Have you ever tried Feed-forward PID Controller?

http://en.wikipedia.org/wiki/PID_controller#Feed-forward

Thanks for the suggestion. However I am supposed to design a backstepping sliding mode controller for joint space torque control. Although there are nonlinear predictors available, the robustness of the system is lost.

Dear Nabantina;

I think backstepping SMC have computation load. I think you can terminal sliding mode controller for your system. fuzzy logic control also can help you.

All the best

Thank you for the suggestion

Have you analysed the causes of the delay?

The data from the motor sensor is sent by the CPU (ATMEGA) in the motor side and the receiving side is a PC. I think due to slower clock frequency in the sensing side this delay is occurring. I have implemented a nonlinear predictor (obtained from literature) but its working range is very low and can be applied only for slow trajectory .

I recommend using optics position sensor instead of magnetics one

You should use a high speed comparator instead of a CPU to output sensor data to PC. The comparator TLV3502 has 1.5ns rise/fall time and has low consumption

Another option is to design the control system in the microcontroller directly, the following microcontroller has all the electronics inside with comparator that controls directly the PWM: dspic33fj16gs502  , its PWM can be controlled within 1ns resolution

Thank you.. I will try that

If you need high tracking performance, feed-forward using an accurate model is really the only way to go. Backstepping is based on model-matching (if I remember correctly) so feed-forward should already be 'baked into' to control law. My suggestions would be to minimize the impact of the time-delay by the usual techniques of reducing the control law gains, reducing the growth rate in the backstepping terms (use something else that the square of the error), and using a sigmoid function in the sliding mode part. Or reducing the actual time-delay, as already suggested; that is the best option.

Dear Eielsen

Regarding to your method,To reduce the sensor's time delay she can use nonlinear controller or reduce the feed-forward controller's gain.

Most of nonlinear controller dependent to system dynamic, I think it can open a new challenge in this project. about the second method I also think it can be good method but how she can reduce these coefficient when she also must to optimize these coefficients.

what do you think about change the type of sensors or design a filters???

All the best

Dear Farzin Piltan,

It has been a while since I worked with non-linear manipulators and backstepping, but in my experience it is very difficult to deal with time-delay in feedback in practice, and makes it very difficult to analyze stability for non-linear systems (I can't remember ever having seen any standard/general approach for analyzing the effect of time-delay in non-linear systems).

With regards to backstepping, I guess the more practical option is to rely on the observer you usually have to design for the backstepping control law, and the feedback of these states together with the feed-forward of the reference through the chosen dynamical model. In my experience then, the more accurate the model is, the better results you get. The simple approach is to reduce/change the gains by trial and error (simulation) in order to find an implementation that is stable (although stability can still not be guaranteed), but of course this increases the bound for the error. I guess this is the trade-off that has to be made. The robustness of backstepping (the varieties that I have seen) really do not extend to the effects of time-delay (and also, notably, does not handle sensor/actuator saturations, which can be a problem since backstepping often generates huge control signals, unless the growth rate of the control law terms is limited...)

I guess a different approach of using an Hinfinity control law (which includes an Hinfinity obeserver/generalized Kalman filter) and feed-forward linearization could be used. This might be a simpler framework to work with since it is possible to include the effects of time-delay in the linear model. Time-delay here also tends to restrict the control law gains, and depending on accuracy of the linearization, the linear model uncertainty can be large, and the two problems combined might make the performance poor, but I guess it is hard to say in general.

Changing the sensors (reducing the actual time-delay), if that is possible, does sounds like the very best option to me... Optical encoders should be really fast if used correctly. For rapid-prototyping and hardware-in-the-loop simulations, I would in general suggest using a regular PC running the MATLAB xPC real-time operating system with a National Instruments DAQ card installed (http://sine.ni.com/ds/app/doc/p/id/ds-15/), since it is usually a fast and relatively inexpensive solution that works without much modification, and since many of the DAQ cards include fast encoder inputs.

That is what I think, anyway :)

Thank you so much for the suggestions. I have constructed a nonlinear observer for the delayed system . Although it works, the robustness as well as the tracking performance is very  much compromised.  But I am going to study the approaches you all have so generously mentioned.

Dear Eielsen

Your idea is so good, what do you think about sliding mode controller, based on discontinuous part?

To improve SMC we can use fuzzy logic or type of filter.

Regards

... Start with something simple - a lead compensator perhaps?

Dear Nabanita,

                  I am doing Ph.d(Mathematics) in the field of dynamical system, Which has Robust control, Networked control system etc. whatever system taking there must be have some delay, how to overcome that is important.In system level you are using Uncertainity means easy to tolerate that one..You just study.. 

Could you please let me know the value of your sensor delay and based on that I could suggest some solutions.

From my experience, industrial manipulator or academic manipulator sensor delay in the order of milli seconds. Example: 100 ms.

Which can be overcome easily with normal robust controller and even if you wish to improve this you can use any probabilistic filter, for example: EKF, etc.

All the best