Structural diagrams of control automata using fuzzy controllers for building control systems are proposed, types of behaviors of such automata that differ from the traditional ones by the possibility of parametric and structural adaptation of behavior, the formation of parallel activity relative to the state activity interval are described. Examples of the use of the proposed functional structures are given.
Since the middle of the last century, finite automata have been used as a model of
control devices for discrete and logical control [
Such machines have limited behavior in the control system. They lack the
mechanisms of structural adaptation of the automaton; the activity of the exits is rigidly
“tied” to the time of the activity of the state. The need for an extended automaton
behavior arises in the design of integrated and cognitive control systems [
The behavior proposed in [
On the basis of definitions (2) and (3), automata with non-binary elements forming the automaton sets X, Y, S and C can be built. At the same time, the author-accessible publications lack the functional structures and mechanisms for realizing the behavior of automata, built on the basis of tuples (2) and (3), which complicates their practical application.
The purpose of this work is to study the functional structures and mechanisms for implementing the extended behavior of automata constructed using Fuzzy controllers. 3
Fuzzy controller is a functional block that implements one of the fuzzy inference
algorithms [
The IEC 61131-7 [
These standards note the advantages of fuzzy controllers compared to other types of controllers, including the simplicity of the implementation of the parametric adaptation of the controller, but there are no recommendations for using fuzzy controllers to build control machines with both binary and non-binary elements of automaton sets. 4
First consider the use of a fuzzy controller for constructing a classic control automaton based on a tuple (1) with binary elements of the sets X, Y, and S. The block diagram of the control automaton based on the fuzzy controller is shown in Fig. 1.
To build the control automaton, the fuzzy controller was used together with the state memory block of the automaton. The controller has two groups of inputs and two groups of outputs. Inputs X of the controller are connected to the outputs of the control object. The current state S of automata is fed to the inputs S of controller. A new state value is formed at the outputs St + 1, into which the control automaton passes to the transition. And outputs Y are connected to executive mechanisms or to inputs of output operating automatic machines.
The controller's operation will be described in the traffic light control system, the block diagram of which is shown in Fig.2. The system implements a state machine whose graph is shown in Fig. 3.
The control device has four states (s0 - Green, s1 - Yellow1, s2 - Red, s3 - Yellow2), four transitions, and four outputs (y0 - Green; y1 - Yellow, Start Timer 1; y2 Red, Start Timer 2; y3 - Yellow, Start Timer 3). One of transitions (x1) is an event transition, the rest (x2 - x4) are time transitions, which is counted using timers.
The states of the automaton S at the input and output of a fuzzy controller are
described as fuzzy variables with membership functions of the “Singletons” type [
The structure of the control device graph defines the control rules that are stored in the fuzzy controller's rule base. These rules are given in table 1.
Transition from s0 to s1
s2
s3
s0 Transition from s1 to s2 Transition from s2 to s3 Transition from s3 to s0
Rule 1 sets the initial state, rules 2 - 5 describe actions in the states, and rules 6 - 9 describe transitions from one state to another.
The fuzzy traffic light control model can be written in FCL notation, as shown in Figure 5.
Next, we consider the use of fuzzy controller for implementing control devices in accordance with the tuples of sets (2) and (3). Note that the activation, outputs and structures functions provided by the tuple (3) must be implemented for each state of the control unit's automaton. To do this, the control device must have a network of fuzzy controllers that interact with each other and with the operating machines of the control device through the memory of parameters, states, controls and the knowledge base. If for some states, the use of fuzzy controllers is redundant, then conventional (FSM) controllers are used to implement state functions. A generalized block diagram of a control system based on networks of operational machines that control fuzzy and FSM controllers is shown in Fig. 6.
The following types of controls are possible in this structure:
Continuous control in the loop Control Object - Sensors - Input operating machines
- Intermediate operating machines 1 - Output operating machines - Actuators. The
operating machines involved in the loop perform a PID or other controller.
Event (logical) control using the FSM controller. Input operation machines
transform analog signals from sensors into an event (binary signal) at the input of the
FSM controller. As a result of this controller operation, its new state and output are
determined. The output operation machines initiate the activation of the actuators
or count down the time intervals necessary for control.
Hybrid control using automatic machines and FSM controller [
Consider the features of the implementation of such controls by example. The fragment of the state graph of the controlling automaton with non-binary elements of the sets is shown in fig. 7.
The elements of the state set sj, si, sk, sl, sm take the values: active, post-active, preactive or passive. The elements of the set of inputs x0 - x3 and outputs yj, yi, yk, yl, ym can be logical, numerical or fuzzy type variables.
Let the state si be active at the current time. The transition to state si was made from state sj. The function of the structure sets the control c2 in state si. Note that the control c2 does not allow the transition from the state si to the state sk. Activation function μi calculate the value of states in the vicinity of the active state: sj is postactive, si is active, sk is passive, sl, sm are pre-active. State values are used by the output functions of these states to determine the level and / or type of activity of the outputs. Post-activity can be used to obtain processing and storage of secondary data that were relevant in the sj state. The pre-activity of a certain state is intended to prepare the necessary data, information and knowledge to perform actions after the activity is received by these states.
The behavior described above can be implemented with the help of fuzzy controllers like control of a traffic light. For example, to calculate the pre-activity in the sl state of the automaton Fig.7 rules like "IF si IS “active” AND x2 IS “probable” AND “structure” IS c2 THEN sl IS “pre-active”" are used. The variables si, x2, Structure, sl, presented in the rule, are linguistic variables with terms and membership functions given in Table. 2.
Variable name si, sl x2 Structure The capabilities of control automata in the form of FSM are not enough to effectively solve the problems of constructing adaptive, integrated, and cognitive control systems.
The decision proposed in [
It follows that the various states of the controlling automaton may have different functions and devices for their realization. This paper describes the use of fuzzy controllers as devices for implementing state functions. The advantages of fuzzy controllers in control tasks are the ability to use the experience of experts, qualitative factors, and the availability of methods for the automatic synthesis of such controllers by training neural networks.
The technique of using fuzzy controllers is presented on examples of traffic control and a generalized control system combining fuzzy controllers and traditional FSM with a set of input, intermediate and operating machines.
Control devices based on fuzzy controllers implement a wide range of control types - continuous, discrete, hybrid, which differ in parametric and structural adaptation capabilities, are easily integrated into hierarchical control structures, and implement nonlinear controllers.
The proposed methods for constructing control automata are proposed to use
cognitive monitoring systems for power transformer parameters [