1997 AISE Annual Meeting
Brian Thomas Boulter
Applied Industrial Control Solutions
231 Skyview Drive
Seven Hills, OH, USA 44131
Applied Industrial Control Solutions
231 Skyview Drive
Seven Hills, OH, USA 44131
© ApICS ® LLC 2000
Abstract - Long portable conveyors used in underground mining applications are currently configured with clutch-type secondary pulleys (trippers) that compensate for tension losses in the conveyor line. To increase the profitability of mining operations it is desirable to increase the length of the mining seams and hence the conveyors. However, as the conveyor length increases the tripper clutch size and cost become prohibitive. To dissipate the absorbed regenerative energy that arises when regulating belt tension, larger clutches require cooling with water or oil cooling systems. Given that the infrastructure required to support such cooling systems is itself expensive and difficult to move the use of active tension regulation with AC or DC drives, which require only an electric feed and are relatively inexpensive and easy to move, provide a cost effective solution. To this point the use of active tension regulation has been avoided due to stability problems associated with the tension regulator. This paper outlines a regulation scheme that addresses these problems and paves the way for cost effective underground mining conveyor solutions using AC or DC drives.
1. INTRODUCTION
Underground mining operations utilize portable conveyors to move material from active mining seams to a central material handling facility. The conveyors must be easily assembled and disassembled to facilitate quick turn around times when moving operations from a depleted seam to a fresh seam. To improve mine productivity, seam lengths and tonnage rates are increasing. Site engineering managers, in their search for cost effective material handling solutions, are specifying longer conveyors, higher material tonnage rates and lower material handling energy costs. As will be shown in later discussion, a cost effective solution for conveyor belt-tension regulation can be achieved using active AC or DC drives rather than passive clutch-based designs. Following is a short description of the typical tripper assisted mining conveyor.
Figure 1. Single Tripper Assisted Conveyor
A tripper assisted underground mining conveyor line with a single tripper consists of a belt used to convey the material, a head pulley with a speed regulated head drive, a secondary pulley (tripper) with a tension regulated secondary drive, a winch driven accumulator, and a tail pulley (Figure 1).
The head pulley sets the conveyor speed and is usually configured as an AC motor that is directly connected to the AC feeder mains. The motor is sized to rotate at top speed at an armature voltage slightly below the feeder line voltage. A mechanical clutch is used to ramp-up the conveyor translational speed to match the AC motor rotational speed. Speed regulation is accomplished by a closed loop (SML) that provides a trim reference (PREF) to the clutch pressure loop (CPL). The CPL may be operated as an open or a closed pressure loop depending on the O.E.M. clutch configuration. The secondary pulley (or tripper) is usually configured as an AC motor that operates in much the same way as the speed regulated pulley with the exception that the trim reference to the clutch pressure loop is provided by a closed tension loop (TML) with feedback from a load cell, similar to that shown in Figure 1. The Accumulator is used to store and release conveyor belt as needed as the tail pulley is moved along the seam that is being mined. The winch is typically driven by an AC or DC motor that is configured as an open loop current or torque regulator (CML). The current or torque reference is set to provide a desired belt tension at or near the head pulley. The tail pulley is not driven but is designed to be easily moved as mining operations move along the active seam.
Figure 2. Single-Line Diagram of the Clutch Tension-Regulated Mining Conveyor.
The tension regulated clutch of the tripper is always in a state of slip and, as a result, heat is constantly generated in the clutch assembly. As described above, a cooling system must be installed on trippers with sufficiently high loads. If a DC or AC drive can be used, the regenerative energy that results from regulating belt tension can be put back into the electric feeder mains as electric energy instead of into the mine shaft environment as heat energy. Figure 3 presents a single-line diagram of the proposed scheme.
Figure 3. Single-Line Diagram of the Drive Tension-Regulated Mining Conveyor.
The tripper CML’s must be designed with regenerative power units to allow for an energy flow from the motor to the feeder mains. Significant energy savings and more responsive tension regulation can be realized with this control topology if the tension regulator is designed with a stable and responsive closed tension loop.
Implementing the tension regulator shown in the architecture described in Figure 3 with a PI only regulator will invariably result in an unstable or extremely de-tuned tension loop. The PI regulator by itself cannot adequately compensate for extremely low frequency damped plant resonances such as those that occur in conveyor applications. A regulation scheme that adequately compensates for the low frequency damped poles and provides a significant improvement in tension regulation as well as significant reduction in energy costs is presented in section 3.
In Section 2, a simple linear model of the conveyor is developed and analyzed. Transfer functions are developed that provide a good approximation of the plant as seen by the tension regulator. These transfer functions provide the basis for determining the regulator structure in section 3. In Section 4 a brief energy analysis that provides a clear energy cost comparison between the current and proposed schemes is presented. Section 5 closes with some concluding observations and remarks.
