I want to approximate nonlinear time delay control system by B-splines and hybrid some of them with other functions (rather orthogonal functions). Can anyone guide or suggest me the way that this idea can be done?
I am assuming you want to model your nonlinear system with the time series data.If not please provide more information about your needs.
B splines can be implemented using curve fitting toolbox in MatLab. The other methods can be, in my opinion,
1. You can choose regressors ( past manipulated inputs which affect your present output due to the internal delays in the system) and model it using PCA.
2. Using Neural Network.However making use of a controller with a neural network real time is somewhat cumbersome.
3. Linearize the system with an appropriate operating point and make use of available linear model representations.
Dear Harish Ramani
Hi and thanks for hints.
my major goal is to perform hybrid of b-splines with for example block-pulse function, then utilize it as a new function for approximating my control(delay) system so that i can reduce the given system to algebraic one(like the attached paper)
best wishes
You can design a feedback controller for nonlinear systems with time delays using Quantitative Feedback Control Theory (QFT). You can do this with a system model or by providing inputs to your plant and measuring plant response.
Thanks all.
Dear's i have following system(attached JPG file) and assume that the nonlinear version is interest.
Dear Bilal
Hi and thanks to answer. you are right but i have mentioned that the nonlinear version of the above system is my interest. like x(t)u(t-1) or x(t)x(t-1)+x^2(t-0.3) and so on...
Dear
i guess you want to solve an optimal control problem for a claas of nonlinear delayed systems. As far as I know, rhere is no way to find rhe exact solution of your optimal control problem. Yet, you can find an approximated solution. Let me know if my guess is ok ornot.
Hi dear batmani
Happy new year.thanks alot.
Yes you are right.i want to approximate time delay nonlinear optimal control system.but i don't know that my idea about b_splines is correct or not?
Happy new year. I do not know what you want to do and which approach you want to follow. By the way, I got my PhD a few months ago and my thesis was related to optimal control problem for a class od nonlinear delayed systems. I think I might be able to help you. This is my phone number. If you want you can call me.
09188395448
With best wishes
Hi.thanks alot.i have saved your number and if it doesn't consuming your valuable time, i will call you as soon as possible(because of norooz,i am not in home).
Again i am grateful and hope you best days and happy year.
I have used neural generalized predictive controller (Neural GPC) before with nonlinear non-minimum phase processes with variable dead time and was sufficient to solve the problem.
You should consider the Tensor Product Model Transformation and its extension to time delay systems. This transformation is able to transform nonlinear state space representations into Tensor Product-type convex polytopic form. Tensor Product functions are actually the superset of the B-splines, so you may can find your way with it.
For further details please visit http://www.tp-control.com/. An application for time delay system is described here:
[1]J. Kuti, P. Galambos, and P. Baranyi, “Delay and Stiffness Dependent Polytopic LPV Modelling of Impedance Controlled Robot Interaction,” in Issues and Challenges of Intelligent Systems and Computational Intelligence, L. T. Kóczy, C. R. Pozna, and J. Kacprzyk, Eds. Springer International Publishing, 2014, pp. 163–174.
[2]P. Galambos and P. Baranyi, “Representing the Model of Impedance Controlled Robot Interaction with Feedback Delay in Polytopic LPV Form: TP Model Transformation based Approach,” Acta Polytechnica Hungarica, vol. 10, no. 1, pp. 139–157, 2013.
[3]P. Galambos, P. Baranyi, and G. Arz, “Tensor product model transformation-based control design for force reflecting tele-grasping under time delay,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 228, no. 4, pp. 765–777, Mar. 2014. URL: http://pic.sagepub.com/content/228/4/765
Feel free to contact me if you find it useful and need further explanation.
Best,
Peter
Hi all
Thanks a lot for great answers. All suggested approaches are interest but i need a way to combine two set of functions(like block pulse and B-splines) to gain a new hybrid function which has the contained functions properties and more accurate than them.
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