CN110989347B - Networked control system and control method based on event trigger mechanism - Google Patents

Networked control system and control method based on event trigger mechanism Download PDF

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CN110989347B
CN110989347B CN201911245333.XA CN201911245333A CN110989347B CN 110989347 B CN110989347 B CN 110989347B CN 201911245333 A CN201911245333 A CN 201911245333A CN 110989347 B CN110989347 B CN 110989347B
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左志强
周天薇
王一晶
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Tianjin University
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Abstract

The invention relates to a networked control system based on an event trigger mechanism, which comprises the steps of firstly establishing a networked control system model, then designing a proper event trigger control strategy and a coding and decoding scheme, and designing a local controller to ensure that the networked control system has a finite gain L2Stability and input feed-forward output feedback passivity. When the triggering condition is met, the information to be transmitted is output after being quantized and coded, and the condition that a networked control system has limited gain L is ensured2Stability and input feedforward output feedback passivity; in addition, the event trigger control strategy based on the reference input and the hysteresis quantizer reduces the information transmission times, and ensures that the information transmitted each time has larger information quantity, thereby greatly reducing the network burden and saving the communication resources; furthermore, reducing the delay through the local controller provides a finite gain L to the networked control system2Stability and input feed-forward output feedback passivity.

Description

Networked control system and control method based on event trigger mechanism
Technical Field
The invention belongs to the field of controller design, and particularly relates to a networked control system and a control method based on an event trigger mechanism, wherein a local controller is utilized to reduce adverse effects of time delay on the performance of the networked control system.
Background
With the rapid development of network technology, communication technology, and computer technology, humans have stepped into a new era of networking. The networked control system is a system for exchanging information among a controlled object, a sensor, a controller and an actuator through a network, and is widely applied to the fields of industrial control, medical treatment, aerospace and the like.
The networked control system has the advantages of simplicity and convenience in installation, easiness in maintenance, high reliability, convenience in resource sharing and the like, but uncertain factors such as quantification and time delay also exist. The event trigger strategy which embodies the real requirements of the networked control system is designed for the networked control system, and the event trigger strategy has important significance for saving communication resources and realizing the stabilization of the networked control system. The conventional time trigger strategy determines whether the time interval between the time of information delivery and the time of last delivery reaches a preset sampling interval.
Because the time trigger strategy is not transmission guided by system requirements, the situations that excessive sampling occurs when some signals change slowly, and rapid changes of the signals cannot be transmitted to a receiving party in time when some signals change rapidly occur easily, so that communication resources are excessively occupied or ideal performance of the system cannot be realized. Unlike the time-triggered strategy, the event-triggered control strategy is a control manner that determines the transmission timing of information with the desired objective as a guide. Because information transmission is not carried out when the event does not occur, the event trigger control reduces unnecessary transmission times, reduces the occupation of communication resources and saves the communication resources and processor resources. Different event trigger control strategies correspond to different system information importance distribution schemes, and different information transmission time and information transmission times are determined. How to reduce the number of information transmissions as much as possible while ensuring system performance and how to make trade-offs between system performance and channel occupancy become key to designing event triggering strategies.
In practical systems, data typically needs to be processed through a quantizer before being transmitted over the network, taking into account network bandwidth limitations and the requirements of digital communications. Due to limited network bandwidth, the transmitted data requires time-sharing communication resources. In addition, because the data receiving and transmitting time of different nodes has certain randomness, a situation that a plurality of nodes transmit data simultaneously may occur, so that the data needs to be queued for transmission. Network-induced delays inevitably occur in networked control systems. The existence of quantization and network-induced delay adversely affects the performance of the networked control system, and poses a serious challenge to the analysis of the networked control system. To date, no event-triggered control strategy based on the reference input and the hysteresis quantizer structure has emerged, as well as the design of local controllers with the adverse effects of reducing latency.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a baseThe control strategy is triggered by the event of the reference input and delay quantizer and the local quantizer for reducing the adverse effect brought by time delay, thereby avoiding the buffeting phenomenon of the networked control system and ensuring the limited gain L of the networked control system under the condition of saving communication resources2Stability and input feedforward output feedback passivity are based on a networked control system of an event trigger mechanism.
The technical scheme adopted by the invention for solving the technical problem is as follows:
