What do you mean by "transfers every input to zero"? The output of the system is always zero?

yes...the step , ramp and the sine wave response of the system is zero....i want to design a pid controller for set point purposes.(step response)

Is your system controllable? I'm asking this because I believe that if the inputs of the system can't alter the system's state then, you can't control it at all. 

yes..it is controlable

Hi,

It makes the judgment so much easier if you can provide more information about the system in terms of transfer function or state space representation. One possibility is that the gain of your system is too low, that's why you get zero for all types of inputs. As you know, transfer function is basically the ratio between output on input. If you have for instance a first order (stable) system with dc gain of 0.0001, the output of system to any step input would be 10000 smaller in magnitude. Therefore, you need a high gain controller to improve the system response.

Rgds,

Based on your question, I got two possibilities, 1) you got zero output no matter the input signal, 2) you design your output to zero for all inputs.

for case #1, I agree with Viswanath that your gain is too low. It means, you have to increase constant for P controller. But P controller never reaches the setting point so you have to add either I or D or both to improve its performance.

for case #2, I think it is easy because you just put all the input signal with very low P constant.

So, which one did you mean?

I have a tf say G(s) = Num/Den... how do i calculate PID for this system?

The problem itself is not scientific. A zero multiplication can always produce zero, despite whatever your input is.

What is your input and output signal? Are they voltages or displacements or angles, etc.? Are you considering negative values?

Dear,

Design a controller which will provide the transfer function with zeros matching with the input the response of the system to this input will always be zero. Thus for step and ramp input you should have a close loop transfer function with min two zeros at origin. Try this and communicate with transfer function if it does not work.

if it is open loop response of the plant that is giving you zero response it means the process gain is close to zero and it can not magnify input signal. You need very large controller gain. if it is close loop response it means you are using wrong close loop transfer function use servo transfer function for setpoint tracking insead. It has the form GK/(1+GK) where G is pant transfer function and K is Controller transfer function. 

To get initial parameters for PID, consider relay feedback procedure to derive the

ultimate gain and ultimate frequency parameters.

TF is G(S)= 10/S^2+20S+1

Your system is both controllable and observable.The dc gain of your system is 10,so I don t understand why you say that your system transfers every input to zero.Maybe something is wrong while modeling your system.An easy way to design a PID controller  is using Ziegler-Nichols method.From the root locus,you can calculate the gain Kcrit that your system is marginally stable.Then,for this Kcrit,you can calculate the critical period of the oscillation  of the output.So,you have everything you need for Ziegler-Nichols method.

C(s) = T(s) R(s)

where r = ref input, T = closed loop transfer function , c – controlled variable (output)

See that T(s)R(s) has no poles at s=0. Then your response will be zero in steady state.

may be you are indirectly saying that set point is zero.

(1) Quote Question #1 "How can one design a PID controller for a system which transfer every input to zero?"

Let us look at the diagram of conventional feedback system (as shown by Figure 1 in the paper [HHHHD03]):

r is the system input,

C(s) is PID controller, u(t) is the controller output,

P(s) is the control plant, commonly determined by physical properties of the system,

y(t) is the system output.

According to the follow-up comment by  Sara Ahmadi  "I want to design a PID controller for set point purposes (step response).", the system input is the unit step, that is, r = 1.

If the system output at steady-state is zero, then the input for PID controller (i.e., the steady state error) will be always  r - y(t) = 1 - 0  = 1.

Consequently, integral term of PID controller will accumulate the error over time, and cause the output u(t) of the PID controller to increase continuously and approach infinity.

Infinite controller output (i.e., u(t) --> infinity) means that an infinite energy consumption is required, this makes the real-world implementation of PID controller impossible.

In summary, we can NOT design a PID controller for a real-world control system which transfers every input to zero.

(2) Quote Question #2 "How can one determine initial value for PID controller parameters?"

Ziegler–Nichols tuning formula has been widely used to determine the initial value of the PID controller parameters. For example. the paper [HHHHD03] uses Ziegler–Nichols tuning formula to set the initial value for the PID controller parameters.

