# Research for the clamping force control of pneumatic manipulator based on the mixed sensitivity method

## Research for the clamping force control of pneumatic manipulator based on the mixed sensitivity method

Available online at www.sciencedirect.com Procedia Engineering 00(2012) (2011) Procedia Engineering 31 1225000–000 – 1233 Procedia Engineering www...

Available online at www.sciencedirect.com

Procedia Engineering 00(2012) (2011) Procedia Engineering 31 1225000–000 – 1233

Procedia Engineering

www.elsevier.com/locate/procedia

International Conference on Advances in Computational Modeling and Simulation

Research for the clamping force control of pneumatic manipulator based on the mixed sensitivity method Peng Yi, Rui-Bo Yuan*, Wei Long, Shao-nan Ba Institute of Fluid Power Control Engineering, Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650093, China

Abstract In this paper, we analyzed uncertainty problems for the system of clamping force control on the condition that its model had been established. To oppose the uncertainty problems caused by many reasons, sensitivity method is mixed based on the control theory of H∞ and robust controller. Then, its control effects were studied by MATLAB. The simulation results showed the effectiveness of this method. They manifested that fault-tolerant, robustness and dynamic performance of the system are improved. It will be able to promote the application of pneumatic manipulator in the field of ultra-precision control.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Technology Keywords: pneumatic manipulator, uncertainty, mixed sensitivity, control of clamping force.

1. INTRODUCTION Mixed sensitivity method is one of the frequency domain design methods in H ∞ control theory. Because it can effectively take robustness and robust stability into account to a system, so it is widely used in the fields of aerospace, military engineering, constructional engineering and others. Undoubtedly, the best example for its application is used for controlling robot [1]. H∞ control method is introduced in this paper in order to research clamping force of pneumatic manipulator. The pneumatic manipulator is SISO * Corresponding author. Tel.: +86-13668732829 E-mail address: [email protected]

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system, whereas the H∞ control theory is used to solve multivariable system. If considering the existence of various uncertainties and external disturbances, using mixed sensitivity method of H∞ control theory to design its controller has very important significance in engineering or theoretical area. It makes the system not only satisfying the requirements of performance but also be good at suppressing external interference, in addition, ensuring the stability of the system. 2. THE MODEL TO CLAMPING FORCE CONTROL SYSTEM OF PNEUMATIC MANIPULATOR

Fig.1 The clamping force control system for pneumatic manipulator

1 -Drive cylinder, 2-Fingers, 3 -Pressure transducer, 4 -Electro-pneumatic proportion pressure valves, 5 -Electro-magnetic direction valve, 6 -Source gas, 7 -Controller

The clamping control system of pneumatic manipulator referred to in this paper is shown as Fig.1. When the pneumatic fingers grip object, the tactile type sensor sends feedback signal to the controller, then the controller issued a command signal to electric-pneumatic proportion pressure valve aimed to control the clamping force through connecting rod. Assuming the temperature field and pressure field are uniform in same cavity. At the same time, air pressure, atmospheric pressure and ambient temperature are stable and constant. Also, the impact to the system caused by gas inertia and gas leakage must be ignored. Regarding the relationship between clamping force and cylinder pressure as proportional system while amplifier is linear [2], finally, relevant system parameters are found out (Table 1). According to equilibrium equations, flow equations of valve and continuity equation, the transfer function diagram of clamping control system are displayed [3-5] (fig.2). Parameters

Table 1 parameters of system Definition Numerical value

Units

m

Weight of spool

0.2

Kg

R

287.1

J/(kgk)

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T K

Temperature

300

Gas constant

1.4

Ct

Gas leak coefficient

0. 255

Kp

Flow-pressure coefficient

2.067 107

m5 /(Ns)

Kx

Flow coefficient

4.15

m2 /s

K0

Elasticity coefficient

145.4

N/m

Kg

Clamping forcepressure coefficient

1.6 104

N/Mpa

A

Area of feedback end face

1.256 103

m2

kf

Amplifier coefficient

1.75

A V

K null null

Fig.2 Diagram for clamping control system of pneumatic manipulator

After replaced with the parameters, the transfer function is

F ( s) 17510  3 2 U ( s) s  127.5s  726.4s  739.2

（1）

Taking linearization into account when we have established model for system, dealing with it like this will ignore the influence arise from high frequency part. At the same time, the cylinder temperature, gas volume, friction in cylinder and so on is changing at any time. We can realize from the above that it is necessary to analyze uncertainty of the complex system. 3. UNCERTAINTY ANALYSIS OF THE SYSTEM There are existing both structural uncertainty and unstructured uncertainty in the pneumatic manipulator control system. This kind of uncertainty will directly affect the accuracy, quickness and stability of the system. Such as the changing load, working conditions and environment can easily lead to parameters change in specific circumstance. The parameters are listed in the table 1 will have an effect on the system. Not only this, each parameter has different influence on system. In this paper, the real primary parameter

