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Equivalent Spring-Mass-Damper system alongwith pneumatic circuit |
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Integrator action can be physically interpreted in following manner |
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It is equivalent to a pneumatic circuit containing flow control valve , 4/2 directional control valve & double acting cylinder. Difference in position or error will control the flow of air to cylinder. Air is compressible. When there is slight difference in reqd. and actual position there will be very small flow of air to the cylinder. As time elapses being no movement of piston pressure of air in cylinder starts increasing (this can be considered as integration over time) & one stage will come where the pressure is such that force exerted due to it on block + spring force will overcome the damping force reqd. to move the block with certain velocity. Hence there will be movement of block which will lead to the reduction of position error. But the reduction in error reduces spring force . So more time will be required for next integrator action than previous one. In this way the steady state error is eliminated. But certain time is required for this action to take place. |
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Explaination is here comes one situation for which the amplitude of vibration is so small that restoring spring force will be very small & if it tries to move the block it cannot do it. Because as soon as block starts moving Damping force comes into picture which will be very high as compared to the spring force( which is function of deflection). Hence the block will come to rest at a position other than BB'. So there is inherently steady state error whenever we will use Proportional & Derivative Control action. But this steady state error is not permitted in certain applications. correct it |
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