2. CONVEYOR MODEL DERIVATION
2.1 NOMENCLATURE
JMOTOR
|
The motor inertia [lb ft^2]
|
JLOAD
|
The reflected pulley (load) inertia [lb ft^2]
|
Ji
|
The i’th lumped inertia JMOTOR + JLOAD [lb ft^2]
|
wi
|
The i'th motor rotational velocity feedback [rpm]
|
qi
|
The i'th motor shaft position [rad]
|
wCMLi
|
The i'th CML bandwidth [rad/sec]
|
KH
|
The head pulley speed loop PI proportional gain
|
wSH
|
The head pulley speed loop PI lead freq. [rad/sec]
|
wCO
|
The i'th speed loop crossover [rad/sec]
|
Ri
|
The i’th pulley radius [ft]
|
GRi
|
The i’th pulley gear ratio
|
Li
|
The i’th tension zone length [ft]
|
Ti
|
The i’th tension zone tension [lb]
|
ti
|
The i’th pulley reflected shaft torque [lb ft]
|
tMAX
|
The i’th motor maximum torque [lb ft]
|
iMAX
|
Maximum CML current. [A]
|
E
|
Belt modulus of elasticity [psi]
|
A
|
Belt cross sectional area [in^2]
|
s
|
The Laplace operator
|
LS
|
Maximum conveyor speed [ft/min]
|
Ki
|
The belt-spring constant (see Eq. 8)
|
tV
|
Belt-span velocity time-constant (see Eq. 9)
|
Wi
|
The span natural frequency [rad/sec] (see Eq. 12)
|
 |
The i'th motor gear-in speed [rpm]
|
2.2 CONVEYOR MODEL
Figure 4 Linearized Conveyor Plant Model
A linearized form (1) of the tension equation described in [1], [2], and [3] and the motor torque balance equation (3) can be combined to develop an approximate linear model of the conveyor (Figures 4 and 5). The model assumes operation with a fixed amount of storage in the accumulator and neglects the non-linear dynamics associated with the bulk movement of the belt and haulage material as described in [1].
(1)
where: 
(2)
(2)
The motor/load torque equation is given as:
(3)
Figure 5. Approximate Linear Conveyor Model
The conveyor belt and haulage-material masses are included in the model by lumping their combined masses at the center point of each belt span, therefore L1 = L2, L3 = L4, and L5 = L6 in Figure 4.
In most mining conveyor applications the accumulator is located very close to the head pulley, therefore the mass of the belt between these two sections can be neglected. The roll inertias in the accumulator are lumped into a single inertia and the stored belt mass and length are lumped with the belt on the side of the accumulator that is away from the head pulley.
The head pulley speed controller GH(s), motor, and clutch are modeled as a PI regulator and a first order lag (Equation 4). The lag corner frequency wCL approximates the bandwidth of the clutch’s pressure loop. The gain term KS is the product of the PI proportional gain and the gain term from the current reference to shaft torque.
(4)
The accumulator current loop GACC(s) (Equation 5), motor and winch are also modeled as a first order lag, the lag corner frequency wACC approximates the bandwidth of the CML. The gain term KA represents the gain from the current reference to shaft torque
(5)
From the analysis of cascaded mass-spring systems in [6], the transfer function from the tripper motor shaft torque tT to the load-cell feedback T2 can be approximated as:
(6)
The dominant low frequency system resonance corner frequency wTEN can be crudely approximated as follows (Equation 7). Care should be taken to ensure the units are correct. For example, the mass in [slugs] and the spring constant in [lbf/ft].
(7)
Experience has shown that considerable damping of the dominant low-frequency pole pair results directly from the conveyor belt construction and the substantial viscous, static and dynamic friction that is found in such systems. The dominant low frequency pole pair is always over-damped in mining conveyor systems. The lower of the two real poles falls in the frequency range of 0.01 to 1 [rad/sec] with the belt loaded, and 0.05 to 5 [rad/sec] with the belt unloaded. The higher of the two real poles falls in the frequency range of .1 to 10 [rad/sec] (belt loaded), and .5 to 50 [rad/sec] (belt unloaded). Additional pole and zero pairs that occur at higher frequencies tend to cancel and do not contribute significantly to the dynamics of the tension control loop.
3. TENSION REGULATOR
3.1 LINEAR ANALYSIS
Using a PI controller for the tension regulator (GT(s)) the asymptotic Bode plot shown in Figure 6 approximates the open loop transfer function (Equation 9) from tripper tension reference to tension feedback. The gain term KT is the product of the PI proportional gain and the gain term from the current reference to shaft torque.
