Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems

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1 Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems Hong Zhao and Pinhas Ben-Tzvi International Journal of Control, Automation and Systems 4(6 (6 5-5 ISSN: (print version eissn:5-49 (electronic version To link to this article:

2 International Journal of Control, Automation and Systems 4(6 ( ISSN: eissn: Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems Hong Zhao and Pinhas Ben-Tzvi* Abstract: Pneumatic systems have been widely used in industrial applications because of their well-known advantages. However, pneumatic systems possess several disadvantages that include strong non-linearity and low natural frequency. These drawbacks make it difficult to obtain satisfactory control performances in comparison to hydraulic and electromechanical systems. In this paper, the fundamental characteristics and nonlinear synchronous control strategy of pneumatic systems are studied. A two-layer sliding mode synchro-system based on friction compensation is applied to electro-pneumatic cylinders and a synchro-pid controller is utilized for position tracking. To validate the developed strategy, experiments with bi-cylinder electro-pneumatic systems were performed. The experimental results demonstrate that the synchronous position control scheme is effective in terms of accuracy and robustness. Keywords: Friction compensation, pneumatic servo system, sliding mode control, synchro-pid controller.. INTRODUCTION With the development of aerospace technologies and modern machine manufacturing, pneumatic actuators have been widely used in numerous engineering areas. The advantages of pneumatic actuators include clean operation and easy serviceability. In most cases, their application is limited to point to point control. The disadvantages of the pneumatic system mainly include air compressibility, strong non-linearity and large mechanical friction. These drawbacks restrict their applications in servo-controlled systems. More effort has been dedicated to improving this research field. Numerous researchers focused their efforts on studying different aspects of pneumatic servo systems, such as air flow, thermodynamics, linear and non-linear dynamics, valve modelling and friction modelling [, ]. Due to high friction in pneumatic systems [3], disturbances lead to system uncertainties. This is usually considered to be the main problem in pneumatic control. In recent years, the development of pneumatic systems and the improvement of control theories has led to the implementation of modern control laws in pneumatic devices [4 ]. Sliding mode control has been used as a robust nonlinear control technique in many applications requiring insensitivity to parametric uncertainty [ 4]. Over the last decade, multi-surface sliding mode control received a lot of attention [5 9], mainly due to the advantages this tool presents, from higher accuracy and the possibility of using continuous control laws, to the possibility of utilizing the Coulomb friction model in control algorithms [] and the finite time convergence for systems with arbitrary relative degrees []. However, new requirements in the performance of pneumatic systems are continually being proposed. The need for motion synchronization between multiple pneumatic actuators for lifting and rolling applications has been the focus of the research efforts [, 3]. In order to eliminate the synchro error and improve the control performance with one air source - especially reducing the effects of static friction - a bi-cylinder controller design is proposed. In this paper, the electropneumatic motion synchronization servo control system with one air source is introduced, and the fundamental characteristics and the nonlinear control strategy of the pneumatic system are studied. A bi-cylinder controller is adopted for the control of the electro-pneumatic synchro position system, and the effectiveness of the proposed technique is demonstrated through simulations and experiments. Manuscript received November 6, 4; revised June 8, 5 and November 3, 5; accepted December 7, 5. Recommended by Associate Editor Won-jong Kim under the direction of Editor Hyouk Ryeol Choi. This work was in part supported by the National Natural Science Foundation of China (Grant No Hong Zhao is with the College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 49, China ( hzhao_cn@63.com. Pinhas Ben-Tzvi is with the Department of Mechanical Engineering and the Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 46, USA ( bentzvi@vt.edu. * Corresponding author. c ICROS, KIEE and Springer 6

