Energy optimization of pneumatic actuating systems using expansion energy and exhaust recycling

Journal of Cleaner Production 254 (2020) 119983

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Energy optimization of pneumatic actuating systems using expansion energy and exhaust recycling Hongwang Du , Chaochun Hu , Wei Xiong *, Zhong’ai Jiang , Lu Wang Ship Electromechanical Equipment Institute, Dalian Maritime University, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 August 2018 Received in revised form 28 December 2019 Accepted 3 January 2020 Available online 6 January 2020

As an important power source in industrial applications, compressed air makes up an increasingly large proportion of total industrial energy consumption. Due to the compression and leakage of air, however, pneumatic actuating systems have suffered from a low utilization of compressed air. Moreover, for a traditional pneumatic circuit, a three-position five-way valve is used to control the air inlet and exhaust with a single pressure, also causing low efficiency. This study proposes a novel bridge circuit to realize energy savings through utilizing compressed air expansion energy and exhaust energy. The circuit consisted of five two-position two-way switch valves. The open-and-close sequence of these valves was used to control the motions of a cylinder piston. This circuit could realize system energy conservation by less air intake and waste air reuse, while simultaneously ensuring that the piston reached the end of its stroke with stability. In order to optimize air consumption, a nonlinear dynamic system optimization model was built based on the idea of dynamic optimization, and the pressure and flow of the pneumatic system and the dynamic equation were considered as constraint conditions. Optimization of the openand-close sequence of the five switch valves in the bridge circuit was conducted using orthogonal collocation on finite elements and the interior point method. Lastly, a bridge actuator test platform was built to test the stability and energy efficiency of the proposed pneumatic circuit based on the open-andclose sequence obtained through the optimization algorithm with different air supply pressures and workloads. Compared with the traditional circuit, the proposed circuit yielded energy savings of 55e87%, and the impact acceleration at the end point is smaller than that at the end point, with only
0.01 e0.02 m/s. These results suggested that the circuit is important for enhancing the utilization of compressed air. © 2020 Elsevier Ltd. All rights reserved.

Handling Editor: Jin-Kuk Kim Keywords: Pneumatic actuating system Energy efficiency Work of expansion energy Exhaust recycling Dynamic optimization

1. Introduction Given its simple structure, portability, low cost, long service life, and ease of installation and maintenance (May et al., 2017; LBNL, 2003), compressed air has been widely used in a variety of industrial fields, such as semiconductor and automobile manufacturing, the machine tool and chemical industry, metallurgy, and production automation. Compressed air consumes about 10% of power in the industrial sector, on average (Martin 1993). However, the energy efficiency of pneumatic systems is low due to the compression and leakage of air. Therefore, enhancing the energy utilization of pneumatic systems to save energy has been a hot topic worldwide (Saidur et al., 2010).

* Corresponding author. E-mail address: [email protected] (W. Xiong). https://doi.org/10.1016/j.jclepro.2020.119983 0959-6526/© 2020 Elsevier Ltd. All rights reserved.

A number of factors influence the efficiency of a pneumatic system. These factors are distributed in various segments of the pneumatic system, including compressed air generation, trans

slija et al., 2016). Researchers have done mission, and utilization (Se considerable analysis of the energy waste that occurs during compressed air generation and transmission and have developed some proven technologies in response to this energy inefficiency. Although utilization of compressed air is not the segment that wastes the most energy among all segments, in studies that have demonstrated reduced compressed air consumption resulting from the use of actuators, the air compressor has been shown to generate less compressed air, which has served to indirectly enhance the energy efficiency of compressed air generation. Therefore, it is of great importance to study energy conservation in the case of compressed air utilization, which is the focus of this study. In this study, energy conservation was effectively realized based on expansion energy and exhaust recycling. By changing the

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H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

coordination between the solenoid valve and the cylinder in the pneumatic circuit, the piston was steadily driven to its stroke end, thereby saving compressed air. In recent years, some researchers have tried to save compressed air by using different combinations of solenoid valves and cylinders. These efforts have resulted in some notable achievements, such as an energy-saving pneumatic circuit with a double-pressure air supply, an exhaust-recycling energy-saving circuit, and an energy-saving circuit that offers separate control of inlet/outlet pressure (Harris et al., 2012a,b). (1) Energy-saving pneumatic circuit with double-pressure air supply. The energy-saving pneumatic circuit with double-pressure air supply follows a basic principle: that the piston works at different air supply pressures as it moves in two different directions by changing the hardware connection of the pneumatics based on the traditional pneumatic circuit. This means that the piston works under a high pressure and returns under a low pressure when there is no load. Beater (2007) used a relief valve connected to the rod chamber to keep the inlet pressure below the preset maximum pressure of the relief value. This setup ensures that the air supply pressure in the return stroke of the cylinder piston is smaller than that in the extending stroke. This system was found to save energy by about 25%. This setup can also be applied to a vertical test platform. Air is supplied at a higher pressure to lift the load when the piston moves upward and is supplied at a lower pressure when the piston moves downward. During this time, load gravity is used to exert the force needed to push the piston to the lowest point. This method saved 75% of compressed air (Senoo et al., 2005). (2) Exhaust-recycling energy-saving circuit. The above circuit can save energy by increasing the utilization ratio of intake pressure, but the idea of an exhaust-recycling energy-saving circuit is to use exhaust energy. In one study, Li et al. (2006) released recycled compressed air from an exhaust chamber into an air tank and re-pressurized it for reuse, which saved about 40% of compressed air. Similarly, some other researchers released part of the compressed air in the exhaust chamber to the inlet chamber by connecting the exhaust chamber and inlet chamber using a switch valve (Yang et al., 2009; Blagojevi c et al., 2013; Shen and Goldfarb, 2007). Applying the condition of accurate system positioning, this method was found to save about 10.9e29.5% of compressed air. The reason for the differing results of these two methods was that different control strategies were used. In a study by Du et al. (2017), both ends of the air compressor were connected to the exhaust chamber and the inlet chamber of a cylinder; the speed of the piston rod was directly controlled by the control motor. By maintaining piston stability, 74% of compressed air was saved. However, the applicability of this method and the robustness of piston rod control remain to be verified. Likewise, Cummins (2016) developed a pneumatic strain energy accumulator that could be used to recycle the exhaust air from the pneumatic system, store it in a high-efficiency process, and then reuse it under a constant pressure to provide power to another pneumatic component. The efficiency of the pneumatic system was enhanced by 31e60% using this method.

