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CHAPTER 6

EXPERIMENTAL STUDY-VIBRATION CONTROL OF

MECHANICAL SUSPENSION SYSTEM

6.1 INTRODUCTION

Due to cost constraints, practical implementation of feedback

control strategy to a laboratory scaled vibration isolator platform is developed

for a single degree of freedom mechanical system. The research is carried out

to investigate the performance of vibration suppression capability of feedback

controller. FLC have been used in many applications like cruise control,

automatic transmissions, cold-rolling mills, image stabilizer for video camera

and a fully automated washing machine. With the proven diversity of FLC, it

is chosen to control the vibration of a mechanical suspension system. Hybrid

techniques using GA/PSO fuzzy logic are applied to typical mechatronics

problem domains because of their inherent capabilities of handling

imprecision and uncertainty with reasonable amount of computational

complexity. Maziah et al (2006) used a physical test rig for vibration isolation

using active force control strategy implemented with Matlab.

Implementation of a fuzzy logic applied to a laboratory scaled

vibration isolator platform is proposed in this work. The laboratory scaled test

rig is developed using LabVIEW simulation that is interfaced with a suitable

data acquisition card (NI USB 6008) via a personal computer as the main

controller. Appropriate vibration source is applied to the proposed system to

test for the system robustness. Experimental results demonstrate the potential

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and superiority of the proposed scheme as a robust vibration suppressor

compared to the other scheme considered in the study.

6.2 ACTIVE VIBRATION CONTROL

Active vibration control is the application of force in an equal and

opposite fashion to the forces imposed by external vibration. With this

application, a precision industrial process can be maintained on a platform

essentially vibration-free.

Figure 6.1 Active vibration control

Force balance equation for an active vibration control system

shown in Figure 6.1 is given as

m( d x/ dt ) = F( t) C ( t ) F (6.1)

where ( ) - displacement of the mass

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- spring constant

C - Damper constant

F - Actuator Force

F( t) - force due to External Vibration source (disturbance).

An active vibration control is a method that relies on the use of an

external power source called actuator (e.g. a hydraulic piston, a piezoelectric

device or an electric motor). The actuator provides a force or displacement to

the system based on the measurement of the response of the system using

feedback control system. Figure 6.1 shows a schematic of an active vibration

control system and it works by measuring the response of the system using

suitable sensors. Sensor output is given to the computer through NI USB 6008

interface card. Based on the control algorithm used, the calculated force signal

is given to the actuator and the controlled force is correspondingly applied to

the system. The actuator force will actually compensate the vibration force in

the system. PID, FLC and PSOFLC are the three control algorithms used in

the experimental study. In addition sliding mode control strategy is also

implemented to the experimental setup.

In active vibration isolation system, feedback circuit consists of an

accelerometer, LVDT and a signal conditioning circuit. The spring supports

the weight of the mass table. The displacement of the mass is detected by a

LVDT displacement transducer. As a result of feedback control action,

stronger suppression of vibrations is achieved as compared to ordinary

damper.

6.2.1 PID Controller

A typical PID control law that can be used in the active vibration

control system is as follows

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G =K e + K e dt + K e (6.2)

where G - control signal

K , K and K - proportional, integral and derivative gains

respectively

e, and e : joint position error, its derivative and integral

respectively

The control signal is a sum of three terms: P term (proportional to

the error), I term (proportional to the integral of the error), and D term

proportional to the derivative of the error). PID controller takes the present,

the past and the future of the error into consideration. PID controllers (P, PI,

PD and PID) can be realized by simply exploiting the controller gains.

Zeigler-Nichols method is used to tune the PID parameters.

6.2.2 Fuzzy Logic Controller

Block diagram of the FLC based vibration control for mechanical

suspension system is shown in Figure 6.2. Actuator dynamics is not

considered for controller implementation. The inputs of the FLC are the

displacement and velocity of the vibrating mass and the output variable is the

voltage which is then converted into current and then applied to the pneumatic

actuator. The input and output membership functions of FLC are given in

Figure 6.3. To avoid trial and error method of tuning the FLC membership

functions, PSO is used to tune the membership functions of the FLC to ensure

optimal control performance. RMS value of displacement is taken as the cost

function and the optimized membership functions of the FLC are shown in

Figure 6.4(a)-(c). The rules are listed as follows.