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lead to parametric uncertainty are K p 、 K x . They are time-varying with the working conditions. Since K x is related to the gain of the open-loop to the system, we don’t consider that it is main changing parameter. Thus, the main parameter contained in structural uncertainty is K p [6]. Moreover, it is existing unstructured uncertainty in system because of un-modeled dynamics and low frequency perturbation. Fig.3 is bode diagram of open-loop transfer function to system when there is additive uncertainty in it. As we can see, curve1, curve2, curve3 respectively represent the additive uncertainty weight that is p1 perturbation range.

0.6 1 0.1 , which is randomly come from  , p2  , p3  s 1 s5 s  10

Fig.3 Bode diagram of open-loop transfer function to additive uncertainty system

From fig.3 we can see that dynamic performance of the system which is influenced by additive uncertainty is very different in low-frequency area. If considering other un-modeled dynamics and deterioration of functional value range for uncertainty, the control performance of system may decline more. From the analyses mentioned above, with the purpose of satisfying certain performance, controller must be properly designed to overcome the influence brought by uncertainty. 4. CONTROLLER DESIGN BASED ON MIXED SENSITIVITY METHOD 4.1. PERFORMANCE INDEX In order to meet the stability and track-able requirements as well as make the system having robustness to oppose uncertainty. Mixed sensitivity method is adopted to design controller. The performance index of robust must satisfy the relational expression is [7]

T z (s) 

WS S WT T

1 

（2）

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4.2. CONTROLLER DESIGN The actual parameters of system are shown in table 1. Assuming that K p changes indefinitely in the range of  100%, expression-1 is regarded as nominal model of the system. Low-frequency part obtain small value in order to reduce errors brought by changes in air pressure, temperature of its surroundings and friction. Meanwhile, the high-frequency part adopts low pass ratio for the purpose of removing high frequency components which are mixed in input (such as the high-frequency interference came of sensor noise or other noise. Repeatedly adjusted to determine the weighting function of sensitivity, it is

WS ( s) 

4.5( s  1.2) s5

（3）

According to the principle of selection to weighting function and combination with the specific surrounding of the system, the middle-low frequency part which has great influence on performance to the system should close to the nominal model[8-10] as far as possible. Repeatedly adjusted to determine the weighting function of fill sensitivity, it is

WT ( s) 

0.1( s  5) s  2.25

（4）

Robust control toolbox of MATLAB is used to simulate, then the results are dealt with optimal reducedorder processing, the model of controller is

K ( s) 

0.2771 s  3.479 108 s 2  15.88s  1.994 106

（5）

5. CONTROLLER’S PREFORMANCE RESEARCH 5.1. DYNAMIC CHARACTERISTICS Fig.4 is unit step response of system, curve 1 is in the situation of non-controller, curve 2 represent there have controller in system.

Fig.4 Unit step response for the system

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Curve 1 indicates that the system is stable when at non-controller situation, at the same time, its amplitude of stability is 23.7 and stable error is 0.8%, but its debug time is 4.8s so that responses of system slowly. Curve 2 shows that the design of controller ensuring system has the same stability because its debug time only 0.6s, it greatly improved the response speed of the system. Sine signal tracking response of system is shown in fig.5. Curve 1 is input of sinusoidal signal (A=1, w=4), curve 2 is tracking response to sinusoidal signal when there is non-controller in system, curve 3 represents sinusoidal signal track to the response when added controller in system.

Fig.5 Tracking response of sinusoidal signal to the system

The figure shows at non-controller situation, the phase lag of the signal is 3/4  ，amplitude descend to 62% of input, it could not track the sinusoidal signal effectively. But after added controller into it, the phase lag of the signal is only 1/50  , amplitude is 105% after the input, the tracking effect is better than the former. The analysis mentioned above indicates that this controller has a significant effect to improve response speed and tracking performance of the system. 5.2. ROBUST RESEARCH TO THE UNCERTAINTY Assuming that K p made uncertain changes in the range of 100% . Unit step response of noncontroller situation is shown in fig.6. The opposite situation is shown in fig.7. Curve 1, 2, 3 represent the amount of variation of K p is 0, +100% , 100% respectively.

