P(s) is plant TF, G(s) is controller then, control effort can be obtained as G(S)/(1+P(s)G(s)).

Thanks patil .. I want to know the references for this control effort information...Because, I see in Astrom's Gang of four transfer function analysis...G(S)/(1+P(s)G(s)) This transfer function tells the process variable variations under load disturbances???...Then how it could be control effort ...kindly explain me???...Thank you

In case of MIMO system, the process variables are affected by the interaction between the control loops.

Recently i read one paper , the control effort can be calculated as U=K*S where U-->control effort,K--> controller, S--> sensitivity function . is this right???.. also plant G(s)=1/(s*(1+T*s)): K is PID controller...if I find the infinity norm of control effort based on U=K*S ..am getting the value as INF due to improper transfer function of U...But I tried based on your suggestion (i.e G(S)/(1+P(s)G(s))) am getting some value..Which is right?...give me some suggestion....

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My answer is correct

Mukesh,

Do you have any text or article talk about this control effort?..for refrences....

You may integrate the square of control signal, the controller output. This is a good index. There are other good indexes: the maximum absolute value of the control signal, for example .

Recently i read the paper titled "Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties., .,Mechatronics (2012)" , the control effort can be calculated as U=K*S where U-->control effort,K--> controller, S--> sensitivity function . is this right???.. also plant G(s)=1/(s*(1+T*s)): K is PID controller...if I find the infinity norm of control effort based on U=K*S ..am getting the value as INF due to improper transfer function of U ..But if the controller is PI am getting the control effort value...But, in the paper they are using PID controller with system G(s) as said above and they got the control effort value... can u give me some suggestion about this problem.....

If you use matlab simulink it is easy to see and compute the control effort. To see it, you just plot the control signal. To have a number for it, for example the integral of the squared control signal, you just take the square of it and sum for all instants, You can also use the multiplying block in simulink followed by an integrator.

This is possible in simulink...how it could be in m.file....

In .m file is also possible: take the vector of the control signal, square each of its elements and add all of them. You may also plot the control signal.

hi,

ONE of the ways to see (plot or manipulate) the control signal is to "implement your second order system in SIMULINK (Level-1 S-Function). Make the controller (e.g. uu = E(kp + kd s+ ki/s)) global (global uu)  in in each sub-function of the S-Function, initialize it with some suitable value in the initialization sub-function and finally output it in the output sub-function. Then either plot it via scope block or import it to the workspace using "to workspace" block.

In MATLAB simulation, control input u(t)=Kpe(t)+Ki int_(e(t))+Kd de/dt can be calculated. However, you can calculate control energy E. For this , calculate u^T u and  integrate it for simulation time.

what is the unit of control effort or control energy. What does negative value of control effort shows. Can anybody guide me regarding it

Please refer to this article:

https://www.researchgate.net/publication/318726178_An_Improved_Active_Disturbance_Rejection_Control_for_a_Differential_Drive_Mobile_Robot_with_Mismatched_Disturbances_and_Uncertainties

Conference Paper An Improved Active Disturbance Rejection Control for a Diffe...

if R(s) is the reference signal, G(s) is the plant, and C(s) is the controller. the o/p of C(s) which is in this case U(s), is given as:

U(s) = C(s)/(1+C(s).G(s)).

I think from an energy perspective, the control effort can be computed as the integral of the square of the control signal. This can be easily achieved in matlab/simulink with a few blocks added to your simulation model. Charcateristic of a good controller I might say generally soeaking should be minimizing of energy or have a stable energy profile

AoA Mohaideen

Check the attached .mfile for PID control design for the second order mass spring system. The transfer function U gives the controller effort in response to a step reference input

Respected Antonio Dourado, Sir can you please give a reference of a book or an article which says "integrate the square of control signal, the controller output"?

I need to quote it. Antonio Dourado

in closed-loop control system to get control effort, load disturbance input should be consider along with reference input or it's not necessarily.