32.2 Neuron Cell A biological neuron is a complicated structure, which receives trains of pulses on hundreds of excitatory and inhibitory inputs.. Because incoming pulses are summed with
Trang 1
32.2 Neuron Cell
A biological neuron is a complicated structure, which receives trains of pulses on hundreds of excitatory
and inhibitory inputs Those incoming pulses are summed with different weights (averaged) during the time period of latent summation If the summed value is higher than a threshold, then the neuron itself
is generating a pulse, which is sent to neighboring neurons Because incoming pulses are summed with time, the neuron generates a pulse train with a higher frequency for higher positive excitation In other words, if the value of the summed weighted inputs is higher, the neuron generates pulses more frequently
At the same time, each neuron is characterized by the nonexcitability for a certain time after the firing pulse This so-called refractory period can be more accurately described as a phenomenon where after excitation the threshold value increases to a very high value and then decreases gradually with a certain time constant The refractory period sets soft upper limits on the frequency of the output pulse train
In the biological neuron, information is sent in the form of frequency modulated pulse trains
This description of neuron action leads to a very complex neuron model, which is not practical McCulloch and Pitts (1943) show that even with a very simple neuron model, it is possible to build logic and memory circuits Furthermore, these simple neurons with thresholds are usually more powerful than typical logic gates used in computers The McCulloch–Pitts neuron model assumes that incoming and outgoing signals may have only binary values 0 and 1 If incoming signals summed through positive or negative weights have a value larger than threshold, then the neuron output is set to 1 Otherwise, it is set to 0
(32.1)
where T is the threshold and net value is the weighted sum of all incoming signals:
(32.2)
Examples of McCulloch–Pitts neurons realizing OR, AND, NOT, and MEMORY operations are shown
in Fig 32.1 Note that the structure of OR and AND gates can be identical With the same structure, other logic functions can be realized, as Fig 32.2 shows
The perceptron model has a similar structure Its input signals, the weights, and the thresholds could have any positive or negative values Usually, instead of using variable threshold, one additional constant input with a negative or positive weight can added to each neuron, as Fig 32.3 shows In this case, the
FIGURE 32.1 OR, AND, NOT, and MEMORY operations using networks with McCulloch–Pitts neuron model.
FIGURE 32.2 Other logic function realized with McCulloch–Pitts neuron model.
0, if net <T
=
net w i
i=1
n
=
+1 +1
+1
A
B
C
T = 0.5
A + B + C
(a)
+1 +1 +1
A
B
C
T = 2.5
ABC
(b)
AND
−1
A T = − 0.5
NOT A
(c)
NOT
+1 +1
T = 0.5 WRITE 1
WRITE 0 −2 (d)
MEMORY OR
+1 +1 +1
A
B
C
T = 1.5 AB + BC + CA (a)
+1 +1 +2
A
B
C
T = 1.5 AB + C (b)
0066_Frame_C32.fm Page 2 Wednesday, January 9, 2002 7:54 PM
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32.2 Neuron Cell
A biological neuron is a complicated structure, which receives trains of pulses on hundreds of excitatory
and inhibitory inputs Those incoming pulses are summed with different weights (averaged) during the time period of latent summation If the summed value is higher than a threshold, then the neuron itself
is generating a pulse, which is sent to neighboring neurons Because incoming pulses are summed with time, the neuron generates a pulse train with a higher frequency for higher positive excitation In other words, if the value of the summed weighted inputs is higher, the neuron generates pulses more frequently
At the same time, each neuron is characterized by the nonexcitability for a certain time after the firing pulse This so-called refractory period can be more accurately described as a phenomenon where after excitation the threshold value increases to a very high value and then decreases gradually with a certain time constant The refractory period sets soft upper limits on the frequency of the output pulse train
In the biological neuron, information is sent in the form of frequency modulated pulse trains
This description of neuron action leads to a very complex neuron model, which is not practical McCulloch and Pitts (1943) show that even with a very simple neuron model, it is possible to build logic and memory circuits Furthermore, these simple neurons with thresholds are usually more powerful than typical logic gates used in computers The McCulloch–Pitts neuron model assumes that incoming and outgoing signals may have only binary values 0 and 1 If incoming signals summed through positive or negative weights have a value larger than threshold, then the neuron output is set to 1 Otherwise, it is set to 0
(32.1)
where T is the threshold and net value is the weighted sum of all incoming signals:
(32.2)
Examples of McCulloch–Pitts neurons realizing OR, AND, NOT, and MEMORY operations are shown
in Fig 32.1 Note that the structure of OR and AND gates can be identical With the same structure, other logic functions can be realized, as Fig 32.2 shows
The perceptron model has a similar structure Its input signals, the weights, and the thresholds could have any positive or negative values Usually, instead of using variable threshold, one additional constant input with a negative or positive weight can added to each neuron, as Fig 32.3 shows In this case, the
FIGURE 32.1 OR, AND, NOT, and MEMORY operations using networks with McCulloch–Pitts neuron model.