3 5 Hong Zhao and Pinhas Ben-Tzvi. SYSTEM DESCRIPTION.. Configuration of the electro-pneumatic position synchro servo control system The proposed servo control system consists of two rodless pneumatic cylinders controlled by two proportional directional valves as shown in Figs. (a and (b. The experimental sampling rate is.5 KHz. The main components of the system are as follows:two Festo electro-pneumatic five-port proportional valves: MPYE-5-/4-B; maximum flow rate 4 l/min, operating voltage DC 4 V, voltage variant: - V, Nominal width 8mm; Two rodless pneumatic cylinders with 6 mm stroke length: DGP- 4-6-PPV-A-B; One air source: maximum pressure.6 MPa, maximum flow rate 5 l/min; Four pressure sensors: PT35-.6MPa-.3, resolution.3%; Two position sensors: MLO-POT-6-TLF, resolution. mm; Mass load A (5.75 kg and B (5.85 kg are mounted on sliding parts, which are connected to the pistons of cylinders A and B, respectively. External forces of 7 N and 34 N are applied to cylinder A to simulate external load disturbances... Computer software The pneumatic control software that we developed for the purpose of this study was the key component in obtaining experimental results. It includes the human-machine interface built in LabWindows/CVI [4], the control algorithm as well as the data processing routines. control algorithm as well as the data processing routines. Displacement sensor A/D Pressure sensor Displacement sensor A/D Pressure sensor Proportional directional control Valve Computer D/A D/A (a Mass Load B Mass load A Pressure sensor A/D Cylinder B Cylinder A Proportional directional control Valve A/D Weight Pressure sensor 3. MATHEMATICAL MODEL 3.. Subsystem (with cylinder A A nonlinear state-space model of the system is derived based on a single cylinder pneumatic model from reference [5], as follows: ẋ = ẋ = x, ( ẋ = A p (p x p x F f F, ( M M M ẋ 3 = ṗ x = krc d C R /T [ ( ( ] A s (u f px A e (u p x f pe p x V + A pl + A p x ka p p x x V + A, (3 pl + A p x ẋ 4 = ṗ x = krc d C R /T [ ( ( ] A s (u f px A e (u p x f pe p x V + A pl A p x ka p p x x + V + A. (4 pl A p x Definitions for other parameters are provided in the nomenclature. (b Fig.. (a Scheme of the experimental system, (b photos of the experimental setup. 3.. Subsystem (with cylinder B ż = ż = z, (5 ż = A p (p z p z F f F, (6 M M M ż 3 = ṗ z = krc d C R /T [ ( ( ] A s (u f pz A e (u p f pe p z V + A pl + A p z ka p p z z V + A, (7 pl + A p z ż 4 = ṗ z = krc d C R /T [ ( ( ] A s (u f pz A e (u p z f pe p z V + A pl A p z ka p p y z + V + A, (8 pl A p z

4 Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems 53 where, f ( pd p u = ( k + k + / k k ( pd / ( k pd p u p u k + / k / / if p atm pu (p d pu C r / if C r (p d pu <. A s, A s, A e and A e are the valve geometric orifice area function, and they are the nonlinear functions of u [] (u-valve input opening size.due to the complexity of the equations, the following linear functions are used for approximation: Fig.. Open-looystem response to a position step input. Fig.. Open-looystem response to a position step input. F f A s (u i = πdu i, (9 A s (u i = πdδ = A f, ( A e (u i = πdδ = A f, ( A e (u i = πdu i, ( v d F s F d k v d k v where, δ is the valve s clearance, A f is valve s leakage measurement, D is the piston s valve diameter, cylinder A system, i = for cylinder B system. k4 k3 F d F s 3.3. Friction model of the system Friction has an accentuated influence on the step or tracking tasks, mainly when the piston velocity is small. From the experimental position step-input response shown in Fig., the dithering effect at the end of the piston stroke is observed. Friction forces are the main factor that affects the performance of the pneumatic servo system controller. Those forces are mainly generated by contact between the piston seals and the cylinder walls. This nonlinear effect becomes even more dominant at lower sliding velocities. Typically, friction forces in the cylinder include static and dynamic components. Stribeck model [5] is one of the widely used friction models, but for our experimental application, we simplified the switching