Only PID Control and Smith Predictor were listed in the “Leaders of the Pack” InTech’s 50 most influential industry innovators since the year 1774. Available from the following link.

http://archive.today/2RoSK

PID Control (the dominant control method in the industrial applications) was listed twice -- (1) John G. Ziegler and Nathaniel B. Nichols and classical PID Control; (2) Karl Johan Åström and modern PID Control (IEEE Medal of Honor, 1993) http://en.wikipedia.org/wiki/IEEE_Medal_of_Honor

[HAH91] C.C. Hang, K.J. Astrom, and W.K. Ho, "Refinements of the Ziegler-Nichols tuning formula," IEE Proceedings on Control Theory and Applications, 138(2), March 1991, pp.111-118. 

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=67610

This paper and selected classic PID tuning methods (co-invented by K.J. Astrom and his student W.K. Ho) have been implemented by Maplesoft Inc. for MapleSim Control Design Toolbox. 

http://www.maplesoft.com/support/help/MapleSim/view.aspx?path=ControlDesign/GainPhaseMargin

A typical PID tuning procedure: (1) Use relay control to estimate the control model (or control plant); (2) Use Z-N formula to initialize Kp and Ki; (3) use trial and error to adjust Kp and Ki or other method such as iterative feedback tuning (IFT), internal model control (IMC), etc.

Iterative feedback tuning (IFT) was proposed to tune controller parameters for system with unknown parameters. A linear control model can be used to approximate non-linear system with unknown parameters roughly, and such control plant approximation may exist large deviation from the real non-linear system, which would cause classical tuning method of PID controller ineffective. IFT was proposed to minimize a given quadratic cost function of the system output error and control effort, thus solving the controller tuning issues caused by plant uncertainty.

H. Hjalmarsson was elected to the Class of 2013 IEEE fellow due to his fundamental contribution to iterative feedback tuning. 

By cooperating with his peer researchers including Stanford University researcher, H. Hjalmarsson integrated iterative feedback tuning with PID controller to solve controller tuning issues caused by plant uncertainty.

[HHHHD03] W.K. Ho, Y. Hong, A. Hansson, H. Hjalmarsson, and J.W. Deng, "Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157. Available in the following RG Link.

https://www.researchgate.net/publication/223504459_Relay_auto-tuning_of_PID_controllers_using_iterative_feedback_tuning

(3) Discussion on control system design

"What are trends in control theory and its applications in physical systems (from a research point of view)?"

https://www.researchgate.net/post/What_are_trends_in_control_theory_and_its_applications_in_physical_systems_from_a_research_point_of_view2

Article Relay auto-tuning of PID controllers using iterative feedback tuning

(4) Quote Ige Gbenge's follow-up question " I have question that can we have zero as one of the PID controller parameters. That is kd=0 or ki=0. "

(I) Yes. We can have zero as one of the PID controller parameters. That is,

kd=0 for PI controller (e.g., Adaptive PI rate controller for Internet Traffic [HY07a])

or ki=0 for PD controller.

[HY07a] Y. Hong and O.W.W. Yang, "Design of Adaptive PI Rate Controller for Best-Effort Traffic in the Internet Based on Phase Margin," IEEE Transactions on Parallel and Distributed Systems, 18(4), April 2007, pp. 550-561.

http://www.researchgate.net/publication/3301176_Design_of_Adaptive_PI_Rate_Controller_for_Best-Effort_Traffic_in_the_Internet_Based_on_Phase_Margin

(II) The paper [HY07b] describes the effect of D parameter for PID Controller.

(II.A) A D (Derivative) controller has the effect increasing the stability of the control system, reducing the overshoot, and improving the transient response [AsHa95].

(II.B) In practice, considering the stochastic characteristic of the network and the complicated implementation of PID controller, we would recommend PI controller in the network traffic control generally, because with the derivative term applied, small amounts of noise (e.g., the short-lived TCP flows) can cause large amount of change in the system output (e.g., great fluctuation of the queue size in the routers) [AsHa95], which may cause excessive buffer overflow and undesirable low flow throughput in the network.

[HY07b] Y. Hong and O.W.W. Yang, "Using Interval Phase Margin Assignment to Self-Tune a PI AQM Controller for TCP Traffic," Telecommunication Systems, Springer, 36(4), December 2007, pp. 161-171.

https://www.researchgate.net/publication/220145542_Using_interval_phase_margin_assignment_to_self-tune_a_PI_AQM_controller_for_TCP_traffic

I have question that can we have zero as one of the PID controller parameters. That is kd=0 or ki=0. Thanks q