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Fig.6 Unit step response for the variation of parameter uncertainty in non-controller case

Fig.7 Unit step response for the variation of parameter uncertainty in adding controller case

From fig 6 we can see that curve 1 after 4.8s of time to reach steady state, its stable amplitude at 23.1, stable error is 2.4%. Besides, curve 1 after 5.2s of time to reach steady state, stable amplitude at 23.7 and stable error of 8.5‰. Curve 3 reached the steady state at 4.6s, its stable amplitude is 24.2 and stable error is 4.3%. All the simulations above prove that parameters uncertain variation have a certain influence on the performance of system. Fig.7 shows that a controller system reaching a stable state is only 0.6s of time, it improves not only the response speed but also ensures the stable error within 2% range. So we can conclude that H∞ mixed sensitivity controller has a good robustness on the changes of parameter uncertainty and ensuring the response speed of system.

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If considering additive uncertainty existed in system, the unit step response curve can be drawn by MATLAB. Fig.8 is in non-controller situation while fig.9 is controller system. curve1, 2, 3 respectively represent randomly select additive uncertainty weights that p1 the range of perturbation area.

0.1 0.6 1 in  , p2  , p3  s  10 s 1 s5

Fig.8 Unit step response of additive uncertainty in non-controller system.

Fig.9 Unit step response of additive uncertainty in controller system

At fig.8, curve 1 after 6s of time to reach steady state, stable amplitude is 31.4 while stable error is 32.6%. Curve 2 after 6.2s of time to reach steady state, stable amplitude is 32.1 while stable error is 35.6%. Curve 3 after 6.5s of time to reach steady state, stable amplitude is 33.2 while stable error is 40.2. At fig.9, adding controller to the system ensures the stabilization time is only 0.6s and the stable error within 5% range. It manifests that H∞ mixed sensitivity controller could ensure the system improving response speed

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and having a good robustness to the additive uncertainty.

6. CONCLUSION Clamping force control system of pneumatic manipulator is uncertainty due to changes of parameters, un-modeled high-frequency or low-frequency perturbation in actual work. All of the uncertainties reduce the dynamic performance of system. To solve this problem, we adopt mixed sensitivity method which is based on H∞ control theory to design controller for the pneumatic manipulator. The research results show that the designing controller effectively clearing up impact on system which brought by structureuncertainty and unstructured-uncertainty. It has good adaptability and robustness. Reference [1] Cao Dongpu, Wang Yiqun, Chen Xing. Robust H∞ Control Theory and Its Applications in Engineering[J]. Chinese Hydraulics & Pneumatics, 2002(8):5-7. (In Chinese) [2] Zhu Chunbo. Research on the Strategies for the Pneumatic Position Servo System Based on the Proportional Pressure Valve[D]. Harbin: Harbin Institute of technology, 2001. (In Chinese) [3] TAPIO V. On the damping of a pneumatic cylinder driven[C]. Beijing:Proceeding of the 3 international symposium on fluid power transmission and control, 1999. [4] J. M. Tressler, T. Clement, H. Kazerooni, M. Lim. Dynamic behavior of pneumatic systems for lower extremity extenders[C].Washington: Proceedings of IEEE International Conference on Robotics and Automation, 2002. [5] Wang Peng. Establishment and Research on Mathematic Model of Proportional Valve Controlled Pneumatic Position Servo-System[J]. Lubrication Engineering, 2003, 23(4):4-6. (In Chinese) [6] Yuan Ruibo, Zhao Keding Xu Hongguang. The Torque Control of an Electro-Hydraulic Servo System Based on Mixed Sensitivity Method[J]. Machine Tool & Hydraulics, 2004(11): 37-39. (In Chinese) [7] Mei Shengwei, Shen Tielong, Liu Kangzhi. Modern Robust Control Theory and Application[M]. Beijing: Tsinghua University press, 2008. (In Chinese) [8] Galindo R, Malabre.M, Kucera.V. Mixed Sensitivity H∞ Control for LTI Systems[C]. Atlantis:43rd IEEE Conference on Decision and Control. 2004. [9] Fales, R Kelkar. A Robust control design for a wheel loader using mixed sensitivity h-infinity and feedback linearization based methods[C]. Portland: Proceedings of American Control Conference, 2005. [10] Ali.H.I, Mohd. Noor. S. B, Bashi. S. M etc. Design of H-infinity based robust control algorithms using particle swarm optimization method[J]. Mediterranean Journal of Measurement and Control, 2010, 6(2):70-81.

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