Question

Design a circuit with one input, x(, and one output, y(, that are related by this differential equation: l d2 2 dt2 '(t) =--x(t

Answer 1

Hi, Please find the solved problem below in the form of photos. The first page describes how to convert the given differential equation in time domain to laplace domain. After that we write the plant transfer function in the form of intergrators, adders/subtractors.

now the second image is attached below.

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In the second page, we discuss about a common generic electrical equivalents for intergrators and adders/subtractors. The derivations are given in the link given below.

https://www.electronics-tutorials.ws/opamp/opamp_5.html

now the third image is uploaded below. this is the actual electrical equivalent of the given equation

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n the third page we directly drew the circuit with all the electrical equivalents. to make an adder, I inverted the input given to the negative terminal of the opamp by using a unity gain subtractor. Then a gain 2 is created with another gain amplifier.Finally the two outputs are added and given to the positive terminal of the subtractor. This completes the given differential equation.

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That's all. Thanks for the opportunity.