Download Multiple layers of neurons

Neural network predictive
control
Neural Network Toolbox
Kinga Batárová
semestral project
supervisor: Ing. Vasičkaninová Anna, PhD.
Bratislava 2015
NEURAL NETWORK - DEFINITION
 Aproximators of functions
 Unknown function - system to
control
 Aproximator – neural network –
plant model
 Same input to the model and to
the system
 Same response of the network
and our system
MULTILAYER PERCEPTRON NEURAL NETWORK
 Multilayer perceptron architecture
 Built up of neurons
 Neurons form layers
 Layers form network
SINGLE – INPUT NEURON
 a - neuron output
 w – scalar weight
 p – scalar input
 b – bias
 n – net input
 f – transfer function
MULTIPLE – INPUT NEURON
• Neuron output
• Net input
LAYERS OF NEURONS
Layer of S neurons
 5 – 10 neurons
Multiple layers of neurons –
3 layer network
NN PREDICTIVE CONTROL
 NN predictive controller uses a neural network model of a nonlinear
plant to predict future plant performance
 Calculation of control input
 Optimization of plant performance
 2 steps
 - system identification
 - controller design - predictive control
SYSTEM IDENTIFICATION
 Train the neural network
 Predict future performance
 Prediction error
PREDICTIVE CONTROL
 The neural network model predicts the plant response over a specified time
horizon
 predictions - used by a numerical optimization program to determine the
control signal that minimizes J
 N1,N2,Nu – time horizons over which the tracking error and the control
increments are evaluated
 u‘- tentative control signal
 yr - desired response
 ym - network model response
PREDICTIVE CONTROL
Predictive Controller


Optimization block
Neural Network Model
APPLICATION OF NN PREDICTIVE CONTROL
FLOW CHEMICAL REACTOR
 Dynamic model of the reactor
−𝑔
𝑑 𝑐𝐴 (𝑡) 𝑞
𝑞
𝜗
= 𝑐𝐴𝑉 − 𝑘∞ 𝑒 𝑡 𝑐𝐴 𝑡 − 𝑐𝐴 (𝑡)
𝑑𝑡
𝑉
𝑉
𝑑 𝜗(𝑡) 𝑞
𝑘∞
= 𝜗𝑣 +
𝑑𝑡
𝑉
−𝑔
𝜗
𝑒 𝑡
𝑐𝐴 𝑡 −∆𝑟 𝐻
𝑞
𝛼𝐴
− 𝜗 𝑡 −
(𝜗 𝑡 − 𝜗𝑐 (𝑡))
𝜌𝑐𝑝
𝑉
𝑉𝜌𝑐𝑝
𝑑 𝜗𝑐 (𝑡) 𝑞𝑐 𝑡 𝜗𝑐𝑣
𝛼𝐴
=
+
𝜗 𝑡 − 𝜗𝑐 𝑡
𝑑𝑡
𝑉𝑐
𝑉𝑐 𝜌𝑐 𝑐𝑝 𝑐
−
𝑞𝑐 𝑡 𝜗𝑐 (𝑡)
𝑉𝑐
SIMULINK SCHEME – NN PREDICTIVE CONTROL
NN PREDICTIVE CONTROL
PLANT IDENTIFICATION
GENERATED TRAINING DATA
NEURAL NETWORK – PLANT MODEL
TRAINING DATA
COMPARISON OF OUTPUT - TEMPERATURE OF ΘS - FROM FROM THE
MODEL AND FROM THE NEURON NETWORK (PLANT MODEL)