Invention | Free Full Text | Simulating Continuous Logic of Control Signals in Cyber-Physical Networks

3.2. Continuum Processor

In ACPNs, the model of the physical process Π (including the computational process) can be represented as elements with four sets of outputs (Fig. 18): X, Q, Z, q(

\overset{￣}{q}

), called a continuous processor (CP).The inputs of the set X are fed signals containing the values of the input parameters

A (t) = X_{1} (t), X_{2} (t), \dots, X_{n} (t)

.From the conclusion rthe result value of the output parameter

r (t) = F (A (t))

is derived. The remaining signals determine the logic of interaction between the CP and the network.

The CP image on the circuit diagram is divided into five rectangular parts that perform different tasks: Synthesis of functional dependencies of the input parameters $A (t)$ Processing of logical input signals ask(t), transmission of synthetic analog signals r(t) to the output and transmits the output logic signal q and $\overset{￣}{q}$ Contains information about connecting or disconnecting signal outputs r.

CP is a combination of analog circuits with a unified functional logical connection structure, which simultaneously solves two problems: calculating the functional dependence of parameters and logical analysis to decide on the method to choose to process the source data. Both tasks are jointly solved within the temporal continuum of source data changes. This is the fundamental difference between the proposed method and circuit solution and traditional computing schemes, which transition from analog to digital forms of signal representation and then to programs. Logical data processing in continuous computing devices is performed within those processes modeled.

Main differences between CP and existing analog processors [33] is the ability to model situations in the time continuum of a system of interactive processes

PI (t) = {PI}_{1} (t), {PI}_{2} (t), \dots, {PI}_{S} (t)

Due to the combination of functional transformations and logical processes in continuous computation (discretization without time intervals), the device is treated as a single information object that responds in real time to changes in physical parameters. CP is a simulation model of a continuous process and, therefore, it can be integrated into technical systems in the form of an appropriate mathematical real-time model. Computational systems become part of continuous physical processes and are one of their links.

The operation of CP is performed according to the rules of predicate logic, combined with the conjunction of three conditions:

$ask (t) \land θ (F, A (t)) = I (A (t)) \land Phi \land θ (F, A (t))$

(17)

where θ, φ, ϑ are binary functions; θ is a check of calculation conditions, φ is a check of initial data preparation, ϑ is a check of constraints, F is a calculation function.

The CP includes a comparator for comparing the value of the analog signal X, a logic gate for verifying the condition (17), and an electronic switch for transmitting the analog signal Z to the network.

The speed of the CP determines the response time of the keys in the logic control circuit, which is about 10-100 ns for modern analog switches. The proposed technical solution therefore provides the ability to control physical processes that vary in time and at frequencies up to tens of megahertz. At high speeds, the energy cost of CP is in mW because the calculation process does not require high-frequency switching.

Let us consider the example of using CP to perform continuous logical operations.

example 1.

The logical NOT operation can be performed by two CP π and

\overset{￣}{PI}

if the input voltage x

ℂ
∩

ℂ
￣

=
∅

. Figure 19 shows the agent circuit that performs the negation operation.The voltage x

ℂ
∪

ℂ
￣

.signal with zone

ℂ

\overset{￣}{ℂ}

Tuples of parameters and analog and logical signals ϑ = (x,q_X) is fed to the CP input.

In case of applying parameters $ℂ$ Region to input, two variants of network reaction are possible:

when signal X voltage enters the area $ℂ$ ,output signal X π will appear at the CP output, and there will be no analog signal at the CP input. $\overset{￣}{PI}$ ;
when signal X voltage enters the area $\overset{￣}{ℂ}$ ,output signal $\overset{￣}{X} = X$ will appear at the output of CP $\overset{￣}{PI}$ there will be no analog signal at the input of CP π.

Therefore, when performing a negation operation, CP $\overset{￣}{PI}$ will change the conditions for transmitting signals X and the conditions that control the aggregate operating mode in CP $\overset{￣}{PI}$ to the opposite person.

By changing the area parameters $ℂ (\overset{￣}{ℂ})$ At the input of CP π, the conditions for using the network under consideration can be reversed.

example 2.

