1IMPLEMENTATION OF HYDRAULICSERVO CONTROLLERS WITH ONLYPOSITION MEASUREAbstractHydraulic actuators have nonlinear dynamics and are often used in environments (robotic, aerospace, underwater explo-rations/inspections, mining) where uncertain disturbances are present. Linear controllers designed using a linearized model of the hydraulic system are widespread. In alternative, nonlinear and ro-bust control techniques can be used to achieve better performances. Among these techniques, sliding mode control with dynamics inversion is a good choice, but it usually requires measurements of actuator’s velocity and hydraulic pressures in addition to actu-ator’s position. This paper presents the design and experimental evaluation of a position controller for an hydraulic actuator where the only available measure is the actuator’s position. A detailed description of servosystem components is firstly presented. Then a linear control law, whose design is based on a linearized model of the actuator, is designed and tested. Finally, a sliding mode control law is developed. Experimental results, carried out on a real case study, have shown the ectiveness of the proposed controllers even when only actuator’s position is available for feedback.Key Words :Hydraulic actuators nonlinear systems nonlinear control system sliding mode control.21. IntroductionHydraulic actuators are used in many industrial appli-cations as they over the following advantages: ness; compactness; payload capability; high immunity to wear thanks to lubricant action of fluid; high speed of response, with fast starts, stops and speed reversals;ability to main-tain their loading capacity indefinitely, while this would usually cause excessive heat generation in electrical com-ponents [1, 2]. Furthermore, their high power-to-weight ratio allows their use in a direct-drive manner, as e.g., in industrial robots, so that wear-sensitive gear-boxes can be avoided.? DIIIE, Universit`a degli Studi di Salerno, Via Ponte Don Melillo, 1-84084, Fisciano(SA), Italy; e-mail: {fbasile, ddel-grosso}@unisa.it Recommended by Prof. Zhihua Qu (paper no. 206-3128)One of their major drawbacks is their strongly non-linear behaviour. The main nonlinearities are: magnetic hysteresis in the armature of the servovalve driving the actuator, usually neglected [3, 4]; static nonlinear relation between the control input and the flow to the actuator; ori-fices tolerances (overlap/underlap), which generate dead-zones; pressure and temperature dependency of isothermal bulk modulus; asymmetry of the hydraulic cylinder [5]; friction force acting on the actuator [6]. Another ma-jor drawback is the dis culty of accurately estimating the model’s parameters, and their variations under dis erent operating conditions. Therefore, to design a servo posi-tion system for an hydraulic actuator nonlinear and robust control techniques have to be used to achieve good per-formances. Today more complex control laws, like inverse dynamics laws, are successfully used in many applications and have been recently applied also to hydraulic servosys-tems [4, 7–10]. It is important to point out that in all these works control laws are presented which rely on mea-surement of at least actuators’s position and velocity and hydraulic pressures.Figure 1. Control architecture’s overview.3The hydraulic actuator considered in this work is com-posed of a flapper-nozzle type two-stage servovalve and an asymmetric hydraulic cylinder. A servo position system has to be devised. First, an accurate model of the actu-ator has been written obtained which takes into account the main phenomena influencing its behaviour. Dynamic parameters were partly available