Neural Simulation and Control.

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

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

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

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

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

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)

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 e(k) u fb (k) u(k)

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)

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

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

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

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 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.

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

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