(9)
Figure 6. Asymptotic Bode Plot of Open Tension Loop (PI Only)
Assume that the tension loop PI lead frequency (i.e. Ki/KP) is tuned to approximately cancel the lower frequency pole (wR1) of the two dominant real plant poles for the loaded conveyor condition. From Figure 6, it is clear that poorly damped tension regulator designs will result for regulators that are tuned with bandwidths (or crossovers) greater than 1/5th of the higher plant pole frequency wR2. Given that wR2 can be as low as 0.5 [rad/sec] loaded, the best tension loop bandwidth that can be expected in the loaded condition is 1/10th [rad/sec]. While this tuning may yield adequate response unloaded, the belt tension will tend to wander when loaded. The resulting lack of low-frequency gain and bandwidth will result in the inability of the loop to adequately regulate tension in the loaded condition.
Figure 7 presents a tension regulation scheme that has been implemented successfully in mine conveyor applications. The use of forcing on the current reference with a lead/lag compensator and a non-linear limiting circuit, discussed in the next section, provided a control structure that allowed for belt-tension regulation regulator bandwidths in the range of 3-7 [rad/sec], a significant improvement over the PI only regulator design.
Figure 7. Tension Regulation Scheme With Lead/Lag Compensator
The approximate linear open loop transfer function of the tension regulator with lead/lag compensation is given below (9).
(9)
Note that the lead/lag compensator lag frequency must be chosen such that the system remains stable in both loaded and unloaded operating conditions. To achieve this result, the lag should be set at approximately twice the crossover of the tension loop with the conveyor unloaded. In addition, to avoid excessive amplification of system noise, the ratio of lag to lead frequencies in the lead/lag compensator should be less than or equal to 10. Applying these two design constraints to (9), the following tuning strategy (10) can be derived.
(10)
To demonstrate the design using the model in Figure 5, Figures 8 and 9 are Bode plots for the transfer functions from tT toT2, and TTR(REF) to T2 (closed tension loop) respectively. The transfer function from tT to T2 is plotted with and without damping. The transfer functions for both fully loaded and empty conveyor conditions are plotted on each Bode plot. The following parameters were used in the model:
Belt Parameters:
| |
E
|
12 e5 [psi] (Combination - rubber and steel)
|
A
|
24 [in^2] (Cross sectional area)
|
d
|
60 [lb / ft^3] (density)
|
Regulator Parameters:
| |
wS
|
10 [rad/sec]
|
KS
|
100
|
wCL
|
150 [rad/sec]
|
wACC
|
150 [rad/sec]
|
KA
|
100
|
KTEN
|
100
|
KT
|
100
|
wT
|
150 [rad/sec]
|
wLD
|
150 [rad/sec]
|
wLG
|
150 [rad/sec]
|
Plant Parameters:
I
|
Ji [lbft^2]
|
WI [lb]
|
LI [ft]
|
Ki[ft]
|
1
|
n/a
|
0.11e5->1.25e5
|
1250
|
n/a
|
2
|
n/a
|
0.11e5->1.25e5
|
1250
|
n/a
|
3
|
n/a
|
0.21e5
|
1250
|
n/a
|
4
|
n/a
|
n/a
|
1250
|
n/a
|
5
|
n/a
|
n/a
|
2250
|
n/a
|
6
|
n/a
|
n/a
|
2250
|
n/a
|
7
|
n/a
|
n/a
|
500
|
n/a
|
H
|
350
|
n/a
|
n/a
|
0.5
|
TR
|
450
|
n/a
|
n/a
|
0.5
|
TL
|
50
|
n/a
|
n/a
|
0.5
|
ACC
|
450
|
n/a
|
n/a
|
0.5
|
Figure 8. Bode Plot of tT to T2 (w/o damping included)
Figure 8. Bode Plot of tT to T2 (damping included)
Figure 9. Bode Plot of TTR(REF) to T2
3.2 TENSION REGULATOR NON-LINEAR ANALYSIS
The tuning strategy described above employs pole-zero cancellation. Typically pole-zero cancellation in the forward path is not desirable because it results in poor recovery from loop saturation [7]. However, in this application it will be shown that uncontrolled loop saturation in the tension regulator does not occur during normal operation. To facilitate a better understanding of the philosophy driving the proposed regulator structure a description of the clutch-type tension regulated tripper follows.
In this implementation clutch pressure is increased (to reduce slip, increase tripper speed and reduce tension in the belt) only when the tension feedback exceeds a pre-set tension set-point. The tension set-point is chosen to bound belt-strain at or below a design margin of safety, if the tension feedback is less than this value no action is taken. The reason for applying this strategy is straight-forward, belt tension increases as material is mined and loaded on the conveyor, to protect the physical integrity of the belt the tension regulator is only required to regulate (i.e. lower) belt tension when safe belt strain is exceeded.
