∞,其中i=1...4。边界初值ρ
i0尽量大,误差收敛速率上界h
i尽量小,收敛误差稳态残差集上界值ρ
i∞尽量大;第二步:调节虚拟控制率增益k
1,k
2,k
3,k
4,当控制率增益k
i调到合适值后;第三步:慢慢适当缩小边界初值ρ
i0,增大误差收敛速率的上界h
i,减小收敛误差稳态残差集上界值ρ
i∞,直到达到预期的控制效果。
图4是本发明控制器作用下的误差收敛仿真曲线图,从图4中可以看出,本发明控制器可以保证位移跟踪误差的收敛速度和控制精度;图5是扰动作用下的跟踪误差收敛仿真曲线图;图5所示***模型在强扰动f(t)=9000sin(10t)作用下的本发明控制器与反步控制器位移跟踪误差对比曲线,从图4和图5对比可以看出,强扰动的存在对反步控制器的控制效果影响很大,使得位移跟踪误差增大,波动频率变高。然而,从图4和图5中也可以看出,本发明控制器对强扰动具有很强的抑制作用,仍可以保证收敛误差的瞬态和稳态性能。
图6是具有未知阀芯死区作用下的误差收敛仿真曲线图;图7是具有未知阀芯死区作用下的阀芯位移仿真曲线图;图6和图7验证本文提出的低复杂控制方案处理未知阀芯死区问题具有更好的鲁棒性。在***模型中加入阀芯未知死区非线性,为了更好的体现出阀芯死区的未知非线性特性,本文采用时变的死区模型斜率m(t)=1+0.3sin(2t),时变死区模型的间断点bl=br=0.3|sin(2t)|,从图7中可以看出,本发明控制器可以有效的补偿阀芯未知死区的不利影响,从图6中可以看出,***即使存在未知的阀芯死区问题,本发明控制器仍能很好的保证跟踪误差的收敛速度和稳态精度。
图8是本发明控制方法与满足规定性能的具有阀芯未知死区的自适应反步控制方式(SPPFBSA)的误差收敛对比仿真曲线图;图9是本发明控制方法与SPPFBSA仿真计算时间与误差调节时间统计图;从图8中可以看出两种控制器都可以保证位移跟踪误差的收敛速度和稳态精度,但是从图9中可以看出,在仿真运行时间上,本发明控制器与SPPFBSA控制器相比减少91.7%,在误差收敛调节时间上减少95.5%。由于本发明控制器设计对模型依赖程度低,与基于反步自适应基础上开发算法相比,计算量很小,并且不用在线学习,故便于实时控制,易于工程实现。
图10是指令信号为TS=3s:x
r=100sin((2*pi*t)/3)mm,本发明控制方法与pid对比位移跟踪实验图;图11是指令信号为TS=3s:x
r=100sin((2*pi*t)/3)mm,本发明控制方法的跟踪误差实验图;图12是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;图13是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法的跟踪误差实验图;图14是指令信号为TS=1s:x
r=50sin(2*pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;图15是指令信号为TS=1s:x
r=50sin(2*pi*t)mm,本发明控制方法的跟踪误差实验图;图16是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;图17是指令信号为TS=2s:x
r=100sin(pi*t)mm,本发明控制方法的跟踪误差实验图;图18是指令信号为TS=2s:x
r=80sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;图19是指令信号为TS=2s:x
r=80sin(pi*t)mm,本发明控制方 法的跟踪误差实验图;图20是指令信号为TS=2s:x
r=60sin(pi*t)mm,本发明控制方法与pid对比位移跟踪实验图;图21是指令信号为TS=2s:x