by the supplier. To vali-date these parameters and identify the others, it was not possible to procede with open-loop experiments but it was mandatory for safety requirements to move the actuator only if closed-loop controlled. To this purpose, a discrete-time linear controller has been first designed based on a linearized model of the actuator. Then, a sliding mode con-trol law has been designed in the continuous-time domain by using a Lyapunov-based approach and implemented in discrete-time without requiring direct measurements of ve-locity and pressures. As it is commonly accepted in prac-tice [11] for control engineers the sliding mode controller designed in continuous-time domain has been implemented in the discrete-time by selecting a ciently fast sampling rate. The model uncertainties, the fact that pressures are not directly measured and frictions are not compensated,and the time delays make the chattering reduction crit-ical [11]. To avoid this undesirable phenomenon [12] a boundary layer approach has been adopted.The main contribution of this paper is to prove that low-cost robust control of hydraulic actuators is possible even if not all the required direct measurements are avail-able. In fact, the proposedcontrollers requires only direct measurement of actuator’s position.42. Experimental Setup2.1 Control ArchitectureThe hydraulic actuator taken into account in this work is a linear single-rod cylinder whose piston’s position is measured by a Linear Variable Dis erential Transformer (LVDT) sensor. The digital control architecture, shown in Fig. 1, has the following features:PowerPC CPU running at 500 MHz; The sampling rate is 500 Hz; 12 bit A/D and D/A converters; Voltage-to-current and current-to-voltage converters with a bandwidth of 10 KHz; LVDT Current Conditioningand Transmitter (LCCT) with a bandwidth of 250 Hz; A 100 Hz second-order Butterworth anti-aliasing filter; Hydraulic system (the actuator) including an LVDT sensor for position measuring. Notice that The only available measure is piston’s position; The digital implementation and the presence of limited bandwidth circuits and filters makes possible to neglect all components over 100 Hz; The presence of quantizers produces a measurement noise, in fact the measures resolution is 2.3 · 10?5 m; The actuator has to work in a wide and variable range of temperatures. 2.2 Implementation IssuesExperimental tests on the real architecture have drawn the attention to some important aspects for the design of both the linear and the robust controller.1. Time delays on feedback chain: A time delay on the feedback chain of about 6 ms has been measured which heavily influences the dynamics and must be taken into account in designing the controllers.2. Noise in the position’s measure: The LVDT sensor’s non-ideal behaviour, joint with the presence of quan-tizers, produces a not-negligible measurement noise. Then, it is necessary to verify the filtering capacity of the controllers, to avoid vibrations of the actuator. 3. Unavailable measures: The only available measure is the actuator’s position. Thus, the proposed sliding mode controller works without the chambers’ pressure measures as commonly required. Actuator’s velocity and acceleration have instead been obtained from 5the position measure by using a derivative filter (see Fig. 2) for which the considered transfer function is: Filter’s parameters have been tuned to realize a deriva-tive behaviour up to 100 Hz without amplifying high-frequency components.Figure 2. Re-constructor filter.63. Model DescriptionThe structure of the electro-hydraulic servoactuator, com-posed of a nozzle-flapper flow control servovalve and an asymmetric