(3) Energy-saving circuit with separate control of inlet/outlet pressure. This circuit is an effective combination of the first two energysaving circuits. The expansion energy and exhaust energy can both be used to achieve energy saving. In the energy-saving pneumatic circuit designed by Wang and Gordon (2012) with separate control of inlet/outlet pressure, the accelerated speed of piston movement was obtained by calculating the pressure difference between the two chambers. The pressure difference was then fed back into the system to control the openings of two proportional valves, thereby controlling the air inlet and displacement and ensuring that the experimental system executed all required motions of the predefined velocity curve as much as possible. This circuit saved about 3e7% of compressed air. In a study by Harris et al. (2014), two three-position four-way switch valves were used to control the vertically-mounted cylinder. When the two solenoid valves were both switched to the left position, they controlled the air inlet of the non-rod and rod chamber; when the two solenoid valves were both switched right, they controlled the exhaust of the non-rod and rod chamber. The optimized solution to the open-and-close sequence of two solenoid valves was conducted using the genetic algorithm. The air consumption could be saved by 29% within one extending-return work cycle of the piston rod. When the piston rod was extended, an air inlet was either present or not present in the non-rod chamber, and there was either air outflow or no air outflow from the rod chamber. Such restrictions resulted in a reduced degree of freedom, thus leading to forceful impact at the end of the stroke. In studies by Doll et al. (2011), Doll and Sawodny (2010), the cylinder inlet and exhaust were controlled by five switch valves. The air inlet of the rod and non-rod chambers was controlled by two valves, and their exhaust was controlled by the other two valves. The pneumatic actuating system was discretized using the implicit midpoint method and optimized using the interior point method based on which the open-and-close sequence of the four switch valves was obtained. A comparison of the bridge circuit experiment with the traditional circuit experiment in the same working conditions suggested that up to 85% of compressed air could be saved by the bridge circuit. However, the problem with the bridge circuit was that the discretization precision of the implicit midpoint method was low. In addition, exhaust recycling of the pneumatic system was not studied. Du et al. (2018) also conducted similar research based on studies of Doll et al. (2011), Doll and Sawodny (2010), with a simpler optimization algorithm and different changing operating conditions. The TOMLAB optimization toolbox in MATLAB was used to find the open-and-close sequence of four valves based on reduced sequential quadratic programming. According to the experiment results, 50% of compressed air was saved in the extending stroke of the piston rod, and this figure increased to 69% in the return stroke. The energy-saving pneumatic circuits introduced above represent a few among many others, but they serve as a sufficient explanation of the increasing efficiency of pneumatic systems. The three aforementioned energy-saving circuits suggest that the double-pressure energy-saving circuit and exhaust-recycling energy-saving circuit are more highly developed, whereas the energy-saving pneumatic circuit with separate control of inlet/ outlet pressure is a more novel idea that requires further development. Although the double-pressure and exhaust-

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

recycling energy-saving circuits afford more precise tracking control, the compressed air savings they yield is unstable. In addition, control algorithms varied with different working conditions, which resulted in poor robustness of the control. The bridge circuit that was later developed was found to save up to 85% of compressed air by using the cylinder inlet/exhaust separate control mechanism, but this test was conducted by changing a single working condition. Moreover, the system discretization method was found to be insufficient in ensuring the open-andclose sequence accuracy of the switch valves. Exhaust recycling of pneumatic systems was not considered in this study. In view of the above limitations, an exhaust-recycling circuit, i.e., the switch valve connection between the inlet chamber and the exhaust chamber, was additionally set up to enhance the utilization of compressed air and the application of the energy-saving circuit with separate control of inlet/outlet pressure based on previous laboratory studies (Du et al., 2018). Compared with the old paper’s idea (Du et al., 2018), we added a by-pass valve; the energy-saving bridge circuit consisted of five two-position two-way switch valves that were used to control the motions of a cylinder piston; the optimization of the openand-close sequence of the five switch valves in the bridge circuit was implemented using orthogonal collocation on finite elements and the interior point method in order to ultimately obtain the open-and-close sequence of the five switch valves; by using a better algorithm (combination of both orthogonal collocation on finite elements and the interior point method), this new circuit has better stability and energy-saving performance. This remainder of this paper is organized as follows:  Section 2 describes the modeling of the pneumatic system.  Section 3 describes the nonlinear dynamic system optimization method that was developed based on the polynomial collocation of finite elements and the interior point method.

m

13

15

9

14

16 17 8

7

6

5

2. Modeling of the energy-saving pneumatic system Fig. 1 shows the diagram of the energy-saving bridge pneumatic circuit. The values 5, 6, 9, 10, and 16 correspond to valves 1 (V1), 2 (V2), 3 (V3), 4 (V4), and 5 (V5), respectively. The air inlet of the nonrod and rod chambers are controlled by V1 and V2, respectively; the exhaust of the non-rod and rod chambers is controlled by V3 and V4, respectively; and the non-rod and rod chambers are connected by V5 so that part of the compressed air in the rod chamber can flow into the non-rod chamber. Compared with the studies conducted by Doll et al. (2011) and Du et al. (2018), the proposed energy-saving bridge pneumatic circuit additionally contains valve V5 for exhaust recycling, which should result in increased energy savings. Due to the compression, heat sensitivity, and low viscosity of air, piston parameters vary with time when the piston is working, which makes the modeling of the pneumatic system difficult. For the sake of analysis, the following assumptions were made (Harris et al., 2012a,b): (1) The working medium is an ideal air that followed the equation of an ideal air state; (2) The air source is a constant pressure source that does not consider pressure loss in the pipeline; (3) Air flow is an isentropic adiabatic process when the system is working; (4) Pressure fields and velocity fields in both cylinder chambers are homogenous; and (5) Internal/external cylinder leakage is ignored.

parameter symbol

meaning

Aki Ar Cv fc fs m

effective area of piston sectional area of piston rod corresponding sonic conductance Coulomb friction maximum static friction load mass mass flow through the ith valve

·

4 3 1

 Section 4 experimentally verifies the energy efficiency of the proposed pneumatic circuit. The operation stability of the piston in its extending stroke under different working conditions are investigated.  Section 5 summarizes conclusions that were drawn from performing this study.