FIGURE 32.2 Other logic function realized with McCulloch–Pitts neuron model.
0, if net <T
=
net w i
i=1
n
=
+1 +1
+1
A
B
C
T = 0.5
A + B + C
(a)
+1 +1 +1
A
B
C
T = 2.5
ABC
(b)
AND
−1
A T = − 0.5
NOT A
(c)
NOT
+1 +1
T = 0.5 WRITE 1
WRITE 0 −2 (d)
MEMORY OR
+1 +1 +1
A
B
C
T = 1.5 AB + BC + CA (a)
+1 +1 +2
A
B
C
T = 1.5 AB + C (b)
0066_Frame_C32.fm Page 2 Wednesday, January 9, 2002 7:54 PM
Trang 3Advanced Control of an Electrohydraulic Axis
33.1 Introduction
33.2 Generalities Concerning ROBI_3, a Cartesian Robot with Three Electrohydraulic Axes
33.3 Mathematical Model and Simulation of Electrohydraulic Axes
The Extended Mathematical Model • Nonlinear Mathematical Model of the Servovalve • Nonlinear Mathematical Model of Linear Hydraulic Motor
33.4 Conventional Controllers Used to Control the Electrohydraulic Axis
PID, PI, PD with Filtering • Observer • Simulation Results
of Electrohydraulic Axis with Conventional Controllers
33.5 Control of Electrohydraulic Axis with Fuzzy Controllers
33.6 Neural Techniques Used to Control the Electrohydraulic Axis
Neural Control Techniques
33.7 Neuro-Fuzzy Techniques Used to Control the Electrohydraulic Axis
C ontrol Structure
33.8 Software Considerations
33.9 Conclusions
33.1 Introduction
Due to the development of technology in the last few years, robots are seen as advanced mechatronic systems which require knowledge from mechanics, actuators, and control in order to perform very complex tasks Different kinds of servo-systems, especially electrohydraulic, could be met at the executive level of the robots Taking into account the most advanced control approaches, this paper deals with the implementation of advanced controllers besides conventional ones which are used in an electrohydraulic system The considered electrohydraulic system is one of the axes of a robot These robots possess three
or more electrohydraulic axes, which are identical with the axis studied in this chapter
An electrohydraulic axis whose mathematical model (MM) is described in this chapter presents a multitude of nonlinearities Conventional controllers are becoming increasingly inappropriate to control the systems with an imprecise model where many nonlinearities are manifested Therefore, advanced techniques such as neural networks and fuzzy algorithms are deeply involved in the control of such systems Neural networks, initially proposed by McCulloch and Pitts, Rosenblatt, Widrow, had several
Florin Ionescu
University of Applied Sciences
Crina Vlad
Politeknica University of Bucharest
Dragos Arotaritei
Aalborg University Esbjerg