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In terms of negative feedback, there exists an analogy between the operational amplifier and the power-steering mechanism of an automobile. The hydraulic pump is analogous to the power supply in an op-amp circuit. The position of the booster-cylinder piston that is linked to the steering is analogous to the op-amp output signal; the mechanical linkage between the control valve and the booster-cylinder piston is analogous to the feedback circuit; the control-valve response to the difference between the input from the steering wheel and the position of the steering linkage is analogous to the op-amp response to its differential input signal. Thus the automotive power- assisted steering system is but an example of negative feedback in a mechanical sense.
Figure 5.6.1 illustrates in a simplified manner how a hydraulic pump driven by the engine continuously supplies pressure to a control valve which in turn supplies the fluid to the two sides of the booster cylinder. A negative feedback path is established from the booster cylinder through the mechanical linkage back to the control valve.
For straight steering, the pressure applied is equal on both sides of the cylinder and, as such, no turning force results.When the steering wheel is moved by the driver to turn the wheels in the desired direction, more pressure is applied to one side of the cylinder or the other. A mechanical feedback arm from the steering linkage causes the valve to return to its neutral position as the wheels turn, thereby allowing the driver to make a gradual turn. As and when the steering wheel is turned, the wheels move a proportional amount rather than moving all the way to the extreme position.
Q. Sketch the idealized (asymptotic) Bode plot for the transfer function Find the angular frequency at which H(ω) is 0dB and the angular frequency at which θ(ω) = -60°.
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