r=60sin(pi*t)mm,本发明控制方法的跟踪误差实验图;从图11,图13,图15,图17,图19和图21中可以看出,不论指令信号的频率和幅值如何变化,本发明控制器可以保证跟踪误差在规定的性能边界中收敛,因此本发明控制器可以保证跟踪误差的收敛速度和稳态精度。从图10,图12,图14,图16,图18和图20中任何一图中可以看出,本发明控制器得到的位移跟踪曲线在缸体上升过程中几乎只有很小的相位滞后,与缸体上升过程相比,在缸体下降时,位移跟踪曲线相位滞后程度较大,但是,本发明控制器的控制效果在位移跟踪的整个过程中,位移跟踪曲线都要比pid位移跟踪曲线相位滞后程度小。
综合图10-图13来看,当指令信号频率越高时,pid跟踪曲线相位滞后程度越高,幅值衰减越大。在稳态时,本发明控制器控制效果,在缸体上升过程时,相位滞后程度基本不变,在缸体下降过程中,相位滞后程度越来越小,幅值基本无衰减。当指令信号频率越高时,pid跟踪误差越来越大,而本发明控制器的跟踪误差基本不变,并且在规定的性能边界中收敛。
综合图17,图19和图21来看,当指令信号频率越高时,pid跟踪误差越来越大,而本发明控制器的跟踪误差基本不变,并且在规定的性能边界中收敛。
以上所述,仅为本发明较佳的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,根据本发明的技术方案及其发明构思加以等同替换或改变,都应涵盖在本发明的保护范围之内。
Claims (8)
- 一种针对非对称伺服液压位置跟踪***的低复杂控制方法,其特征在于:包括以下步骤:S1:建立单出杆的伺服液压***模型;S2:根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器;S3:根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性。
- 根据权利要求1所述的一种针对非对称伺服液压位置跟踪***的低复杂控制方法,其特征还在于:所述建立单出杆的伺服液压***模型表达式的过程如下:根据牛顿第二定律建立液压缸体的动力学模型:其中:f(t)表示各种干扰,x和m分别表示负载的位置和质量,B是粘性阻尼系数,K是负载的等效弹簧刚度,当负载是惯性负载时,K=0,F=A 1*P 1-A 2*P 2是液压作动器输出的主动力,其中P 1,P 2是液压缸大小腔压力,A 1,A 2是大小腔活塞的有效面积;采用三位五通伺服阀,负载压力动力学通过如下公式表示:式中:V 1,V 2分别为有杆腔和无杆腔容积,V 1=V 01+A 1x,V 2=V 02-A 2x,V 01和V 02分别为活塞处于初始位置时,无杆腔和有杆腔容积,C t为液压缸内部的泄露系数,C e为液压缸的外泄露系数,β e为油液弹性模量;Q 1是有杆腔液压油流量,Q 2是无杆腔液压油流量;P s为液压***供油压力,P r为液压***回油压力,C d为节流口的流量系数,w是滑阀面积梯度,ρ是油液密度,x v是伺服阀的阀芯;通过电压或电流输入u来控制伺服阀的阀芯位移x v,进而获得所需要的对应的力,伺服阀的动态特性如下所示:τ是伺服阀动力学模型的时间常数,u(t)是电流输入;考虑了存在未知死区的阀芯位移Γ(x v),其表达式如下:参数m r和m l代表死区特性曲线的左右斜率,参数b r和b l代表输入非线性的断点;阀芯死区表示为Γ(x v)=m(t)x v+d(t),m(t),d(t)表达式如下所示:
- 根据权利要求1所述的一种针对非对称伺服液压位置跟踪***的低复杂控制方法,其特征还在于:所述根据单出杆的伺服液压***模型,采用低复杂控制策略设计出单出杆的伺服液压***的控制器的过程如下:定义误差变量:z 1=x 1-x r z 2=x 2-α 1 z 3=F-α 2 z 4=x 5-α 3 (17)其中,α 1,α 2,α 3是虚拟控制量,x 1r是液压位置跟踪***的指令信号,F(F=A 1x 3-A 2x 4)是作动器输出的主动力,z 1是位置跟踪误差,z ii=2...4是控制误差,四个正的光滑递减函数 选做规定性能函数,定义标准化误差ζ i,对z ii=1...4做误差转换,转换后的误差 如下:选取虚拟控制器如下:
