PID controller is reportedly widely built and used in control systems engineering for industrial applications. The PID-controller has a transfer function as: (Kd*s^2+Kp*s+Ki)/s.
Therefore, it seems such a transfer function box, could be built in terms of an electronic circuit component.
Meanwhile, the order of an observer-based controller is higher than a PID-controller, as for example you see in the snap-shot from Ogata control engineering book, attached. Since Ogata is a practical engineering text-book, therefore I guess such an observer-based controller could be practically built as an electronic circuit and then embedded as a controller.
Moreover, we usually build transfer function blocks, simply in Matlab Simulink. But is it possible, practical, simple, and convenient to build such blocks as an integrated electronic element in a circuit, while they are of high order?
My main question:
There is a controller, with a transfer-function:
H_controller(s)=N(s)/D(s),
Where:
N(s)=b0*s^m+b1*s^(m-1)+b2*s^(m-2)+…+bm,
And:
D(s)=a0*s^n+a1*s^(n-1)+a2*s^(n-2)+…+an.
Moreover, m=10, n=10, or, n=11.
The digested question:
Is it possible, and practical to design an electronic circuitry for a box, with the transfer function: H_box=H_controller(s)=N(s)/D(s)?
Warning: I have no experience to build a real electronic circuitry, and my question is only the possibility and practicality of designing a circuit for such a transfer function box. Do not mind about the performance of the controller or any other stability concern with regard to that. Only the possibility and practicality of designing an electronic box which has an equivalent transfer function: H_box=H_controller(s)=N(s)/D(s).
The box is in feed-forward path.
Dear Saeb AmirAhmadi Chomachar ,
The transfer function H(s)= N(s)/D(s)
has the form of filter characteristics.
Such general transfer characteristics has zeros and poles.
The filter which contains zeros and poles are elliptic filters.
Such filters can be implemented by using op amps+ discrete RC elements
They can be built completely integrated using switched capacitor filters
They can be also implemented by using gm-C filters.
For such filter design using active filters please follow the reference: https://www.sciencedirect.com/book/9780750675475/analog-and-digital-filter-design
Bestwishes
Note that in terms of hardware while you can easily design transfer function like
K1(s) = A + B/s + C/s^2 + D/s^3 .. you cannot really provide K2(s) = A*s + B*s^2..
That is because that involves differentiation, which is very noisy operation - you actually need infinite bandwidth and infinite gain at high frequencies.
Unlike that, the integration (or 1/s) is 'nice' operation as it limits the bandwidth and suppresses the noise. The integration however suffers from drifts and decay - as in principle infinite time constant required. It is however still easier to approximate infinite time constant in analog way, and absolutely achievable in digital way.
The circuits mentioned above can be realized using opamps, there are classical solutions for that. In practice, it is however always approximations
Kint(s) = B/s --> B /(1 + 1/tau ) tau is 'large' time - might be hours
Kdiff(s) = A *s --> A*s /(1 1+s*tau ) tau is very short - might be 100nsec
Alternatively,and often better now, it can be done using ADC--> FPGA (or uC) --> DAC. There will be however some quantization noise and sampling related bandwidth limitations and aliasing.
Dear Saeb AmirAhmadi Chomachar ,
The transfer function H(s)= N(s)/D(s)
has the form of filter characteristics.
Such general transfer characteristics has zeros and poles.
The filter which contains zeros and poles are elliptic filters.
Such filters can be implemented by using op amps+ discrete RC elements
They can be built completely integrated using switched capacitor filters
They can be also implemented by using gm-C filters.
For such filter design using active filters please follow the reference: https://www.sciencedirect.com/book/9780750675475/analog-and-digital-filter-design
Bestwishes
Yes. Analogue computers did exactly this before digital computers (PDP11), using analogue to digital conversion and FORTRAN took over.
Analogue computers were implemented using operational amplifiers and capacitors to create integrators and op-amps with resistors to create gains and summing junctions.
Rearranging the transfer functions as state equations is the key.
Yes it is possible to design an electronic circuit for transfer function by using simple RLC circuit components. (Amplifiers and filters)
Dear all responders. I was offline for one month. Right now, I read your comments, and based on those comments, I concluded, such a box is possible to be built, integrated, and embedded as an electronic component. Thank you professor Abdelhalim abdelnaby Zekry and all other contributors to this discussion.
The transfer function box, is part of my control strategy and the robust controller for double-integrator system in Laplace domain. Please see the recent update to my project:
https://www.researchgate.net/project/hyper-exponential-control-theory-HECT
This link will be useful https://www.electronics-tutorials.ws/systems/electronic-system.html
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