Table 1 Modeling related parameters.

12 10

11

2 Valve drive module

3

Data acquisition card

1-Air supply, 2-Air tank, 3-Stress reducing valve, 4, 13, 14Pressure sensors, 5, 6, 9, 10, 16-Switching valves (defined as V1, V2, V3, V4, V5), 7, 8-Flow sensors, 11, 12-Silencer, 15Cylinder, 17-One-way valve. Fig. 1. Schematic diagram of the novel pneumatic system.

mi n P0 pd pu R T0 u2f0; 1g v Vi(x) _ V_ i ðxÞ vs Vti

a d b m r0

air polytrophic index external environmental pressure downstream air pressure upstream air pressure air constant air temperature on-off position of ith valve velocity volume of the ith chamber chamber volume gradient Stribeck velocity dead zone of the ith chamber critical pressure ratio arbitrary index viscous friction coefficient dynamic friction factor air density under the standard condition

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H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

Using the above assumptions, the dynamic characteristic equation of the energy-saving pneumatic circuit system was obtained according to the law of conservation of mass, the law of conservation of energy, and Newton’s second law of motion. Compressed air consumption of the system was obtained using the integral of mass flow. All modeling related parameters are shown in Table 1 (Du et al., 2018).

second law, the kinematic equation of the pneumatic circuit could be derived as follows (Du et al., 2018).

x€ ¼

 1 Aka pa
Akb pb
Ar P0
Ff m

i h d Ff ¼ b,v þ fc þ ðfs
fc Þe½
ðv=vs Þ  sgnðvÞ

(6a)

(6b)

2.1. Mass flow equations The mass flow through the solenoid valve Vi is represented here by mi (i ¼ 1, 2, 3, 4, 5). If the non-rod and rod chambers of the cylinder, the mass flow into the non-rod chamber, and the mass flow into rod chamber are defined as a, b, ma, and mb, respectively, the mass flow equations for the two chambers are Eqs. (1) and (2). ·

·

·

·

·

·

·

·

ma ¼ m1
m3 þ m5

(1)

mb ¼ m2
m4
m5

(2)

According to international standard ISO6358 (Turkseven and Ueda, 2016), the flow characteristics of pneumatic parts can be described by the velocity of flow conductivity, Cv, and the critical pressure ratio, a. Thus, Eq. (3) can be used to formulate the mass flow through the solenoid valve as follows: ·

mi ¼ ui ,Cv r0 4ðpu ; pd ; aÞ,pu

i2f1; 2; 3; 4; 5g

(3)

2.4. System air consumption equation In this study, air consumption was characterized using standard liters. System consumption of the air was first obtained by using the mass flow integral of air into the system, and then total mass was converted into standard liters based on standard air density. Since V1 and V2 are the only two switch valves controlling the cylinder inlet, the integral of the mass flow through these two valves is required. Eq. (7) represents the system air consumption equation:

ðtf  Vst ¼ CV P0 t0

 u1 ,4ðP0 ; Pa ; aÞ dt þu2 ,4ðP0 ; Pb ; aÞ

(7)

where t0 and tf are the starting and ending times of system operation (unit: s), respectively.

Stream function 4ð,Þ could be modeled as the following Eq. (4).

pd 8 > pu > > > ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > u
aC > pd p B > u > u1
@ a > A > :t 1
a pu

3. Dynamic optimization of the energy-saving system 3.1. Optimization description

(4)

2.2. Differential equation of pressure Based on the hypotheses above, the air is considered as ideal air and air flow is an adiabatic process that ignores air leakage. Eq. (5), the differential equation of pressure within the two-cylinder chambers, can be derived based on the ideal air equation and the first law of thermodynamics, as follows: ·

pi ¼

· n ðRT0 mi
pi , Vi ðxÞÞ; i2fa; bg Vi ðxÞ þ Vti

(5)

2.3. Kinematic equation of the cylinder Force analysis of the piston was conducted for this study. Suppose that the non-rod chamber of the cylinder is the inlet chamber and the rod chamber is the exhaust chamber. As shown in Fig. 1, the cylinder piston is subjected to the thrust to the right by the air in the non-rod chamber and the resistance to the left by the air in the rod chamber. The piston rod is subjected to atmospheric resistance to the left and frictional resistance between the piston and the cylinder barrel. Referring to Newton’s

In this study, the piston of the energy-saving bridge pneumatic circuit system was designed to travel steadily by controlling the open-and-close sequence of the five switch valves, thus minimizing the amount of air consumed. Therefore, air consumption was selected as the objective function. Since air consumption is determined by the opening time of the switching valves, the switching time of the valves was used as the control variable. Cylinder chamber pressure, piston displacement, and piston speed varied with different cylinders and air supply pressures, which were considered as constraint conditions. Piston displacement, piston speed, and the pressure of chamber a and chamber b are denoted as x1, x2, x3, x4, respectively u : ¼ ½u1 ; u2 ; u3 ; u4 ; u5 ; is the variable describing the open-and-close sequence of the five switch valves. The mathematical optimization model of the energy-saving bridge pneumatic circuit system is as follows:

argmin JðxðtÞ; uðtÞÞ; uðtÞ2f0; 1g5 st:th: xðtÞ ¼ fðxðtÞ; uðtÞÞ and xðt  0 Þ¼ x0 and x tf ¼ xf

