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Neural Simulation and Control.

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Simulation Input/Output models Proces u(k) y(k+d) d(k) The NARMA model:

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Simulation Input/Output models Proces u(k) y(k+d) d(k) NN TDL... TDL... TDL... y NN (k+d) e + - q -d

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State space model If the state is observable: F u(k)x(k+1) d(k) NN F eFeF + - G + NN G - y(k+1) eGeG

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Data collection • Steady-state in at least three levels. • The important frequency. • All inputs should be independent.

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Neural control FeedForward: The inverst model. Proces u(k)y(k+1) d(k) NN TDL... TDL... TDL... e + - d(k) u(k-1)

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FeedForward: The inverst model. Proces u(k) y(k+1) d(k) NN y ref (k+1) y ref (k). d(k) d(k-1). u(k-1) d(k-2). The reference signal y ref is generated by a reference model. Problem: • All Zeros have to be inside the unit circle. • The process have to be a low-pass filter. (DC gain > 0) • Steady-state should be well defined. • No compensation for non-measured disturbances ( No feedback)

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Fixed Stabilizing Feedback Control With Neural net based feed-forward Neural net Inverse model Process Feedback controller Refference model d(k) y(k) u NN (k)y ref (k+1) + d non (k) q -1 + - e(k) u fb (k) u(k)

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Neural net based feedback controller Process u(k) d(k) y(k+1) NN-simulator + - y NN (k+1) NN-controller d(k) y ref (k+1) d(k) y(k) f f f f ... 1 y(k) + - - + y ref (k+1) e(k)

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Fixed Stabilizing Feedback Control With Neural net based feed-back optimaizer Process Feedback controller + + - e(k+1) u fb (k) u(k) u NN (k) y ref (k+1) y(k+1) d(k) Process + u(k) u NN (k) y(k+1) d(k) + - y ref (k+1) e(k+1) Feedback controller u fb (k) CL-process

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Fixed Stabilizing Feedback Control With Neural net based feed-forward CL-Process u NN (k) d(k)y ref (k+1) e(k+1) NN-simulator + - e NN (k+1) NN-controller d(k) y ref (k+1) d(k) y ref (k+1) f f f f ... 1

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Neural network Model Predictive Control Reference Model Optimization NN Process Simulator NN Controller Process

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Neural network Model Predictive Control Reference Model Optimization NN Process Simulator NN Controller Process 1.A reference trajectory y ref (k+p), p = 1... N is defined which describes the desired process trajectory over the prediction horizon. 2.At each sampling time, the value of the controlled variable y(k+p) is predicted over the prediction horizon p = 1... N. Based on the future values of the control Variable u(k+p) within a control horizon p = 1... N U, where N U <= N. If N U < N then u(k+p) = u(k+N U ), k = N U +1... N. 3. The vector of future controls u(k+p) is computed such that a cost function depending on the predicted control errors is minimized. The first element of the control vector is applied to the process.

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Interpolation and Extrapolation x x x x x x x x x x x x

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Combined linear and NN model Process u Linear model + - y lin e non-lin y NN model - y NN + Linear model u NN model + + y NN y lin

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