# How to compare power requirements for different control design approaches?

I am trying to fairly compare different control design approaches. As an example, below I present two similar but different techniques which are:

1. Control system with state feedback
2. Control system with state feedback and observer

The plant input is voltage. What I have done

I designed both systems on Simulink, with the idea that I would be able to check the input to the plant and get an RMS and current reading to get instantaneous power.

Both plants are the same, and so is the input.  I am trying to get a voltage and current reading after the summing junction, before entering the plant so I am using the Multi-meter block by Simulink. However I get no available measurements: Am I using the wrong tool to get read the VRMS and current?

Any suggestions on how I can compare power requirements for these two different control design approaches would be appreciated.

This could be an alternative technique: What is the output of a PID controller (or any controller in general)?

• In my opinion it is no direct/clear relation between the control system used and its power consumption. Power consumption is related to the physical implementation of the system. Though obviously a more complex system generally would require more power. But assuming similar complexity it is the implementation that counts. – Bimpelrekkie Jan 22 at 8:18
• Agreed @Bimpelrekkie, physical implementation is directly related to the power consumption, but I would like to get a rough idea beforehand. For the same plant I designed a (simple) PID controller, a complex compensator, and the two design approaches mentioned above. I would expect that the simplest controller would utilize less power consumption and would like to test this out on Simulink. – Rrz0 Jan 22 at 8:24
• Why would the simplest controller use the least power? An advanced controller could use less power overall due to the accuracy and perhaps speed of action... – Solar Mike Jan 22 at 8:32
• Perhaps Matlab already has a function to show you how many operations are needed for a certain implementation.If not you would need models that include this power consumption. These are not common so you might have to make these models yourself. You could for example use a point system, where one operation on an integer takes one point (of power). Do that for all blocks you use, add up all the points. That number is than a relative indicator of the power consumption. – Bimpelrekkie Jan 22 at 8:35
• @SolarMike, what you say makes sense... I was thinking on the lines of a simple PID controller going against a full state feedback controller which requires information of all the states through the use of sensors etc. My logic could be flawed, and a simulation showing some rough comparison would be all the more useful to allow me (and others with similar misconceptions) to visualize the differences without an actual implementation. – Rrz0 Jan 22 at 8:36

There are norms that can be used to "measure" (also to compare) signals ($$\L_1\$$, $$\L_2\$$ and $$\L_{\infty}\$$) and systems ($$\H_2\$$ and $$\H_{\infty}\$$) for SISO and MIMO cases. There are deterministic and stochastic interpretations for it. For example, $$\H_2\$$ norm of a stable system $$\H\$$ is the root-mean-square of the impulse response of the system. In stochastic terms, the $$\H_2\$$ norm measures the steady-state covariance (or power) of the output response $$\y = H\omega\$$ to unit white noise inputs $$\\omega\$$. Specifically in Matlab, n = norm(sys) or n = norm(sys,2) returns the root-mean-squares of the impulse response of the linear dynamic system model sys. For a signal $$\x\$$, the $$\L_2\$$ norm represents the total energy (use norm(x,2)). In other hand, the RMS value is associated with the average power. In this case, you can use the rms function in Matlab.