(8)

According to the states of various switch valves, there are five binary control variables ui, which poses a problem relating to mixed integer nonlinear programming. Currently, solutions to such optimization problems include the branch and bound algorithm (Calogiuri et al., 2019), the outer approximation

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

Start

Discretize model

Solve NLP problem (IPOPT)

Gradient calculation

Optimum solution

End

8 > > > > > > <

Jacobi and Hessian matrix

> > > > > > :

Fig. 2. Solving nonlinear dynamic optimization by simultaneous method.

x1i;j
εi
1 ¼ hi

m X

aj;k w1i;k ;

εi
εi
1 ¼ hi

m X

bk w1i;k ;

ðcj Y

m i¼1;sk

(1) To convert the differential-algebraic equation in the original model into the algebraic equation, a new variable w1(t) was introduced to replace x_1 ðtÞ, thereby converting the differential-algebraic equation in the original model into Eq. (9).

w_ 1 ðtÞ ¼ x2 ; x_1 ðtÞ ¼ w1 ðtÞ

(9)

(2) The time domain was divided into n finite element intervals, t0 < t1 < t2 < t3 / < tn
1 < tn , where tf ¼ tn. Thus, the length of each finite element interval was hi ¼ ti
ti
1 . Regardless of the selection of collocation points, each finite element interval was collocated with m collocation points, denoted as fc1 ; c2 /cm g. The Lagrange interpolation polynomial was used to approximate Eq. (9) and obtain Eq. (10), where x1i;j ; w1i;j are the numerical values corresponding to x1 ; w1 on the jth collocation point within the ith finite element, respectively, and εi is the numerical value of x1 corresponding to ft0 ; t1 ; t2 ; t3 ; /; tn
1 ; tn g.

c
ci ck
ci

 dc

bk ¼

ð1 Y

m i¼1;sk

0

c
ci 1
ci

 dc (10)

(3) According to the features of the simultaneous method, for specific collocation points, if the collocation points coincided with the finite element nodes, the discretization equation could be further reduced. In this study, the Lobatto quadrature orthogonal collocation method was used. The first and last collocation points of Lobatto orthogonal collocation coincided with the front endpoint and the back endpoint. The nodal connection equation could be omitted without affecting the continuity of discretized function. Thus, Eq. (11) was obtained.

εi
1 ¼ x1 i;1 ¼ x1 i ¼ 1; 2; 3; /; n:

Currently, the most widely used method to solve nonlinear dynamic optimization with differential-algebraic equations is the simultaneous method (Sager 2009). When nonlinear dynamic optimization containing differential-algebraic equations is performed using the simultaneous method, orthogonal collocation on a finite element is used to discretize the state variable and control variable at multiple finite element collocation points. Using discretization, a model is turned into a large-scale nonlinear optimization, which is then solved using the nonlinear optimization algorithm. The flow diagram of solving the nonlinear dynamic optimization using the simultaneous method is shown in Fig. 2, where IPOPT represented Internal Point Optimizer. The discretization of the optimization described above was conducted using the steps below:

i ¼ 1;2;,,,;n:

k¼1

0

3.2. An orthogonal collocation-based simultaneous approach

j ¼ 1;2;,,,;m:

k¼1

aj;k ¼ algorithm (Boukouvala et al., 2016), and the dynamic programming algorithm, all of which offer poor solutions for energy efficiency and none of which specify the convergence and global minimum. Therefore, we ignored whether the control variable was an integer and allowed a [0,1] time interval for the control variable. Using this alternate approach, the mixed integer nonlinear dynamic programming was converted into nonlinear dynamic programming. The control variable was also modified to [0,1]. To be consistent with the switch valves in practical application, the continuous signal of the time sequence obtained by optimization must be converted into the binary input signal. In this study, the continuous signal obtained by optimization was converted into the binary signal using the threshold value method with a threshold value of 0.5.

5

ði
1Þ;4

w1

i;1

¼ w1

ði
1Þ;4

(11)

To further simplify the discretization equation, the coincident collocation points were simplified into the same point, followed by re-permutation of all collocation points within the time domain interval to obtain the collocation points N¼(m
1)*n (initial value points excluded). Then, Eq. (12) was obtained by expressing Eq. (10) in a unified pattern.

x1i
xi
j ¼ hi

4 X

aj;k w1ðiþk
j
1Þ

k¼1

i ¼ 1; 2; /; N j ¼ ðði
1Þmodð4
1ÞÞ þ 1

(12)

The distribution of collocation points by the four-level Lobatto orthogonal collocation method was obtained by Eq. (13).

ðc1 ; c2 ; c3 ; c4 ÞT ¼ 0;

pffiffiffi pffiffiffi !T 5
5 5þ 5 ; ;1 10 10

(13)

Similarly, the discretization equations of piston speed and the pressure of two-cylinder chambers was also derived. The nonlinear system optimization model was collated into Eq. (14): where ld and lu are the maximum and minimum displacement, respectively; vd and vu are the maximum and minimum speed, respectively; P1d and P1u are the maximum and minimum pressure of chamber a, respectively; P2d and P2u are the maximum and minimum pressure of chamber b, respectively. Using discretization, the original problem of dynamic optimization was converted into one of nonlinear optimization. Model size was in direct proportion to the total number of collocation points. The larger the total number of collocation points, the larger the solution size. When there were a sufficient number of collocation points, nonlinear optimization was transformed into largescale nonlinear optimization.