the utility model provides a networked control system based on event trigger mechanism, includes controlled object and controller, and the controlled object input is connected with the controller output through zero order retainer, decoder, encoder and trigger, and the controller input is connected with controlled object output through zero order retainer, decoder, encoder and trigger, its characterized in that:
a local controller LCP is arranged between the zero-order keeper at the input end of the controlled object and the decoder2The output end of the controller is connected with one end of a hysteresis quantizer, and the other end of the hysteresis quantizer is connected with a trigger connected with the output end of the controller;
a local controller LCC is arranged between a zero-order retainer at the input end of the controller and the decoder, the output end of a controlled object is connected with one end of another hysteresis quantizer, and the other end of the another hysteresis quantizer is connected with a trigger connected with the output end of the controlled object;
connecting local controllers LCP between encoder and decoder at the controller input1The local controller LCP1The other end of the zero-order retainer is connected with one end of a zero-order retainer, and the other end of the zero-order retainer is connected with the input end of the controlled object.
Furthermore, the one lag quantizer and the other lag quantizer function to quantize the input signal and output the quantized signal.
Another object of the present invention is to provide a control method for a networked control system based on an event trigger mechanism, which is characterized in that: the control system comprises the control method, and the control method comprises the following steps:
first setting
Firstly, establishing a nonlinear controlled object, a controller and a networked control system model
Figure BDA0002307373520000021
Figure BDA0002307373520000022
Figure BDA0002307373520000023
Wherein the content of the first and second substances,
Figure BDA0002307373520000024
state, measurement output and input of a controlled object;
Figure BDA0002307373520000025
is the state, measurement output, input of the controller;
Figure BDA0002307373520000026
respectively a reference input, a state and a measurement output of the networked control system;
fp(·,·)，hp(·,·)，fc(·,·)，hc(-) f (-) h) are respectively corresponding nonlinear functions;
② there is disturbance at the controller input
||w(t)||2≤Δw＝δw(t)u(t)
Wherein, | | · | | is a Euclid norm,
Figure BDA0002307373520000027
the controlled object and the controller are both input feedforward output feedback passive and input feedforward and outputThe index of feedback is ap，bpAnd ac，bc；
④dp(tk)，dc(τj) Respectively controlled object to controller channel and controller to controlled object channel at trigger time tkAnd τjThe time-varying delay of (2) satisfies:
Figure BDA0002307373520000028
wherein the content of the first and second substances,
Figure BDA0002307373520000029
and
Figure BDA00023073735200000210
the maximum time delay change rate from the controlled object to the controller channel and the maximum time delay change rate from the controller to the controlled object channel are respectively;
constructing a hysteresis quantizer based on the uniform quantizer
Figure BDA0002307373520000031
Wherein the content of the first and second substances,
Figure BDA0002307373520000032
non-negative integer, Δ is the maximum quantization error.
And taking the jumping moment of the quantization level as a trigger moment, and triggering a control strategy by the controlled object output end based on the reference input and the event of the hysteresis quantizer:
Figure BDA0002307373520000033
wherein, tkThe trigger time of the output end of the controlled object is the trigger time of the output end of the controlled object;
Figure BDA0002307373520000034
for controlled object transmissionThe output end is provided with a hysteresis quantizer in the form of a fifth step; deltap＝δp(t) u (t) is the maximum quantization error;
Figure BDA0002307373520000035
is the lag quantizer parameter; u (t) is a reference input of the networked control system;
the controller output triggers a control strategy based on the reference input and the event of the hysteresis quantizer:
Figure BDA0002307373520000036
wherein, taujThe trigger time of the output end of the controller;
Figure BDA0002307373520000037
a hysteresis quantizer having the form of equation (5) for the controller output; deltac＝δc(t) u (t) is the quantization error;
Figure BDA0002307373520000038
is the lag quantizer parameter; u (t) is a reference input of the networked control system; when the event trigger control strategy (6) is met, the output of the controlled object is sampled, and the value of the sampled output is transmitted through a channel after being coded; otherwise, no information transfer is performed. Similarly, when the event-triggered control strategy (7) is satisfied, the output of the controller is sampled and its value is encoded and passed through the channel; otherwise, no information transfer is performed.
Decoding scheme
At triggering time tkDesign of controlled object output yp(tk) Corresponding transmission code word
Figure BDA0002307373520000039
Wherein the content of the first and second substances,
Figure BDA00023073735200000310
triggering the needed transmission code word for the first time;
Figure BDA00023073735200000311
for triggering a time tk+1A transmission codeword as needed;
considering the time delay d existing in the channel at the output end of the controlled objectp(t) designing a decoding scheme according to the transmitted codeword
Figure BDA00023073735200000312
Wherein the content of the first and second substances,
Figure BDA00023073735200000313
a decoding scheme for first decoding;
Figure BDA00023073735200000314
a decoding scheme for decoding the (k + 1) th time;
② at the triggering time τjDesign controller output yc(τj) Corresponding transmission code word
Figure BDA0002307373520000041
Wherein the content of the first and second substances,
Figure BDA0002307373520000042
triggering the needed transmission code word for the first time;
Figure BDA0002307373520000043
for the triggering time tauj+1A transmission codeword as needed;
in view of the time delay d existing in the channel at the output of the controllerc(t) designing a decoding scheme according to the transmitted codeword
Figure BDA0002307373520000044
Wherein the content of the first and second substances,
Figure BDA0002307373520000045