hydraulic actuator, is shown in Fig. 3 where the scale factors for the valve and the actuator are erent for sake of clarity. All the symbols reported in Fig. 3 are defined in Table 1 and will be used in the model description below.Figure 3. Hydraulic servoactuator layout.3.1 Servovalve Model3.1.1 Servovalve Nonlinear ModelThe nonlinear model of the nozzle-flapper valve [1, 2] can be represented by the scheme in Fig. 4 where its main elements are shown. The input is the electrical current of the torque motor I which is transformed in a torque at the armature:As the rotation of the armature is very small, a simplified linear relation is often considered:7The equation describing the armature flapper’s dy-namics relating armature torque to flapper displacement (in case of small rotation) is:The equations describing nozzle’s flows relating flapper displacement to flows on spool’s sides are:8液壓伺服控制器的執(zhí)行位置測量摘 要液壓執(zhí)行器有非線性動力特性，并且經(jīng)常在機械，航空航天，水下檢驗環(huán)境中使用，檢測其中的不確定干擾存在。線性控制器的設(shè)計普遍采用線性模型的液壓系統(tǒng)。如果使用非線性和魯棒控制技術(shù)作為替代可以實現(xiàn)更好的性能。在這些技術(shù)中，采用動態(tài)逆滑?？刂剖且粋€很好的選擇，但它通常需要除了實際位置的測量還需要執(zhí)行器的速度和液壓壓力測量。本文提出的是一個液壓制動器的位置控制器設(shè)計的實驗。一個詳細說明的伺服系統(tǒng)組件首先被提出。然后，是基于線性模型的執(zhí)行機構(gòu)的線性控制法的設(shè)計和測試。最后，研制了一種滑?？刂坡伞嶒灲Y(jié)果，在一個真實的案例研究，證明所提出控制器即使當(dāng)只有致作動器的位置是可用于反饋的時候依然有效。關(guān)鍵詞 ： 液壓作動器 非線性系統(tǒng) 非線性控制系統(tǒng) 滑模控制9第一章 介紹液壓執(zhí)行器有許多工業(yè)應(yīng)用因為以下優(yōu)點：剛性，緊湊性，載荷能力，由于液體流動的高抗磨損性；響應(yīng)速度快，具有快速啟動，停止和速度逆轉(zhuǎn)；保持無限容量裝載的能力，但這通常會導(dǎo)致電氣部件過熱。此外，他們的高功率重量比允許他們使用直接驅(qū)動的方式，例如，在工業(yè)機器人中，這樣可以避免磨損敏感的齒輪箱。其主要缺點之一是其強烈的非線性行為。主要的非線性是：伺服閥驅(qū)動致動器電樞中的磁滯，這經(jīng)常被忽視；在輸入控制和執(zhí)行器流動中的靜態(tài)非線性關(guān)系；產(chǎn)生死區(qū)的孔公差；壓力和等溫體積彈性模量的溫度依賴性；液壓缸的不對稱；作用在致動器摩擦力。另一個主要的缺點是難以準(zhǔn)確估計模型的參數(shù)和不同試驗條件下的變化的參數(shù)。因此，為了為液壓致動器技術(shù)的非線性設(shè)計一個伺服位置系統(tǒng)，需要應(yīng)用魯棒控制技術(shù)以獲得更好的性能。今天，更復(fù)雜的控制規(guī)律，如逆動力學(xué)規(guī)律，成功地應(yīng)用在許多應(yīng)用程序并且最近也適用于液壓伺服系統(tǒng)。需要指出的是，在所有這些工作的控制律的提出依靠執(zhí)行器位置和液壓壓力的測量。這項工作中的液壓執(zhí)行機構(gòu)是由噴嘴擋板式二級電液伺服閥和非對稱液壓缸組成。一個伺服位置系統(tǒng)必須設(shè)計。首先，已經(jīng)提到執(zhí)行器的精確模型需要考慮到那些影響其性能的主要現(xiàn)象。一部分動態(tài)參數(shù)可從供應(yīng)商獲得。為了驗證這些參數(shù)并確定其他參數(shù)，進行開環(huán)試驗是不可能的，安全需求當(dāng)閉環(huán)控制去移動執(zhí)行器是強制性的。為了這個目的，基于線性模型的執(zhí)行器首先設(shè)計出了一個離散時間線性控制器。然后，一個滑動模式控制法已被設(shè)計在連續(xù)時間域通過使用一個 Lyapunov 為基礎(chǔ)的方法，在離散時間實現(xiàn)而不需要速度和壓力的直接測量。通過選擇一個快速采樣率，在連續(xù)時間域設(shè)計的控制工程師的滑動模式控制器在離散時間實施的設(shè)計在實踐中普遍被接受。模型的不確定性，事實上，壓力并不是直接測量和摩擦沒有補償，并且時間的延遲使抖振臨界降低。為了避免這種不良現(xiàn)象，采納邊界層的方法。10圖 1 控制架構(gòu)的概述第二章 實驗設(shè)置2.1 控制結(jié)構(gòu)這項工作中的液壓執(zhí)行機構(gòu)是一個線性單桿缸，線性單桿缸活塞的位置由一個線性可變地微分變壓器（LVDT）傳感器測量。數(shù)字控制結(jié)構(gòu)，有以下特點：?powerpc CPU 運行在 500 MHz；?采樣率是 500 Hz；?12 位 A / D 和 D / A 轉(zhuǎn)換器；?10 kHz 帶寬的電壓 -電流和電流- 電壓轉(zhuǎn)換器；?250Hz 帶寬的電流調(diào)節(jié)和發(fā)射機；?100Hz 的二階巴特沃斯抗混疊濾波器；?液壓系統(tǒng)包括一個 LVDT 傳感器的位置測量注意?唯一的變量是活塞的位置；?數(shù)字實現(xiàn)和有限的帶寬的電路存在和過濾器可以忽略所有組件在 100 赫茲；?量化器產(chǎn)生的測量噪聲的存在，事實上，測量分辨率為 2.3 · 10?5米；?執(zhí)行器在一個廣泛的和可變的溫度范圍內(nèi)工作。2.2 實施問題關(guān)于真實結(jié)構(gòu)實驗測試，注意一些重要的關(guān)于線性和魯棒控制器的設(shè)計方面問題1.時間延遲反饋鏈：一個約 6 毫秒的已嚴(yán)重影響動態(tài)的時間反饋鏈延遲被檢測出測量，而且這是設(shè)計控制器必須考慮的問題。2.位置測量的噪聲：LVDT 傳感器的非理想特性，與量化器的連接處，產(chǎn)生一個不可忽略的測量噪聲。然后，為了避免致動器的振動，驗證控制器的過濾能力是很重要的。3.不變量測量：可用的唯一變量是執(zhí)行器的位置。因此，建議的滑動模式控制器在沒有腔內(nèi)壓力作為一般工作條件進行工作。執(zhí)行機構(gòu)的速度和加速度通過使用微分濾波11器測量得到，這種方式定義為傳遞函數(shù)：濾波器的參數(shù)在沒有放大高頻組件的情況下已經(jīng)實現(xiàn)導(dǎo)數(shù)的行為上升到 100 赫茲第三章 模型描述電液伺服執(zhí)行器的結(jié)構(gòu)，由一個噴嘴擋板式流量控制閥和一個非對稱液壓作動器，如圖 3 所示。圖中閥門和執(zhí)行器為了看得清楚，調(diào)大了比例。所有的符號在圖 3 報告表1 所示，將用下面的模型描述：圖 3 液壓伺服作動器布局3.1 伺服閥模型3.1.1 伺服閥的非線性模型噴嘴擋板閥的非線性模型可以表示在圖 4 中，其主要內(nèi)容是所示的方案。輸入的轉(zhuǎn)矩電動機我這電流轉(zhuǎn)化成扭矩在電樞：當(dāng)電樞旋轉(zhuǎn)是非常小的，通常被認為是一個簡化的線性關(guān)系：12電樞擋板的動力學(xué)與電樞轉(zhuǎn)矩擋板位移方程（在小角度旋轉(zhuǎn)的情況下）是：噴嘴的流量與擋板位移對閥芯的側(cè)流方程：