6

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

sequence based on the interior point method could be obtained using the following steps:

argmin Vst ðNÞ; uðtÞ2½0; 15 xðti;j ;ui;j Þ;t0 ;tf

1) The logarithmic obstacle term was included in the objective function of Eq. (15) to convert the original problem into Eq. (16):

st:th: w1i ðtÞ ¼ x2



8  > 1 > > > Aka x3i
Akb x4i
Ar p0
Ff i w2i ðtÞ ¼¼ > > m > > > > > > > > > > n > > w3i ¼ ðRT0 mai
x3i ,Vai Þ > > V þ Vta > ai > > > > > > > > > > n > > w4i ¼ ðRT0 mbi
x4i ,Vbi Þ > > > Vbi þ Vtb > > > > > <

x

:

x3i 2½p1d ; p1u 

8 < Vf ðxÞ þ VcðxÞl
n ¼ 0 cðxÞ ¼ 0 : XVe
me ¼ 0

(16)

(17)

where Vf ðxÞ is the derivative of the objective function; VcðxÞ is the Jacobian matrix of the equality constraint; l and v are the Lagrange multiplier and dual variable, respectively; X and V are diagonal matrices; x is diagonal elements.

p ¼ 1; 2; 3; 4

2) Eq. (17) was linearized using Newton’s method to obtain the linear equation set at iteration points ðxi ; li ; vi Þ along the search directions ðdi ; dli ; dni Þ, as shown by Eq. (18).

2

Wi

6 T 6A 4 i Vi

Ai 0 0

30

1

0 1 gi þ Ai li
ni 7B l C B C @ A ci 0 7 5@ di A ¼
n X n
m e i i Xi di


I

di

(18)

i ¼ 1; 2; /N where Wi is the Hessian matrix of the Lagrange function in original proposition; ATi is the Jacobian matrix of the equality constraint; and gi is the gradient of the objective function. By eliminating the search direction of the inequality constraint multiplier, the following equations could be derived:

x2i 2½vd ; vu  x4i 2½p2d ; p2u 

"

and

8 < ½x11 ; x21 ; x31 ; x41  ¼ x1t0 ; x2t0 ; x3t0 ; x4t0 i h : ½x1N ; x2N ; x3N ; x4N  ¼ x1tf ; x2tf ; x3tf ; x4tf

W i þ 2i

Ai

ATi

0

#

di

lþ i

!

 ¼


V4m ðxi Þ ci

 (19)

þ where 2i ¼ X
1 i Vi . By obtaining di ; li , we concluded that

(14) In view of Eq. (14), the nonlinear optimization algorithm could be used to find the solution. Models with lower degrees of freedom and sparser structures are usually solved using the interior point method or the sequence quadratic program (SQP). In this study, the former was used. The premise of the interior point method €chter and Biegler, 2006) is that the boundary constraint of (Wa nonlinear optimization is converted into obstacle terms and included in the objective function. This way, the original problem was turned into a problem with or without the equality constraint. This avoided the solution bottleneck brought on by the need to identify the efficiency set, convert the original problem into a series of subproblems, and then find the solutions to the obstacle factors. Nonlinear optimization, i.e., Eq. (14), was described by Eq. (15).

8 < min x : s:t:

i¼1

cðxÞ ¼ 0

where m is the obstacle factor in descending order. The KarushKuhn-Tucker (KKT) conditions for finding the solution to nonlinear optimization is shown in Eq. (17):

0

and 8 < x1i 2½ld ; lu 

n       X 4m x ¼ f x
m ln xðiÞ

s:t:

w5i ¼ Cv P0 ½u1i ,4ðP0 ; x3i ; aÞ þ u2i ,4ðP0 ; x4i ; aÞ > > > > > > > > > > cj >  > 4 ð > tf X > c
cr 4 > > x
x ¼ P dc wp;ðiþk
j
1Þ > p; i p; ði
jÞ r¼1;sk > n ck
cr > > k¼1 > > 0 > > > > > > > > > > cj  > 4 ð > X > c
cr > > P4r¼1;sk dc w5ðiþk
j
1Þ VstðiÞ
Vstði
jÞ ¼ hi > > > ck
cr > k¼1 : j ¼ ðði
1Þmodð4
1ÞÞ þ 1

min

n
1 dli ¼ lþ i
li ; di ¼ mX i e
ni
2i di :

To analyze the convergence, Ai was decomposed to obtain Zi 2Rnðn
mÞ and Yi 2Rnm . The orthogonal basis of Rn comprised the column vectors of matrix ½ Zi Yi . A basis of null space ATi was Zi . Eq. (20) was obtained by decomposing the search direction as follows:

di ¼ Yi q_ i þ Zi p_ i

(20)

where the expressions of q_ i and p_ i are shown in Eq. (21).

i
1 h 8 < q_ i ¼
ATi Yi ci i   h : _ T pi ¼
Z i Hi Zi Z Ti gi
mX
1 i e þ Hi q i

(21)

f ðxÞ cðxÞ ¼ 0 x> ¼ 0

(15)

According to Boukouvala et al. (2016), the solution to the valve

3) Once the search direction was obtained, the new iteration point was defined, as shown in Eq. (22):

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

8 > x ¼ xi þ ai di > < iþ1 liþ1 ¼ li þ ai dli > > v v :v iþ1 ¼ vi þ ai di

7

(22)

where ai and av are obtained through a linear search and satisfy the reserved boundary conditions, as shown in Eq. (23):

(

xi þ ai di > ¼ ð1
tÞxi vi þ avi dvi > ¼ ð1
tÞvi

(23)

where t2ð0; 1Þ is a constant close to 1. 4) To ensure the global convergence of the algorithm, a onedimensional filter search-based linear search method was used in this study. The difference between the one-dimensional filter search algorithm and traditional one-dimensional search algorithms was that the iteration could proceed as long as the iteration condition satisfied one of the multi-objective problems. With certain conditions satisfied, the one-dimensional filter search algorithm could be turned into a traditional one with filtering functions. In addition, the filtering functions meant that unsatisfactory iterations would be recorded so that the search would be prohibited in the event of the same conditions in the next iteration. The proposed nonlinear optimization algorithm was implemented based on Visual Studio 2015 and an advanced microprocessor programming language (AMPL) (Fourer et al., 2003). The sequence of the five switch valves can be obtained as long as the physical parameters of all the components in the pneumatic actuating system and the boundary conditions for optimization are given.