process between the Coulomb static friction and the Coulomb dynamic friction. The chosen model is shown in Fig. 3. When v >, F f = F s k v for v < v d, F f = F s F d + k v for v v d, (3 where v d is the velocity cut-off point. When v<, the rest can be deduced by analogy. From experimental tests on the pneumatic cylinders, the friction parameters were estimated and summarized in Table. Fig. 3. Simplified friction force model. Table. Friction parameters summary. Cylinder k k 4 F d (N F d (N F s (N F s (N A B CONTROL DESIGN STRATEGY The block diagram of the proposed controller is shown in Fig. 4. It consists of two cylinder controllers, and a synchro PID controller. Each of the cylinder controllers includes a second order sliding mode controller and a friction compensator. The synchro PID controller coordinates the operation of the two cylinder controllers and improves the synchro motion control of the cylinders. The bi-cylinder synchro controller is required to maintain the displacement error between subsystems and to less than a specified tolerance, keeping their corresponding displacement values to approximately the same. This requirement can be expressed mathematically as follows: max x(t z(t e t t [a,b], (4 where e t is the permitted position tolerance (it is chosen to eliminate the large error in position tracking, x(t is

5 54 Hong Zhao and Pinhas Ben-Tzvi the real position of cylinder A, z(t is the real position of cylinder B, and [a,b] is the time domain. Let e sy = x(t z(t, t [a,b]. The synchro PID controller is given by: K sy e sy + K sy e sy dt u ad = de sy +K sy3 dt, e sy <, e sy, K sy e sy + K sy e sy dt u ad = de sy +K sy3, e sy > dt, e sy. (5a (5b As the synchro PID controllers are made to adjust the difference between two cylinder s displacements, u ad is added in cylinder A control signal and u ad is added to cylinder B s control signal. Whene sy = x(t z(t <, cylinder A should be adjusted to keep up with cylinder B s displacement and u ad should be positive and u ad is zero. When e sy = x(t z(t >, cylinder B should be adjusted to keep up with cylinder A s displacement and u ad should be positive and u ad is zero. In order to adjust the parameters of the synchro PID controller, the integral absolute error (IAE performance minimization measure is considered. The synchro PID controller s parameters are set as follows: K sy =, K sy =.5, K sy3 =.. Based on the mathematical model presented in the previous section, it is clear that pressure functions in the pneumatic cylinder are nonlinear; hence the pressure drop is taken as the sliding mode layers. The bi-layer sliding mode control strategy with friction compensation is proposed in order to overcome friction disturbances in the cylinders. Inner pressure loop control enhances the speed of the system response and attenuates fluctuations in the pressure, hence improving the system tracking accuracy. The control approach is developed as follows. 4.. Control rule in cylinder A For the purpose of controller design, if the nonlinear pneumatic model is rewritten in the affine function form with (-(4, we can get ẋ = x ẋ = p A p K f x F kcsgn(x (6a M M ṗ = (ṗ x ṗ x = f (x + g (x u, From (6a, ẋ = A x + B p + q, ṗ = (ṗ x ṗ x = f (x + g (x u (6b (6c control approach is developed as follows. yd d/dt d/dt Friction compensation Two-layer sliding mode controller Two-layer sliding mode controller Friction compensation ua ub xv xv u uad uad Cylinder A plant Synchro PID controller Synchro PID controller u Cylinder B plant Fig. 4. Block diagram of the integrated control strategy for the bi-cylinder actuator. [ with x = [x, x ] T, A = K f [ ] M q = F kcsgn(x, M esy ] [, B = Ap M ka p ẋp x f (x = V + A pl + A p x ka p ẋp x V + A pl A p x ( krc dc A f p x f ( p e R / p x T V + A pl + A p x + A f f ( p x V + A pl A p x g (x = krc dc πd R / T (, f ( p x V + A pl + A p x p x f ( p e p + x V + A. pl A p x It should be noted that the ccontrollability of the plant is proven using (6b and the controllability matrix. p x, p x cannot be in excess of the range between the supply pressure and the exhaust pressure p e, therefore the function f (... is always positive and g does exist. The maximum value of g satisfies max g gm. Generally, the static friction force F kc sgn(x cannot be measured accurately but it is assumed that the maximum value of static friction is known. Since x d and p d are bounded, q in (6b can be treated as a bounded uncertainty. The simplified diagram for pressure drop is shown in Fig. 5. Let the inner loop tracking error be e p = p p d x z ],