- 根据权利要求1所述的一种针对非对称伺服液压位置跟踪***的低复杂控制方法,其特征还在于:所述根据单出杆的伺服液压***的控制器及单出杆的伺服液压***模型,证明单出杆的伺服液压***的稳定性的过程如下:S3-1:利用初值定理,证明标准化误差向量在时间段t∈[0,τ max)时,在非空开集合Ω ζ中存在最大解;S3-2:当标准化误差向量在时间段t∈[0,τ max)上,在非空开集合Ω ζ中存在最大解时,虚拟控制器以及伺服液压***的控制器,对于t∈[0,τ max)能保证闭环信号有界;S3-3:利用初值提议证明当S3-2中的τ max=+∞时,所有闭环信号有界仍是正确的。
- 根据权利要求4所述的一种针对非对称伺服液压位置跟踪***的低复杂控制方法,其特征还在于:所述利用初值定理,证明标准化误差向量在时间段t∈[0,τ max)时,在非空开集合Ω ζ中存在最大解:非空的开集合Ω ζ,选择性能函数ρ i时,满足:ρ i(0)>min{δ -i,δ - i}|z i(0)|,i=1...4由此可得:|ζ i(0)|<min{δ -i,δ - i},i=1...4,因此,标准化误差向量ζ(0)∈Ω ζ;由于期望的追踪轨迹x r,性能函数ρ i(t),i=1...4,中间控制信号α i,i=1...3和控制率u是连续光滑可导的,阀芯死区位置跟踪***的状态方程中的动力学变量是连续可导的函数,故式标准化误差向量中函数L(t,ζ)关于时间t是分段连续的,且在开集合Ω ζ中,ζ满足利普希茨条件;初值定理中的条件都满足,所以在时间段[0,τ max)中,标准化误差向量存在唯一的最大解ζ(t)∈Ω ζ,对于 都能保证ζ i(t)∈Ω ζ,i=1...4。
- 根据权利要求4所述的一种针对非对称伺服液压位置跟踪***的低复杂控制方法,其特征还在于:所述当标准化误差向量在时间段t∈[0,τ max)上,在非空开集合Ω ζ中存在最大解时,虚拟控制器以及伺服液压***的控制器,对于t∈[0,τ max)能保证闭环信号有界的的过程如下:进一步可得:△ 1(t)=r 1k 1(32)由(31)和(32)得:(33)和(34)符合不等式引理形式,由不等式引理可知,因为a 1有界,即 |a 1|<A 1,0<△ 1(t)<r M1k 1,所以 因为 有界,可得-δ -1ρ 1(t)<z 1<δ - 1ρ 1(t),所以对于 跟踪误差z 1在规定的边界内衰减;保证在时间段t∈[0,τ max)跟踪误差z 1在规定性能边界中收敛,因为指令是有界正弦信号,所以状态变量x 1是有界的;进一步可得:由(36)和(37)得:(38)和(39)符合不等式引理形式,由不等式引理可知,因为a 2有界即 使得|a 2|<A 2, 所以 由于 有界,可得-δ -2ρ 2(t)<z 2<δ - 2ρ 2(t),所以对于 保证控制误差z 2有界和状态变量x 2有界;将式(10),(24),(11)和(21)带入(40)中得:其中V 1=V 01+A 1x,V 2=V 02-A 2x;(43)和(44)符合不等式引理形式,由不等式引理可知,因为a 3有界,即 使得|a 3|<A 3, 所以 由于 有界,可得- δ -3ρ 3(t)<z 3<δ - 3ρ 3(t),所以对于 保证控制误差z 3有界和主动力u a有界,从状态方程的数学表达式上看,状态变量x 3和x 4是有界的,并且它们都小于液压源P s的压力值;进一步得:
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