A device that performs the XOR function of two parameters is shown in Figure 20. It consists of two CPs, π₁ and π₂whose functional input is fed by the analog signal x₁ and x₂.The logic input receives the ready signal φ, which is generated by the circuit to check whether the signals ×1 and ×2 fall within their allowed value range

ℂ_{1}

and

ℂ_{2}

. Logic ready signal φ(x₁) is simultaneously transferred to the second logic input of CP π₁ and goes through the inverter to the second logic input of CP π₂. Logic ready signal φ(x₂) are simultaneously transferred to the logical first input of CP π₂ and goes through the inverter to the logical first input of CP π₁. This connection ensures blocking of both CPs with or without simultaneous signal supply x₁ and x₂ at the input. Otherwise, one of the CPs is opened for processing and transmitted to the output of one of the signals f.₁ or f₂. The analog signal present at the device output is reported by the logic signal q.

Logic ready signalφ(X₁) and φ(X₂) from the circuit that checks whether the signal satisfies condition (17) X₁ and X₂.

example 3.

Suppose you need to generate a control signal:

$Z_{\lor} = {\begin{matrix} \begin{matrix} F_{1} (X_{1}, X_{2}) & I F & X_{1} ε ℂ_{1}, X_{2} ε ℂ_{2} \end{matrix} \\ \begin{matrix} F_{2} (X_{1}) & I F & X_{1} ε ℂ_{1}, X_{2} \notin ℂ_{2} \end{matrix} \\ \begin{matrix} F_{3} (X_{2}) & I F & X_{1} \notin ℂ_{1}, X_{2} ε ℂ_{2} \end{matrix} \end{matrix}$

(18)

function f₁(X₁,X₂) has the highest priority among tasks.If two signals x then use it₁,X₂ applied to the input of the device and does not violate the condition (1) of the selection function Z = f₁(X₁,X₂). function f₂(X₁) applies when there is at least one requirement to use function f₁ Violated, signal x₁ applied to the input, selects the condition(1) of the function f₂ There is no violation, and the limit on the value Z = f₂(X₁) are satisfied. function f₃(X₃) applies when there is at least one requirement to use function f₁ and f₂ Violated, signal x₂ applied to the input, selects the condition(1) of the function f₃ No violation.

This task is achieved through separate combinations of analog signals (Figure 21). The device handles input voltage x₁ and x₂ and the logic level of the signaling flag φ(x₁) and φ(x₂).exist

X_{1} ε ℂ_{1}, X_{2} ε ℂ_{2}

Output of CP π₁ is connected and its inverse logic signal q₁ Block CP π₂ and π₃.exist

X_{1} ε ℂ_{1}, X_{2} \notin ℂ_{2}

signal f₂(x) Connect to the output of the device.exist

X_{1} \notin ℂ_{1}, X_{2} ε ℂ_{2}

signal f₃(x) Connect to the output of the device.

The examples provided demonstrate the general functionality of CP embedded in various analog signal logic processing circuits. Hardware support for continuous logic allows you to create ACPN element libraries.

One of the most important properties of CP-based circuits is the relatively low frequency of changes in the voltage levels of the signals transmitted in the network. In digital computing devices, sequential computations require high-frequency clock signals. In CP, the functional dependence of the signal is continuously synthesized based on the given node values using interpolation methods. In this case, the frequency band of the analog signal is determined by the physical processes in the control object. It has a much narrower frequency band than digital pulses.

The frequency of signal changes is low, causing the communication lines to remain electrically shorted even if the ACPN units are sufficiently far apart from each other. Therefore, the coordination of ACPN devices is simplified compared to digital networks, and the implementation of distributed control systems for large objects is also simplified.

The frequency characteristics of the circuits on the CP are related to technical and physical limitations. Technical limitations are determined by the capabilities of the element library. Physical limitations are related to the specific implementation of ACPN. The main factor in physical limitations is the size of the control object.

Figure 22 shows the distribution of the rudder control unit on the fuselage.

ACPN functionally connects aggregates to perform automatic control of the flight stabilization process. Polymer spacing of tens of meters makes it possible to synthesize control signals in the frequency range of 1 MHz. In this case, the fluctuating characteristics of the connecting cables do not occur and the design of the control system is simplified. The structural simplification of the control system makes it possible to enhance its capabilities in improving reliability by connecting redundant communication channels.

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Invention | Free Full Text | Simulating Continuous Logic of Control Signals in Cyber-Physical Networks

3.2. Continuum Processor

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