6 Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems 55 For the outer loop (position loop, p d is chosen to make the function (ẍ ÿ d + ξ (ẋ ẏ d + ξ (x y d =. (8 Fig. 5. The block diagram of the single cylinder system with simplified pressure control strategy. and choose the control input u f l as follows: u f l = g (x ( f (x + ṗ d k ep ( p p d. (7 Then we can get ṗ = ṗ d k ep ( p p d. (8 A simplified control approach can be adopted by making p p d as x y d. For the inner loop (pressure loop, k is chosen to make the function ė p + k ep e p. (9 Then p p d. Let s define the sliding surface by σ = p p d. Then: σ = ṗ ṗ d = f + g u ṗ d. ( If the Lyapunov function is chosen to be V lya =.5σ, then V lya = σ σ. To ensure that V lya = σ σ is a negative-definite function, we choose the control law u s. When σ < and σ > u σ > g f g ṗ d When σ > and σ <. ( u σ < g ( f ṗ d. ( However, by the triangle inequality g f + g ṗ d > g ( f ṗ d. (3 Then g f + g m α > g ( f ṗ d. Therefore, the system can be stabilized by means of control law { g f + g m α, σ < u σ = ( (4 g f + g m α, σ >, and and u σ = κ sgn(σ, κ >, (5 V lya = σ σ <, (6 u cy = u f l κ sgnσ. (7 The control objective is to obtain the state X in order to track a desired state Y d = (y d,ẏ d,ÿ d, in the presence of model uncertainties and unknown disturbances. p = M A p ẍ + A p (K f ẋ + F kc sgn(ẋ. (9 From (8, we get ẍ = ÿ d ξ ė ξ e, where e = x y d. The above control law is based on the exact cylinder friction model. This means that there are no other disturbances on the friction factors K f andf kc. In fact, p d should be modified to improve the robustness of the system. Therefore, a pseudo control input w is added in order to eliminate the changing effects of the friction factors. The expression for p d then becomes and p d = M A p [ÿ d ξ (ẋ ẏ d ξ (x y d ] + A p ( K f ẋ + F kc sgnẋ + M w + k ėp, (3 p p d = M A p (ë + ξ ė + ξ e + A p ( K f ẋ + F kc sgn(ẋ M w k ėp. (3 External force F is eliminated from equation (3 since this controller is insensitive to external force disturbances. For p p d, equation (3 becomes: ë + ξ ė + ξ e + M ( K f ẋ + F kc sgnẋ w =, (3 where K f = K f K f and F kc = F kc F kc are the friction factors differences, and K f and F kc are the exact friction factors. The second sliding surface is chosen ase = x y d. Choosing the sliding mode then s = ė + c e = (ẋ ẏ d + c (x y d,c >, (33 ṡ = ë + c ė = (ẍ ÿ d + c (ẋ ẏ d = A ẋ + B ṗ + q ÿ d c ẋ c ẏ d, ṡ = (A c I(A x + B p + q + B ( f + g u + q ÿ d c ẏ d. (34

7 56 Hong Zhao and Pinhas Ben-Tzvi Let the Lyapunov function be V lya = s, then V lya = s ṡ. When s < and ṡ >, u s > B g [(A c I(A x + B p + q +B f + q ẍ d c ẋ d ]. (35 When s > and ṡ <, u s < B g [(A c I(A x + B p + q +B f + q ẍ d c ẋ d ]. (36 and So u s = ε sgn(s, (37 V lya = s ṡ <. (38 Finally, the variable structure control is u cy = w ε sgn(s,ε >. (39 Combining functions (7 and (39 into one control function, the integrated control law becomes u a = u f l + w κ sgnσ ε sgn(s, κ >, ε >, (4 where K f is the coefficient of viscous friction; F kc is Coulomb friction in cylinder A; σ and s are the first layer of sliding mode and synthetic sliding mode in cylinder A, respectively. 4.. Control rule in cylinder B The second layer of the sliding surface is: s = ė + c e, c >. (4 The control rule is: u b = u f l + w κ sgnσ ε sgn(s, κ >, ε >, (4 where e = z y d. Parameter definitions in this section are similar to the previous sections for cylinder A with the only difference that subscript in this section pertains to cylinder B Friction compensation As mentioned in Table, the maximum static friction is 89. N. When the pressure in the cylinder is below. MPa, the force is 5. N and as such friction cannot be neglected. Therefore, this friction needs to be compensated, and the adopted compensation rule was chosen as follows: { e > e x v = d and u, u >, (43 e e d or u, u =, where e d is the error tolerance; u, u are the control value before friction compensation; =., =.4 are the friction compensation values. 