Fig. 3. Open-and-close sequence of the five valves with supply pressure of 0.5 MPa and the load of 78.5 kg.

whole trip. The by-pass valve V5 opened from 0.23 to 0.7s, to ensure that the piston is able to reach the end of the stroke and save energy again.

3.3. Optimal solution results Based on the optimization program written in AMPL, the internal point solver is used to gain the open-and-close sequence of five switch valves in the bridge circuit. When optimizing, the relevant parameters are set up, as shown in Table 2. Based on the optimized parameters shown in Table 1, the openand-close sequence of the five switch valves obtained through the optimization solution is shown in Fig. 3. According to the optimized sequence, the inlet valve V1 in the system started running open, closed at 0.16s, and then remained closed throughout the trip. The piston continued to move by using the compressed air expansion energy, so as to improve energy efficiency. Exhaust valve 4 started running open, and closed from 0.18 to 0.22s and 0.4e0.7s to prevent the piston speed from being too high by the aid of back pressure. V2 and V3 remained off during the

4. Experimental verification of the energy-saving system 4.1. Test platform Based on the proposed energy conservation circuit, a test

Table 2 Parameters required for optimization. parameters

symbol

value

Load [kg] Distance [m] Air pressure [MPa] Piston diameter [m] Rod diameter [m] End time [s] Condition (t0 ¼ 0 s) Condition (tf ¼ 0.6 s) Finite elements Configuration points

m L P0 D d tf x0 xf ne nc

78.5 0.6 0.5 0.063 0.02 0.7 [0 m, 0 m/s, 0.1 MPa, 0.1 MPa] [0.6 m, 0 m/s, 0.1 MPa, 0.1 MPa] 140 4

Fig. 4. Platform of the energy-saving pneumatic circuit.

8

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

platform was built, shown as Fig. 4. This test platform included a cylinder, five two-position twoway solenoid valves, two pressure sensors, two flow meters, and a displacement sensor. All details of the above components were shown as Table 3. The pressure sensor was used to measure the pressure of the two chambers of the cylinder. The flow meter was used to measure the volume flow rate of air entering the two chambers of the cylinder, and the displacement sensor was used to detect position of the piston. Open-and-close sequence of the five valves was transmissed through a data acquisition card. Also, all data from sensors could be displayed through a PC monitor connected with the card.

4.2. Experimental verification of stability Based on the test platform, experimental research was carried out to prove the stability of the bridge-type circuit, compared with the traditional circuit. Under the same working conditions, speed at the stroke end was analyzed. For traditional circuit, the impact and bounce of the piston become more serious when the load or the air supply pressure become larger (Kang et al., 2009). Our proposed bridge-type circuit only had slight impact and bounce, which could be neglected. Impact refers to the collision between the piston and the end cap when the piston reached the end of the stroke. Bounce refers to the phenomenon that the piston moves back at the end of the stroke because of the nonzero velocity. To prove the stability of our circuit, working Conditions of the cylinder was changed compared with the parameters in Table 2, including load, air pressure and end time shown as Table 4. Then the control factor (finite elements ne and configuration points nc) of the optimization algorithm should be different with Table 2. Then the open-and-close sequence of the five switch valves was obtained by finding the optimized solution in the aforementioned program, as shown in Fig. 5. According to the sequence obtained by the optimized solution, the inlet valve V1 was opened on system startup and closed in 0.11 s. The piston was driven to complete the rest of the stroke by the expansion energy of the compressed air inflated in the chamber. The compressed air remaining in the inlet chamber was discharged so that the piston traveled to the end of the stroke smoothly, 0.79 s after the system startup. V4, which controlled the discharge of exhaust chamber, was also opened on system startup and closed twice during system operation. The first time V4 was closed was between 0.15 and 0.24 s after system startup, during which time the exhaust chamber was subject to back pressure that reduced piston speed. The second time V4 was closed was between 0.44 and 0.79 s after system startup. Compressed air in the exhaust chamber passed into inlet chamber through V5 during the 0.44e0.71 s after system startup. The exhaust chamber was subject to back pressure during the 0.71e0.79 s after system startup. Piston speed decreased, thus reducing the impact on the cylinder head by the piston at the end of the stroke. V4 was opened 0.79 s after

Table 4 Relevant parameters of the system, including experimental and FE analysis parameters. parameters

symbol

value

Load [kg] Air pressure [MPa] End time [s] Finite elements Configuration points

m pu tf ne nc

118.5 0.7 0.8 140 4

system startup. In the meantime, any compressed air remaining in the exhaust chamber was discharged. V5 was opened 0.19e0.71 s after system startup, during which time part of the compressed air passed from the exhaust chamber into the inlet chamber. The bridge circuit experiment was carried out based on the open-and-close sequence of five switch valves obtained by the optimized solution. By contrast, the traditional circuit experiment was also carried out under the same working conditions of air supply pressure, load, and full stroke time. The signals acquired by the acquisition card were processed properly and drawn into graphs for comparative analysis, as shown in Fig. 6. Pa1, Pb1, Pa2, Pb2, s1, s2, v1, v2, Q1 and Q2 respectively represented the intake chamber pressure of the bridge circuit, the exhaust chamber pressure of the bridge circuit, the intake chamber pressure of the traditional circuit, the exhaust chamber pressure of the traditional circuit, the displacement of the bridge circuit, the displacement of the traditional circuit, the speed of the bridge circuit, the speed of the traditional circuit, the air consumption of the bridge circuit, the air consumption of the traditional circuit. The characteristics of presented system and traditional pneumatic system in the same working conditions suggested that both circuits showed the same dynamic performance before V1 was

Table 3 Models and specifications of experimental components. Components

Model

Manufactor

Air cylinder Pressure sensor Valve Flow meter Displacement sensor Air tank Stress reducing valve Data acquisition card

CDA2L63-600N-M9BW PSE540A-R06 VX230FG SFAB1000UWQ102SVM12 RPM1000MD601V410100 VBAT20A-DNQ0031 IR3020 PCI-1710HG

SMC SMC SMC Festo MTS SMC SMC Advantech

Fig. 5. Open-and-close sequence of valves with supply pressure of 0.7 MPa and the load of 118.5 Kg.