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If displacement is LOW and velocity is LOW then actuator is CLOSE LOW.

If displacement is LOW and velocity is GOOD then actuator is CLOSE LOW.

If displacement is LOW and velocity is HIGH then actuator is OPEN MEDIUM.

If displacement is GOOD and velocity is LOW then actuator is CLOSE LOW.

If displacement is GOOD and velocity is GOOD then actuator is OPEN MEDIUM.

If displacement is GOOD and velocity is HIGH then actuator is OPEN FAST.

If displacement is HIGH and velocity is LOW then actuator is OPEN FAST.

If displacement is HIGH and velocity is GOOD then actuator is OPEN FAST.

If displacement is HIGH and velocity is HIGH then actuator is OPEN FAST

Figure 6.2 Block diagram of FLC based mechanical suspension system

Figure 6.3 Membership functions of input and output variable

Input Output

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Figure 6.4(a) Membership function of displacement

Figure 6.4(b) Membership function of velocity

Figure 6.4(c) Membership function of voltage

6.2.3 Sliding Mode Control

SMC technique is designed to drive the state trajectory towards the

sliding surface. Sliding mode controller design starts with the design of the

sliding surface that ensures the stability of the system. Let the time varying

switching surface, S(x, t) = 0 in the state space

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S(x, t ) = + c e( t) (6.3)

‘c’ is strictly positive. Displacement of the vibrating mass is taken as the

error. The control law that satisfies the sliding mode condition for the system

is given by equation (4.7) as discussed in chapter 4. Vibration isolation is

validated using SMC. SMC algorithm is validated experimentally.

6.3 ACTIVE VIBRATION ISOLATOR (AVI)

The design of an AVI experimental rig is based on the working

principle of active vibration control through sensors, actuators and control

techniques within the mechanical structures. Figure 6.5 shows the proposed

design schematic for Test rig using digital controller and the experimental rig

is shown in Figure 6.6. It is an integration of the mechanical parts,

electric/electronic devices and computer control to make the rig functional as

an active vibration isolator.

Figure 6.5 Block diagram of proposed rig

Pneumatic actuator is used for its quick response and safe

operation. The components used to build this actuator are double acting type

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of pneumatic cylinder, eletcro-pneuamtic positioner (i.e.) an I/P converter and

an electronic positioner, air-filter and regulator. Electro-Pneumatic actuator is

chosen because it matched the demand, control configuration and cost.

Random disturbances are produced by the vibrator motor which is placed on

top of the mass table. Vibrations are generated by an electric motor (220 V,

50Hz) with an unbalanced mass on its drive shaft.

Figure 6.6 Active vibration isolator rig

AVI rig integrates both the software and hardware elements

through NI USB 6008 interface card.

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6.4 EXPERIMENTAL RESULTS

The parameters of the AVI rig are listed as follows.

Size of the frame:

Length - 600*10 m

Breadth - 400*10 m

Mass of the table - 6 kg.

Spring constant - 300N/m

Pneumatic Actuator:

Cylinder diameter - 25*10 m

Cylinder height - 140*10 m

Pressure limit - 1 bar

Maximum travel - 25*10 m

Analog signals from the accelerometer and displacement sensor are

given to a digital computer by using DAQ card NIUSB6008. Computer

generates a signal to be given to the pneumatic actuator for nullifying the

effect of disturbance on the mass. Voltage signal is taken through the output

ports of the DAQ card and is converted into a current signal by a suitable V/I

converter. This current signal is given as the input to the electro pneumatic

actuator which produces the control force to suppress the vibrations. The

flowchart describing the procedure of vibration control of the mechanical

suspension system in LabVIEW platform is given in Figure 6.7.

Vibration isolation is validated using PID, FLC, PSOFLC and SMC

algorithms. System parameters and conditions are maintained the same for all

the schemes except for the vibration frequency. Random vibration frequency

is increased by altering the unbalanced mass on the vibration motor for

validating the SMC algorithm.