5. EXPERIMENTAL RESULTS 5.. Fundamental performance analysis of the pneumatic position synchro system Experiments were conducted to thoroughly study the performance of the pneumatic synchro system control. Experimental results for an open-looystem response to a step input are shown in Figs., 6, 7, and 8. Fig. shows the displacement response of each piston moving from the initial position ( [mm] to the final position of 6 [mm]. The chamber diameter is 4 [mm], and the supply pressure is set to.6 [MPa]. Fig. 6 shows the pressure in each cylinder. Fig. 7 shows the displacement of each piston moving from the final to the initial position. Fig. 8 shows the pressure variations in each cylinder. It can be seen from Figs., 6, 7, and 8 that air compressibility introduces time delay in the piston response. Figs. and 7 show that the two cylinders are operating under two different pressures. The cylinder with the lower pressure exhibited more delay in the response and was affected by dithering at the end of the stroke from [mm] to 6 [mm]. One reason is due to the friction in the cylinders and the other may be attributed to the structure of the cylinder. The inlet and outlet of the rodless pneumatic cylinders are located on the same side. Because air must flow through a long outlet hole in the cylinder, the resistance is relatively larger and hence the flow is not smooth. According to Fig. 7, when the pistons displace from 6 [mm] to [mm], the outlet hole becomes the inlet hole, and hence pressure dithering is no longer produced. But because the two cylinders operate under one common air source, the pressure in each cylinder is practically not the same. The pressure in cylinder B is lower than that of cylinder A. Therefore, chattering is produced in the chamber of cylinder B as shown in Fig. 8(b. The static friction and dynamic friction in the cylinder and air compressibility made the left chamber in the cylinder show the chattering phenomenon, especially in cylinder B. The pressure of the left chamber is low and below a certain value. If the pressure in the left chamber of cylinder B is estimated as.5 MPa, the force in the left chamber becomes 88.4 N and the maximum static friction is 75.5 N. The static friction and dynamic friction affect the piston displacement and the pressure in the chamber becomes oscillatory. The load masses, friction, leakage and other effects in both cylinders A and B are not completely identical. In addition, pneumatic systems have the inherent disadvantage of strong nonlinearity and low natural frequency. For all these reasons, it is usually difficult to obtain satisfactory synchro control performances using traditional control methods. 5.. Performance of PID controller in tracking Fig. 9 shows the experimental results with an ideal sinusoidal displacement input y d (t = [3 + sin

8 Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems 57 6 (a Pressure in Cylinder A. p [kpa] (a Pressure in Cylinder A. - Right Chamber - Left Chamber 5 (b Pressure in Cylinder B. p [kpa] (b Pressure in Cylinder B. - Right Chamber - Left Chamber Fig. 6. Pressure in cylinders A and B. x,z[mm] Cylinder B - Cylinder A Fig. 8. Pressure in cylinders A and B from the other direction. x,z[mm] z Ideal input x 5 5 Fig. 7. Open-looystem response to a step input from the other direction t[sec] Fig. 9. Tracking synchro control with PID controller..5 (.34t] [mm] and two displacement output responses x, z, for cylinders A and B, respectively. The system is controlled using a classical PID controller with the following control parameters: For cylinder A: k p = 6, k i =.5, k d =.; and for cylinder B; k p = 7, k i =.4, k d =.5. It is clear from Fig. 9 that the response curves are distorted and fail to track the sinusoidal input due to nonlinear friction effects. The experimental results show that the displacement synchro relative error between cylinder A and cylinder B is 5% Simulation of the synchronous control strategy In order to compare the proposed controller with the PID controller, the response simulation is performed. Fig. shows the simulation results with an ideal sinusoidal displacement input y d (t = [.sin(.34t] [mm] and two displacement output responses x, z, for cylinders A and x,z [m] Displacement simulation in cylinder A Displacement simulation in cylinder B The ideal input Fig.. Tracking synchro control with the proposed controller. B, respectively. From Fig., the proposed controller shows better performances in synchro-tracking. The sliding mode control signal is shown in Fig. and the total control signal is shown in Fig..