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

Fig. 6. Comparison between bridge and traditional circuit: (a) chamber pressure, (b) cylinder displacement, (c) motion speed, (d) air consumption.

closed. This was because the open-and-close sequence of the presented system was the same as that of the traditional pneumatic system upon system startup. After V1 was closed, however, the pressure in the inlet chamber of bridge circuit declined faster. The piston started decelerating when the sum of the pressure and friction in the exhaust chamber was larger than the pressure in the inlet chamber. Afterwards, V5 was opened and some of the compressed air in the exhaust chamber flowed into the inlet chamber. The velocity curve indicated that significant impact and bounce was observed in the traditional circuit, while such phenomena were considerably reduced in the bridge circuit when the piston reached the end of its stroke. To further verify the stability of the bridge circuit, the bridge circuit and traditional circuit were experimentally investigated under different working conditions, such as with different air supply pressures and loads. Considering that the velocity curve reflected circuit stability, the velocity curves of the traditional and bridge circuits were comparatively analyzed, as shown in Fig. 7. The velocity curves when the air supply pressure and load were 0.3 MPa and 48.5 kg, 0.4 MPa and 58.5 kg, 0.5 MPa and 78.5 kg, and 0.6 MPa and 98.5 kg are shown in Fig. 7aed, respectively. The selection of air supply pressure and load was determined by the sample manual of the type of cylinder. According to the comparison between the velocity curves of bridge and traditional circuits investigated under different working

9

conditions, such as different air supply pressure and load, a significant impact and bounce could be observed in the traditional circuit when the piston traveled to the end of the stroke. A similar phenomenon was also observed in the bridge circuit, but with a significantly reduced magnitude, which suggested that the bridge circuit offered better stability than the traditional circuit. Compared with the studies by Doll et al. (2011) and Du et al. (2018), the system stability was enhanced after V5 was added for exhaust recycling. According to Doll et al. (2011), cylinder stability was shown only at the end of the stroke in most working conditions. However, crawling or impact was evident for the pneumatic system at the end of the stroke. Crawling referred to the stop-and-go phenomenon of the cylinder when it moved at a low speed. Impact referred to the collision of cylinders against end caps at the end of stroke due to excessive speed. The study by Doll et al. (2011) was limited to a cylinder diameter of 16 mm and a full stroke time of 0.4 s. Also, the range of impact at the end of the stroke was
0.2e0.05 m/s. Du et al. (2018) considered the crawling or impact when piston movement ends, yet the range of impact was
0.1e0.3 m/s. As shown in Fig. 7, the range of impact at the end of the stroke was
0.01e0.02 m/s when the exhaust-recycling valve V5 was mounted to the bridge circuit. It could thus be concluded that the proposed circuit and optimization algorithm showed better stability than those developed by Doll et al. (2011) and Du et al. (2018). 4.3. Experimental verification of energy conservation In this section, the experimental investigation of the bridge and traditional circuits was continued based on the test platform used to analyze the air consumption of both circuits and thereby validate energy saving characteristics of the presented bridge-type circuit. To begin with, the energy efficiency was analyzed when the cylinder diameter, stroke, air supply pressure, and load were 63 mm, 600 mm, 0.7 MPa, and 118.5 kg, respectively. It could be seen from the air consumption graph (Fig. 6-(d)) that the bridge circuit did not consume compressed air in the extending stroke when V1 was closed; a total volume of 1.48 L compressed air was consumed throughout the process. In comparison, the air consumption and working time of the traditional circuit were in direct proportion throughout the process, during which 10.2 L of compressed air was consumed. This suggested that the bridge circuit saved 85.5% of compressed air. To further validate energy saving characteristics, we let the cylinder run continuously in the two different circuits (the traditional circuit and the proposed bridge circuit), under different air supply and load. The air consumption of traditional and bridge circuits was analyzed in different working conditions. Cylinder ran three times under the same supply pressure and load. Table 5 shows the air consumption and the energy-saving outcome of both circuits under different working conditions. The values in the table are the average of the three times. The value of Q1 and Q2 was

Table 5 Air consumption of system of different working conditions.

Fig. 7. Velocity comparison between bridge and traditional circuit: (a) 0.3 MPa and 48.5 kg, (b) 0.4 MPa and 58.5 kg, (c) 0.5 MPa and 78.5 kg, (d) 0.6 MPa and 98.5 kg.

Air pressure [MPa]

Load [kg]

Q1 [L]

Q2 [L]

Energy savings

0.3 0.3 0.4 0.5 0.5 0.5 0.6 0.7 0.7 0.7

38.5 48.5 58.5 58.5 68.5 78.5 98.5 98.5 108.5 118.5

2.23 2.06 1.71 1.69 1.54 1.75 1.50 1.32 1.45 1.48

5.01 5.02 6.63 7.30 7.46 7.50 10.1 9.83 9.97 10.2

55.5% 59.0% 74.2% 76.8% 79.4% 76.7% 85.1% 86.6% 85.4% 85.5%

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H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