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Vibration isolation of the mechanical suspension system is

achieved experimentally with the help of feedback controllers in an active

mode. For PID controller, proportional, integral and derivative gains are

tuned through Zeigler-Nichols approach. Tuned PID parameters are K = 3 ,

K = 20 and K = 0.01. The position and acceleration signals are measured

using sensors installed at a suitable position in the rig. The experiment has

been carried out for the random frequency generated by the vibration motor.

Random vibrations are generated by an electric motor with an unbalanced

mass on its drive shaft.

Figure 6.7 Flow chart for vibration control of mechanical suspension

system

(0-5V)

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Figure 6.8 Displacement of mass in passive mode

Figure 6.9 Displacement of mass– PID

Figure 6.10 Displacement of mass – FLC

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Figure 6.11 Displacement of mass – PSOFLC

Figure 6.8 shows the displacement response for the passive mode of

operation. Difference between the peak undershoot to peak overshoot is about

1.5 cm. Figure 6.9 illustrates the displacement response for a PID controller.

Actuator represents the control input to the AVI system. As the control signal

builds up the displacement of the vibrating mass is brought down. Figure 6.10

reveals that FLC gives a better performance than PID and the displacement

nearly reaches equilibrium position. It is obvious from Figure 6.11, by using

PSOFLC technique the mass is perfectly brought to the equilibrium position

in a faster time and hardly any vibration occur. It is demonstrated that

vibrations are completely brought down by the active mode and at the same

time PSOFLC performs better than FLC and PID in terms of settling time.

FLC based control produced faster settling time of 5 seconds compared to

20 seconds by FLC and 35 seconds for the PID scheme.

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Figure 6.12 Acceleration in passive mode

Figure 6.13 Acceleration in active mode – PID

Figure 6.14 Acceleration in active mode – FLC

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Figure 6.15 Acceleration in Active Mode - PSOFLC

Figures 6.12-6.15 represent the acceleration response of the

mechanical suspension system for passive, PID, FLC and PSOFLC based

controller respectively. Figure 6.13 illustrates that after 35 seconds

acceleration is brought to almost zero by PID control scheme. Figure 6.14

shows an improvement in the acceleration performance by the FLC scheme

and the acceleration is brought down to zero after 20 seconds. PSOFLC based

active vibration isolation provides smooth response and it is obvious from

Figure 6.15 where acceleration is almost zero by 5 seconds. Thus all three

active vibration control schemes have shown the capability to suppress the

vibration up to 98%. It is demonstrated from the experimental results, that

PSOFLC based active vibration control provided better performance than its

counterpart. It clearly shows that working of PSOFLC performs better than

PID with quick response action.

Figure 6.16 shows the displacement of the vibrating mass for SMC

scheme. Random frequency is increased for the SMC of AVI system.

Difference between the peak undershoot to peak overshoot is reduced from

16mm to about 1.2 mm. Vibrating mass is brought to the equilibrium position

by 1 second. Figure 6.17 illustrate the SMC based acceleration response of the

AVI system. Experimental results prove the effectiveness of the SMC scheme

in vibration isolation of the mechanical suspension system.

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Figure 6.16 Displacement - SMC

Figure 6.17 Acceleration - SMC

6. 5 CONCLUSION

AVI test rig has been developed in real time and control of

vibrations using the PID, FLC, PSOFLC and SMC with the help of the

LabVIEW software is experimented. From the experimental results it is

observed that the system could be maintained in an equilibrium position by

arresting the vibrations given externally from the vibration source (vibrator

motor). From the results obtained, it is clear that the active vibration isolator

using FLC gives a better performance than PID and passive isolator. Overall,

the PSOFLC control scheme gives the better performance in compensating

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the disturbances (vibrations at random) introduced into the suspension system.

This clearly demonstrates the potential of the PSOFLC scheme to be

implemented in real-time arising from the fact that the control algorithm is

mathematically simple and computationally not intensive. Effectiveness of the

SMC is also demonstrated for AVI setup.