9 sliding mode signal [V] 58 Hong Zhao and Pinhas Ben-Tzvi 3 -Displacement response of cylinder A -Displacement response of cylinder B x,z[mm] Fig.. The proposed sliding model signal. Time/s.5 Fig. 3.The response of the synchro control without external force Fig. 3. The response of the synchro control without external force using the proposed control strategy. control signal[v] t[sec] Fig.. The proposed control signal. x,z,e [mm] Displacement response of cylinder A - Displacement response of cylinder B 3-The ideal input 4-The Synchro error between cylinder A and B Experimental performance of the proposed synchronous control strategy Fig. 3 shows the experimental results of the displacement output of cylinders A and B performed under different displacement inputs. In this experiment, we used the synchronous control strategy and two-layer sliding mode control with feedback linearization based on friction compensation as proposed earlier. No external load was applied to cylinder A. Fig. shows the step response (with 3 [mm] steize, with maximum relative synchro error of 3%. Fig. 4 shows the experimental results for the synchro tracking sinusoidal displacement curve without an external force. For the ideal displacement input y d (t = [3 + sin(.34t] [mm], the maximum relative synchro error was 5%. The ideal displacement input is labeled as number 3 in Figs Since the cylinder stroke is 6 mm, it is straightforward to choose the tracking of the sinusoidal displacement from the middle of the cylinder. The input signal frequency was based on the fact that typically pneumatic system s frequency is low. The system s response to step and sinusoidal signal and the choice of the signal s excitation frequency was based on what other researchers usually studied in analysis of single cylinder systems. Fig. 5 shows the synchro tracking results with the Fig. 4. Tracking of the synchro control without external force using the new control strategy. x, z, e [mm] Displacement response of cylinder A -Displacement response of cylinder B 3- The Ideal input 4-The synchro error between cylinder A and B Fig. 5. Tracking of synchro control with 7 N external force. N external force applied to cylinder A, for which the maximum relative synchro error was 5%. The results show that the control strategy possesses certain robustness to external disturbances. Fig. 6 shows the synchro tracking results with the 34 N external force applied to cylinder

10 Synchronous Position Control Strategy for Bi-cylinder Electro-pneumatic Systems 59 x,z,e [mm] Displacement response of cylinder A -Displacement response of cylinder B 3-The ideal input 4-The Synchro error between cylinder A and B Fig. 6. The tracking of synchro control with 34 N external force. A, for which the maximum relative synchro error was 8%. According to the experimental results, the proposed control strategy performed much better compared to the PID controller. The synchro error was reduced and the control accuracy was enhanced. 6. CONCLUSION In this paper, the system model was developed using both theoretical and experimental methods. A synchronous position control strategy was proposed to achieve good position tracking performances in the presence of load disturbances and system uncertainties. Since electro-pneumatic systems are highly nonlinear especially at low velocities a bi-cylinder sliding mode controller was used to eliminate chattering in the cylinder and improve the system robustness. Experimental results showed the controller s insensitivity to external disturbances and ability to reduce the synchro position error. This technique can be readily applied to