calculated by Eq. (7), where the volume flow rate of air was measured by the flow meter. In this paper, air consumption savings (calculated by (Q2-Q1)/ Q2) are assumed to be equivalent to energy savings. Air consumption was saved by about 55e59% at the air supply pressure of 0.3 MPa and around 74e87% at the air supply pressure of 0.4e0.7 MPa. Table 5 indicates suggests there was roughly equal air consumption (1e3 L) of the bridge circuit under different working conditions. Comparatively, the air consumption of the traditional circuit varied between 5 and 10 L under different working conditions since there was an evident relationship between the air consumption and cylinder size in the pneumatic system. Energy consumption of presented bridge-type circuit varied only slightly under different working conditions since the same cylinder was used. According to the results, it was indicated that the new system consumed less compressed air and afforded noticeable energy savings; it saved over 50% of compressed air under different working conditions and 87% at the maximum. Moreover, for the data of air pressure and energy savings in Table 5, a t-test: paired double sample mean analysis was done in Microsoft Excel, to illustrate the difference in the impact of pressure changes on energy savings. The t-test, also known as Student’s ttest, is mainly used for normal distribution with small sample size (e.g. n < 30) and unknown population standard deviation, to get the difference of pressure change to energy saving. The t-test uses tdistribution theory to deduce the probability of difference occurrence, so as to compare whether the difference between the two means is significant (Boneau 1960). After calculation, the absolute value of the t-statistic was 11.95, while the two-tailed critical value (t0.05/2-value of two-tailed test) was 2.26. Since the former was larger than the latter and the p-value was smaller than 0.01, it was concluded that savings increased with increasing pressure. Meanwhile, the piston was found to travel smoothly without a noticeable impact at the end of the stroke. The bridge circuit developed by Doll et al. (2011) with a cylinder diameter of 16 mm exhibited strong energy-saving performance, with a maximum energy savings of 85%. With a cylinder diameter of 63 mm, the maximum energy savings of the proposed bridge circuit reached 87%, which was even higher than that of the circuit developed by Doll et al. (2011). This was attributed to the adoption of the exhaust-recycling valve V5 and enhanced robustness of the proposed optimization algorithm. The working conditions used by Du et al. (2018) were consistent with those used in this study, but the circuit they developed yielded an energy savings of only 50e62%. In comparison, our proposed circuit yielded energy savings of 55e87%, which further evidenced its enhanced performance in energy conservation. 5. Conclusion In view of the limitations of traditional pneumatic circuits controlled by low-efficiency compressed air utilization threeposition, five-way switch valves, we developed a novel bridge circuit with which energy conservation was realized using compressed air expansion energy and exhaust recycling. Our primary observations were as follows: (1) A bridge circuit controlled by five switch valves was proposed based on the idea of the work of compressed air expansion energy. To optimize air consumption, a process control optimization model was built using system pressure, flow, and kinetic equations as constraint conditions. The optimization of the open-and-close sequence of the five switch valves in the bridge circuit was implemented using orthogonal collocation on finite elements and the interior

point method in order to ultimately obtain the open-andclose sequence of the five switch valves. (2) A test platform for the energy-saving bridge pneumatic circuit was built to compare the dynamic features and energy efficiency of the presented and common pneumatic system with different conditions and to verify which circuit offered better stability and energy-saving performance. Both a noticeable impact and bounce were observed in the traditional circuit under several different air pressures and loads when the piston traveled to the end of the stroke. When it came to the proposed circuit, however, the range of impact at the end of the stroke was between
0.01e0.02 m/s. The piston traveled smoothly to the stroke end of the cylinder with little impact or bounce. When the cylinder diameter of the traditional circuit was 63 mm, the air consumption of the proposed circuit was between 1 and 3 L under different working conditions. Conversely, this figure was 5e10 L in the traditional circuit. Compared with the traditional circuit, the proposed circuit yielded energy savings of 55%e87%. (3) When the cylinder diameter was 63 mm, the applicable air supply pressure and load were 0.3e0.7 MPa and 38.5e118.5 kg, respectively. When the full stroke time was set too long or short, the piston bounced or could not travel to the end of the stroke, which indicated that the range of the application of the bridge circuit still remains to be further investigated. In summary, the proposed bridge circuit demonstrated better energy-saving performance and stability, compared with previous studies.The bridge circuit developed by Doll et al. (2011) could gain energy savings of 85% and developed by Du et al. (2018) yielded an energy savings of only 50e62%, while our proposed bridge circuit reached 87%. On the other hand, because the range of impact at the end of the stroke was only
0.01e0.02 m/s, the proposed circuit and optimization algorithm showed better stability than those developed by Doll et al. (2011) (
0.2e0.05 m/s) and Du et al. (2018) (
0.1e0.3 m/s). These two advantages were attributed to the adoption of the exhaust-recycling valve V5 and enhanced robustness of the proposed optimization algorithm. The research of this paper partly overcame the low energy utilization that traditional circuits suffer from and laid a good technical foundation for further research into the energy conservation of pneumatic systems. However, the circuit is not ready for practical application. There is still considerable work to be done in this field, including: 1) The development of an integrated embedded controller. The control system could be realized based on an ARM (Advanced RISC Machine) processor. The processor could be used to get the sensor data, perform the optimization algorithm calculation, and give voltage signals toe the five valves. 2) Research into the other features of the bridge circuit, such as adaptive cushioning, which can be performed by replacing the traditional physical cylinder cushioning and controlling the open-and-close sequence of switch valves. To realize adaptive cushioning, acceleration in the cylinder operation could be the optimization target to replace the air consumption, compared to energy saving research. 3) The digital control valve would be developed based on the proposed bridge circuit. The structure of the valve can be realized based on the idea of piezoelectricity. This could ensure the accuracy of the control sequence of the switching valve in the bridge circuit.

H. Du et al. / Journal of Cleaner Production 254 (2020) 119983

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Hongwang Du: Writing - review & editing, Conceptualization, Methodology. Chaochun Hu: Writing - original draft. Wei Xiong: Visualization, Investigation, Supervision. Zhong’ai Jiang: Validation. Lu Wang: Data curation. Acknowledgment The work in this paper was supported by the National Natural Science Foundation of China (51175053) and the Fundamental Research Funds for the Central Universities of China (3132019117 and 3132019352). We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript. References Beater, P., 2007. Pneumatic Drives: System Design, Modelling and Control. Springer Verlag.

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