Page 608 - Mechatronics with Experiments

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pump efficiency of 80% and neglecting the losses at the valve? Assume 100% efficiency for the
hydraulic motor. See Figure 7.83.
3. Consider the two-axis hydraulic motion system shown in Figure 7.13. The system is to operate
under the control of an operator. The operator commands the desired speed of each cylinder by two
joysticks. There is no need for sensors since this is an operator in the loop control system. Cylinder
1 needs to be able to provide a force of 5000 Nt at a rated speed of 0.5m∕s, and maximum no-load
speed of 1.0m∕s. Cylinder 2 needs to be able to provide 2500 Nt force at the same rated speed, and
has the same maximum no-load speed as cylinder 1.

(a) Select components and size them for a completely hydro-mechanical control of the system.
There should be no digital or analog computers involved. Draw the block diagram of the control
system, and indicate the function of each component in the circuit. Assume that we use a fixed
displacement pump. As a designer make decisions regarding the anticipated realistic pressure
that can be delivered at the cylinder ports and decide on a realistic cylinder bore size.
(b) Select components for an embedded computer controlled system. Discuss the differences between
this design and the previous design in terms of the components and their differences.
4. Consider hydraulic fluid in a hydraulic hose that has some entrapped air in it. Let the hose
diameter be D = 6 in and wall thickness of the hose is x = 1 in. Let the Young’s modulus of the hose
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material be E = 30 × 10 psi. Determine the effective bulk modulus for zero and 1% air entrapment,
for operating pressures of 500 psi and 5000 psi.
5. Let us consider a single axis EH motion control system with the following parameters. For
the cylinder bore diameter, consider the following size information: d = 10 cm, and the rod
bore
diameter d rod = 5cm, stoke is L = 1.0 m. Let us approximate the bulk modulus of hydraulic fluid to
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5
be 2.5 × 10 psi = 1.723 × 10 Pa = 1.723 GPa. The mass carried by the cylinder (including the mass
of the rod and piston and load) is M = 200 kg.
(a) Determine the lowest natural frequency of the system due to the compressibility of the fluid in
the cylinder and the inertia.
(b) What is the maximum recommended closed loop control system bandwidth?
6. Consider a single axis electrohydraulic motion control system as shown in Figure 7.90 and its
block diagram representation in Figure 7.89. We assume that the cylinder is rigidly connected to its
base and load. Let us consider the small movements of the valve around its null position, that is a
case that is maintaining a commanded position.
1. amplifier gain is K = 200 mA∕10 V = 20 mA∕V,
sa
3
3
2. valve gain around the null position operation, K = 20 (in ∕s)∕200 mA = 0.1(in ∕s)∕mA,
q
2
3. cross-sectional area of the cylinder is A = 2.0in on both sides (rod is extended to both sides),
c
4. the sensor gain is K = 10 V∕10 = 1 V∕in,
fx
5. deadband of the valve is 2% of the maximum input current, i db = 0.02 ⋅ i max = 0.02 ⋅ 200 mA =
4mA.
2
Assume that the total inertial load the cylinder moves is W = 1000 lb, m = 1000 lb∕386 in∕s =
2
2.59 lb s ∕in, and the cylinder is currently at the mid position of its total travel range of l = 10 in.
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Note that the approximate bulk modulus of the hydraulic fluid is = 2.5 × 10 psi.
In terms of the amplifier gain, what is necessary to reduce the positioning error? Is there an
upper limit set on the value of the amplifier gain? If so, determine that limit. Discuss the limitations
imposed on the amplifier gain by the small positioning error requirement and closed loop system
stability. Determine the amplifier gain that provides the maximum practical closed loop bandwidth
while minimizing the positioning error due to the deadband of the valve.
7. Consider the single axis EH motion control system shown in Figure 7.85. The system needs to
operate in two modes under the control of a programmed embedded computer:
Mode 1: closed loop speed control where the commanded speed is obtained from a programmed

command generator. The cylinder speed is measured and a closed loop control algorithm
implemented in the electronic control unit (ECU) which controls the valve.