bi-cylinder systems by choosing suitable PID parameters for the synchro PID controllers. As condition limits, the proposed control strategy only used two cylinders with one air source. Since in many industrial applications there is only one air source for many cylinders, the nonlinearity resulting from low pressure makes the control condition more serious in terms of air compressibility and friction effects. Future work will study the performance of multi-cylinder systems with low pressure conditions. A p u M M x x NOMENCLATURE - Piston area - Valve input opening size - Mass load of cylinder A - Mass load of cylinder B - Piston output displacement of cylinder A - Piston output displacement of cylinder A x - Piston output velocity of cylinder A p x (x 3 - Left chamber pressure of the cylinder A p x (x 4 - Right chamber pressure of the cylinder A z - Piston output displacement of cylinder B z - Piston output displacement of cylinder B z - Piston output velocity of cylinder B p z (z 3 - Left chamber pressure of the cylinder B p z (z 4 - Right chamber pressure of the cylinder B - Supply pressure p e - Exhaust pressure P d - Downstream pressure P u - Upstream pressure P atm - Atmospheric pressure F f - Friction force in cylinder A F - External force in cylinder A k - Specific heat k =.4 C r - Critical pressure ratio =.58 C d - Valve orifice discharge coefficient =.8 C = k ( (k+/(k k+ =.685 (constant V - Initial volumes of the chamber V - The volumes of the long hole in the cylinder L - Piston stroke R - Gas Constant [J/kg K] δ - Valve s clearance A f - Valve s leakage measure T - Absolute temperature T = 94 K F f - Friction force in cylinder B F - External force in cylinder B D - Piston of valve s diameter v d - Velocity cut-off point K f - Exact viscous friction factor - Exact Coulomb friction factor F kc REFERENCES [] S. Scavarda, A. Lellal, and E. Richard, Linear zed models for an electro pneumatic cylinder servovalve system, Proc. of the 3rd International Conference in Advanced Robotics, pp. 3-5, 987. [] M. Sorli, G. Figliolini, and S. Pastorelli, Dynamic model and experimental investigation of a pneumatic proportional pressure valve, IEEE/ASME Trans. Mechatronics, vol. 9, pp , 4. [3] J. Wang, J. D. Wang, N. Daw, Q. H. Wu, Identification of pneumatic cylinder friction parameters using genetic algorithms, IEEE/ASME Trans. Mechatronics, vol. 9, pp. - 7, 4 [4] G. M. Bone, M. Xue, and J. Flett, Position control of hybrid pneumatic-electric actuators using discrete-valued model-predictive control, Mechatronics, vol. 5, pp. -, 5. [click] [5] P. Harris, S. Nolan, and G. E. O Donnell, Energy optimisation of pneumatic actuator systems in manufacturing, Journal of Cleaner Production, vol. 7, pp , 4. [click]

11 5 Hong Zhao and Pinhas Ben-Tzvi [6] J. Li, K. Kawashima, T. Fujita, and T. Kagawa, Control design of a pneumatic cylinder with distributed model of pipelines, Precision Engineering, vol. 37, no. 4, pp , 3. [click] [7] B. S. Park and S. J. Yoo, Adaptive leader-follower formation control of mobile robots with unknown skidding and slipping effects, International Journal of Control, Automation and Systems, vol. 3, no. 3, pp , 5. [click] [8] Z. Qiu, B. Wang, X. Zhang, and J. Han, Direct adaptive fuzzy control of a translating piezoelectric flexible manipulator driven by a pneumatic rodless cylinder, Mechanical Systems and Signal Processing, vol. 36, no., pp.9-36, 3. [click] [9] J. K. Lee, Y. H. Choi, and J. B. Park, Sliding mode tracking control of mobile robots with approach angle in cartesian coordinates, International Journal of Control, Automation and Systems, vol. 3, no. 3, pp , 5. [click] [] G. M. Bone