A similar non-linear control strategy may be employed using DC or AC drive technologies, Figure 10 is a block diagram of a tension regulator that exhibits such behavior. The basic concept of operation follows: If the error is less than zero a compare block outputs a Boolean that resets the lead/lag filter in the forward path. When the reset is true the lead/lag compensator will pass the integer at the ‘IV’ input (-5 is shown) directly to its output. Therefore a condition where belt tension is less than the set-point will result in the controller effectively running open loop while slowly discharging the integrator in the PI. As the integrator discharges, belt tension will increase until the negative error passes through zero. When this occurs the regulator operates as a linear tension regulator and reduces tension. To avoid wind-up in the integrator a limit block after the PI clamps both the CML reference and the PI integrator whenever a positive or negative limit is reached in the CML reference.
Figure 10. Tension Regulator Block Diagram
The nature of the application is such that the rate of change in belt tension is always slow relative to the bandwidth of the tension loop (i.e. as material is loaded onto an empty belt, or as the integrator discharges), in addition all tension command references are ramped such that their rate of change is also slow relative to the bandwidth of the tension regulator, this results in smooth transitions in and out of the linear regulation mode at all times. Assuming that the expected tension drop across the bridle never exceeds the design maximum, the tension regulator design philosophy inherently prevents the occurrence of loop saturation.
4. ENERGY COST ANALYSIS
The use of regenerative drives in the tripper can result in significant energy savings, The following analysis provides an enlightening perspective on the potential for energy cost reduction using active regulation with drives as opposed to passive regulation with clutches.
The relationship between the power that is to be regenerated in the tripper and the tension drop across the tripper is given in Equation (11).
(11)
The energy cost per-hour associated with wasting this energy in the form of heat is:
(12)
Assuming an efficiency rating of 85% in the regeneration process the energy savings can be approximated as:
(13)
Using typical values in Eq’s 11,12, and 13, (600 [ft/min] conveyor speed, motor base speed of 1150 [r.p.m], roll radius of 1.5 [ft], gear ratio of 16:1, energy cost of 0.5 
2.5 [cents/kW hr]), assuming the conveyor down-time is 5%, and the average tension drop across the tripper is 20000 [lb], the net energy savings per year can be approximated as:
2.5 [cents/kW hr]), assuming the conveyor down-time is 5%, and the average tension drop across the tripper is 20000 [lb], the net energy savings per year can be approximated as:
In addition to the expected energy savings from regeneration, the cost of operating the tripper cooling system can be a significant energy cost (approximately 1k 5k [$/yr]). Additional cost reductions can be realized from the time saved when moving the tripper. These savings will depend on the disassembly/assembly-crew work-efficiency and could vary from 1 to 10 production days per year (or cost savings equivalent to as much as 3% of the mine operating profit).
5k [$/yr]). Additional cost reductions can be realized from the time saved when moving the tripper. These savings will depend on the disassembly/assembly-crew work-efficiency and could vary from 1 to 10 production days per year (or cost savings equivalent to as much as 3% of the mine operating profit).
An additional cost consideration must be made with respect to the drive technology used. If DC drives are used, regeneration is straight forward and is accomplished with the use of a 12 or 24 diode power-module with bridge-reversing capabilities. The use of AC drive technology will require two inverters and an interim DC buss. The initial cost of the AC solution is therefore higher than the DC solution. The main advantage that is realized when employing the AC solution is that the AC motor does not require brush maintenance and the frame sizes are smaller resulting in a reduction in the expense of the motor.
5. CONCLUSIONS
In long conveyor applications that employ trippers, AC and/or DC static drives can provide a cost effective solution for regulating tension, if a stable tension regulator can be designed. The tension regulation scheme that is presented here-in has been shown in both simulation and field testing to provide a stable and responsive tension regulator architecture for these applications.
In the process of designing material handling solutions for mines, mining engineers should consider the cost benefits resulting from deploying AC/DC drives for tripper assisted conveyor belt tension regulation.
References
[1] Boulter, B.T. Fox, H.W.,"Advanced Dynamic Simulation", ApICS LLC Training Course Material 2000.
[2] Carter, W.C., "Reducing Transient Strains in Elastic Processes" , Control Engineering Mar. 1965. pp. 84-87.
[3] Wolferman, W., "Tension Control of Webs - A Review of the Problems and Solutions in the Present and Future", Tab 15,Proceedings of the 3rd IWHC International Web Handling Conference, Oklahoma State University June 1995.
[4] Fox, S.J., Lilley, D.G., "Computer Simulation Of Web Dynamics", Proceedings of the 1st IWHC International Web Handling Conference Tab 20. Oklahoma State University, March 1991.
[5] Lin, K., "WTS 6.0 A Computer-Based Analysis Program For Multi-Span Web Transport Systems", Oklahoma State University 1994.
[7] Clark, R. N., "Another Reason to Eschew Pole-Zero Cancellation" , IEEE Control Systems Magazine, April. 1988. pp. 87-88.
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