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Eduard Petlenkov , TTÜ automaatikainstituudi dotsent eduard.petlenkov@ttu.ee

NN-based model structures for identification and control of nonlinear systems . Non-fully connected neural networks. Eduard Petlenkov , TTÜ automaatikainstituudi dotsent eduard.petlenkov@ttu.ee. Model Based Control. Model s tructure independent. Model s tructure dependent.

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Eduard Petlenkov , TTÜ automaatikainstituudi dotsent eduard.petlenkov@ttu.ee

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  1. NN-basedmodelstructuresforidentification and controlofnonlinearsystems.Non-fullyconnectedneuralnetworks Eduard Petlenkov, TTÜ automaatikainstituudi dotsent eduard.petlenkov@ttu.ee

  2. Model Based Control Model structure independent Model structure dependent Neural Networks (NN) based Models • Easy realization of the model’s structure relevant to the control algorithm • Adaptivity by using network’s ability to learn • Analytical models (for example, state-space representation of nonlinear models) • Choosing proper structure of the model may increase accuracy of the model • Adaptivity by using network’s ability to learn • Model may become • Nonanalytical or hardly analytical • Overparameterized • Restricted class of systems to which the control technique can be applied

  3. H(s), H(z) Linear dynamic system with static actuator nonlinearity

  4. Neural Network Structurefordynamic systems with static actuator nonlinearity

  5. DC Servo Motor with Nonlinear Driver Vo(t) Vi(t) y(t) DC Servo Motor

  6. Identification of the DC Servo Motor

  7. NARX (Nonlinear Autoregressive Exogenous) model: ANARX (Additive Nonlinear Autoregressive Exogenous) model: or Nonlinear Discrete-Time Input-Output Models

  8. Advantages of ANARX Structure over NARX • Easy to change the order of the model • Always realizable in the classical state-space form • Linearizable by dynamic feedback

  9. 1st sub-layer is a sigmoid function n-th sub-layer Neural Network based ANARX (NN-ANARX) Model

  10. NN-ANARX model ANARX model ANARX Model based Dynamic Output Feedback Linearization Algorithm NN

  11. HSA* NN-based ANARX model Parameters (W1, …, Wn, C1, …, Cn) NN-ANARX Model based Control of Nonlinear Systems Controller u(t) Nonlinear System y(t) Dynamic Output Feedback Linearization Reference signal v(t) * HSA=History-Stack Adaptation

  12. NN-ANARX Model based Control of Nonlinear MIMO Systems:Problem Statement SISO systems: Numerical calculation of u(t) by Newton’s Method, which needs several iterations to converge MIMO systems: Numerical algorithms do not converge or calculation takes too much time

  13. 1st sub-layer (linear) n-th sub-layer (nonlinear) NN-based Simplified ANARX Model (NN-SANARX)

  14. (*) Let’s define: where If m=r and T2 is not singular or close to singular then NN-SANARX Model based Control (1) =

  15. NN-SANARX Model based Control (2)

  16. u1 y1 u2 y2 Identification by MIMO NN-SANARX model Numerical Example

  17. Numerical Example: NN-based SANARX model

  18. Numerical Example: Control (1/2)

  19. Numerical Example: Control (2/2)

  20. Dynamic Output Feedback Linearization Algorithm u(t) Nonlinear system y(t) v(t) NN-based ANARX model Parameters (a1, …, an, b1, …, bn) Parameters (W1, …, Wn, C1, …, Cn) reference model Model Reference Control

  21. Reference model Dynamic output feedback linearization of ANARX model

  22. NN-ANARX model NN-ANARX Model based Reference Model Control Dynamic output feedback linearization of NN-ANARX model

  23. NumericalExample: JCSTR model Input-Output equation:

  24. Example: Control Task Linear second order discrete time reference model with poles p1=-0.9, p2=0.8, zero n1=-0.5, steady-state gain Kss=1 Parameters of the reference model for control algorithm are as follows: It defines the desired behavior of the closed loop system (=control system)

  25. Example: NN-based modeland control First sub-layer is linear and Here We know that Thus,

  26. Example: NN-based modeland control

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