and S. Ning, Experimental comparison of position tracking control algorithms for pneumatic cylinder actuators, IEEE/ASME Trans. on Mechatronics, vol., pp , 7. [] T. Nguyen, J. Leavitt, F. Jabbari, and J. E. Bobrow, Accurate sliding-mode control of pneumatic systems using low-cost solenoid valves, IEEE/ASME Trans. Mechatronics, vol., pp. 6-9, 7. [] B. Xu, S. Abe, and N. Sakagami, Robust nonlinear controller for underwater vehicle-manipulator system, Proc. of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 7-76, 5. [3] M. Taghizadeh, A. Ghaffari, and F. Najafi, Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic Circuit, ISA Transactions, vol. 48, no. 4, pp. 5-58, 9. [4] S. Sivrioglu and K. Nonami, Sliding mode control with time-varying hyper plane for AMB systems, IEEE/ASME Trans. Mechatronics, vol. 3, no., pp. 5-59, 998. [5] L. Fridman, Singularly perturbed analysis of chattering in relay control systems, IEEE Trans. on Automatic Control, vol. 47, pp ,. [6] G. Bartolini, A. Ferrara, and E. Usai, Chattering avoidance by second order sliding-mode control, IEEE Trans. on Automatic Control, vol. 43, pp. 4-46, Feb [7] A. C. Huang and Y.C. Chen, Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties, Automatica, vol. 4, no., pp , 8. [click] [8] S. Khoo, Z. Man, and S. Zhao, Comments on adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties, Automatica, vol. 44, pp , 8. [click] [9] Y. Orlov, L. Aguilar, and J. C. Cadiou, Switched chattering control vs. backlash/friction phenomena in electrical servo-motors, Int. J. Control, vol. 76, no. 9, pp , 3. [click] [] I. Boiko, L. Fridman, and M. I. Castellanos, Analysis of second-order sliding-mode algorithms in the frequency domain, IEEE Transactions on Automatic Control, vol. 49, no. 6, pp , 4. [] K. Sato and Y. Sano, Practical and intuitive controller design method for precision positioning of a pneumatic cylinder actuator stage, Precision Engineering, vol. 38, no. 4, pp. 73-7, 4. [click] [] V. Yuriy, V. P. Yuriy, and A. A. Sergey, Computer simulation of electro-pneumatic drives for vertical motion mobile robots, Procedia Engineering, vol., pp. 3-, 5. [click] [3] F. Abry, X. Brun, M. Di Loreto, S. Sesmat, and É. Bideaux, Piston position estimation for an electro-pneumatic actuator at standstill, Control Engineering Practice, vol. 4, pp , 5. [click] [4] National Instruments; Available: lwcvi/ [5] B. Armstrong-Helouvry, Control of Machines with Friction, Kluwer Academic, Boston, 99. Hong Zhao received her Ph.D. degree from Xi an Jiaotong University, Xi an, Shannxi Province, China in 3. She is currently an Associate Professor in China University of Petroleum (Beijing. Her research interests include mechanical and electrical transmission control, virtual instrument measurement and control technology. Pinhas Ben-Tzvi received his B.S. degree (summa cum laude in mechanical engineering from the Technion Israel Institute of Technology, Israel and his M.S. and Ph.D. degrees in mechanical engineering from the University of Toronto, Canada. He is currently an Associate Professor of Mechanical Engineering and Electrical and Computer Engineering, and the founding Director of the Robotics and Mechatronics Laboratory at Virginia Tech. His current research interests include robotics and intelligent autonomous systems, human-robot interactions, mechatronics, mechanism design and system integration, dynamic systems and control, and novel sensing and actuation. Application areas are varied and range from search & rescue on rough terrain to medical diagnostics, surgery, and therapy. Dr. Ben-Tzvi is a senior member of IEEE and a member of ASME.