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A NOVEL DATA-DRIVEN CONTROL APPROACH FOR A CLASS OF DISCRETE-TIME NONLINEAR

SYSTEMS

GUIDE:VINOD.B.R

PRESENTED BY:MUHAMED SHEREEF P

M1,AEI

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CONTENTSIntroductionData driven ControlMFACAdvantages of MFAC ApproachDynamic Linearization techniqueMFAC System design and stability analysis PPD estimationCFDL-MFACExperimental InvestigationConclusionReferences

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INTRODUCTIONADAPTIVE CONTROL: In adaptive control the

controller will modify its behavior in response to changes in the dynamics of the process and the character of the disturbances

Most adaptive techniques and methodologies typically assume that the structure of the system is known linear and the parameter may be unknown or slow time-varying

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In the case of complex practical systems the structure of the plant is often difficult to determine and the parameters are hard to identify

This is the motivation for Data driven control approach

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Data driven control

In this method designing of controller merely using input and output measurement data of the plant

So model of the plant is not requiredData driven control methods :Virtual

Reference Feed back Tuning(VRFT),Iterative Learning Control(ILC), Model Free Adaptive Control(MFAC)

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MFACThis is proposed for a class of general discrete

time SISO nonlinear systemsInstead of identifying a more or less nonlinear

model of a plant, an equivalent dynamical linearization model is built along the dynamic operation points of the closed-loop system using a new dynamic linearization technique with a novel concept called pseudo-partial derivative (PPD)

The time-varying PPD could be estimated merely using the I/O measurement data of a controlled plant

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The dynamic linearization techniques include the partial form dynamic linearization (PFDL), the compact form dynamic linearization (CFDL), and the full form dynamic linearization (FFDL).

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Advantages of MFAC approachMFAC just depends on the real-time

measurement data of the controlled plant, which implies that we can develop a general controller for a class of the industrial practical processes independently

MFAC does not require any external testing signals and any training process , therefore it is a lower cost controller

MFAC is simple and easily implemented with small computational burden and has strong robustness

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Under some practical assumptions, the monotonic convergence and bounded-input bounded-output (BIBO) stability of the CFDL-based MFAC (CFDL-MFAC) approach can be guaranteed, which are the highlight features compared with other data-driven control approaches

MFAC prototype has been successfully implemented in many practical applications, e.g., chemical industry, linear motor control, injection modelling process, PH value control, and so on

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DYNAMIC LINEARIZATION TECHNIQUE

The discrete-time SISO nonlinear system to be controlled is given as follows:

where and are the system output and input at time , respectively, and are the unknown orders, and is an unknown nonlinear function.

The PFDL of the nonlinear system is based on following assumptions.

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. The partial derivatives of with respect to control input are continuous control input length constant of linearization

. System () is generalized Lipschitz, that is , for any and

where

U

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Theorem1There exists a parameter vector , called the

PPD vector, such that system () can be transformed into the following equivalent PFDL description:

U

where and

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Consider the LTI system

Where= &=

If is a stable polynomial, could be expressed as where

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The model is an approximation of the true system if the order of is sufficiently large

Model can be rewritten in the following form:

Comparing & we can see that• is time –invariant when

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MFAC System design and stability analysisFor the one-step-ahead controller, excessive

control effort is required to bring to in one step.

: reference signal

So the following control input index function is used to design the control law:

is a weighting constant

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Substituting into , differentiating w.r.t. , and letting it be zero gives

Where is a step-size vector,

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Remarksonstrains the PPD from changing too quicklys an important parameter for the MFAC

system design. Suitable choice of can guarantee the stability or improve the performance of the control system

Since is time varying, we use the modified projection algorithm to estimate

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PPD estimation

:weighting factorestimation value of Using optimal condition , we have =

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: step-size constant, Combining control law and parameter

estimation , the PFDL-MFAC scheme is designed as follows:

=

= if

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For a simple SISO nonlinear system, could be set as

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CFDL-MFAC=

= if

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EXPERIMENTAL INVESTIGATION

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Three data-driven control approaches, including MFAC,VRFT, and IFT, have been implemented on a three-tank system (Fig. 1) to investigate the control performance of the proposed approach

The parameters of PFDL-MFAC scheme – are

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Root mean square

integral time absolute error

total sum of squares

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MFAC VRFT IFT

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CONCLUSIONThe MFAC approach is easy to implement.

The control performance of MFAC is better than that of the other two approaches

The MFAC is the online adaptive control approach and does not need any measurement data collection procedure

For IFT approach, the control performance is not as good as that of MFAC and VRFT

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REFERENCESM. C. Campi, A. Lecchini, and S. M. Savaresi, “Virtual Reference

Feedback Tuning (VRFT): A newdirect approach to the design of feedback controllers,” in Proc. 39th IEEE Conf. Decision Control, Sydney,Australia, Dec. 2000, pp. 623–629.

M. C. Campi and S. M. Savaresi, “Direct nonlinear control design:The virtual reference feedback tuning (VRFT) approach,” IEEE Trans. Autom. Control, vol. 51, no. 1, pp. 14–27, 2006.

H. Hjalmarsson, M. Gevers, and S. Gunnarsson, “Iterative feedback tuning—Theory and applications,” IEEE Control Syst. Mag., vol. L8,no. 4, pp. 26–41, 1998.

Z. S. Hou and J. X. Xu, “On data-driven control theory: The state of the art and perspective,” ACTA Automatica Sinica, vol. 35, no. 6, pp. 650–667, 2009.