a decoding scheme for first decoding;
Figure BDA0002307373520000046
a decoding scheme for decoding the j +1 th time;
the controlled object and the controller have limited output change rate and are set to exist
Figure BDA0002307373520000047
Satisfy the requirement of
Figure BDA0002307373520000048
Figure BDA0002307373520000049
Due to yp(t) and yc(T) has a finite rate of change, and the trigger interval Δ T of the controlled objectp[k+1]And the trigger time interval Delta T of the output end of the controllerc[j+1]Are respectively as
Figure BDA00023073735200000410
Wherein, Delta Tp[k+1]And Δ Tc[j+1]Quantizer parameters of the controlled object and the controller output end respectively;
partial controller
Figure BDA00023073735200000411
Wherein c and p1、p2Respectively local controllers LCC, LCP1、LCP2The control gain of (1);
sixth, a method for constructing
Figure BDA00023073735200000412
Storage function of and
Figure BDA00023073735200000413
and reference input u (t)
The controller satisfies the passivity of input feedforward and output feedback, and the indexes of the input feedforward and the output feedback are acAnd bcIf present, a constant
Figure BDA00023073735200000414
So that
Figure BDA00023073735200000415
And local controller parameters c, p1And p2Satisfies the following conditions:
Figure BDA00023073735200000416
then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizer
Figure BDA00023073735200000417
Output is as
Figure BDA00023073735200000418
Is/are as follows
Figure BDA00023073735200000419
Satisfy the requirement of
Figure BDA00023073735200000420
Wherein, Vc(t) is a memory function of the controller; parameter(s)
Figure BDA00023073735200000421
Are respectively as
Figure BDA0002307373520000051
Figure BDA0002307373520000052
Figure BDA0002307373520000053
The killed control system H has a limited gain L2Sufficient condition for stability
If present, is
Figure BDA0002307373520000054
When it is satisfied with
Figure BDA0002307373520000055
And is
Figure BDA0002307373520000056
And is
Figure BDA0002307373520000057
When the input is u (t) and the output is yp(t) is a finite gain L2Is stable;
and when the conditions in the step sixteenth and the step fourth are both satisfied, the control system satisfies
Figure BDA0002307373520000058
Wherein, it is made
Figure BDA0002307373520000059
The input feedforward index a and the output feedback index b satisfy
Figure BDA00023073735200000510
Figure BDA00023073735200000511
The invention has the beneficial effects that:
in the invention, firstly, a networked control system model is established, and thenDesigning a proper event trigger control strategy and a corresponding coding and decoding scheme, and designing a local controller on the basis of the strategy to ensure that a networked control system has a limited gain L2Stability and input feed-forward output feedback passivity. When the trigger condition in the event trigger control strategy is met, the information to be transmitted is quantized and coded and then transmitted to the receiving end, so that the networked control system is ensured to have limited gain L2Stability and input feedforward output feedback passivity; in addition, because the event trigger control strategy based on the reference input and the hysteresis quantizer greatly reduces the information transmission times and ensures that the information transmitted each time has larger information quantity, the event trigger control strategy greatly reduces the network burden and saves the communication resources; furthermore, reducing the delay through the local controller provides a finite gain L to the networked control system2Stability and input feed-forward output feedback passivity.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention;
FIG. 2 is a schematic diagram of the triggering of an event-triggered control strategy based on a reference input and a hysteresis quantizer;
FIG. 3 is a networked control system formed by a double-wheel differential wheel type mobile robot Qbot 2 and an upper computer;
FIG. 4 is a communication structure of a networked control system;
FIG. 5 is a Qbot 2 model of a two-wheeled differential wheeled mobile robot;
FIG. 6 is an experimental trail of a wheeled mobile robot;
FIG. 7 is
Figure BDA00023073735200000512
ux(t) and trigger time
Figure BDA00023073735200000513
The relationship between;
FIG. 8 is
Figure BDA0002307373520000061
uz(t) and trigger time
Figure BDA0002307373520000062
The relationship between;
fig. 9 is a schematic diagram of a prior art system.
Detailed Description
The present invention is further illustrated by the following examples, which are intended to be illustrative, not limiting and are not intended to limit the scope of the invention.
The present invention, as shown in fig. 1, proposes an event-triggered control strategy based on a reference input and a hysteresis quantizer and a local quantizer for reducing adverse effects caused by time delay, so as to ensure that a networked control system has a finite gain L2Stability and input feed-forward output feedback passivity.
Compared with the system diagram of the prior art shown in fig. 9, when the trigger condition in the event trigger control strategy based on the reference input and the hysteresis quantizer is satisfied, the information to be transmitted is quantized and encoded and then transmitted to the receiving end, thereby ensuring that the networked control system has the finite gain L2Stability and input feed-forward output feedback passivity. Because the event trigger control strategy based on the reference input and the hysteresis quantizer greatly reduces the information transmission times and ensures that the information transmitted each time has larger information quantity, the event trigger control strategy greatly reduces the network burden and saves the communication resources. In addition, a local controller is designed for reducing the finite gain L of the time delay to the networked control system2Stability and input feed-forward output feedback passivity.
The specific implementation mode is as follows: firstly, a networked control system model is established, and then a proper event triggering control strategy and a corresponding coding and decoding scheme are designed. On the basis, the local controller is designed to ensure that the networked control system has a limited gain L2Stability and input feed-forward output feedback passivity.
In order to more clearly illustrate the objects, technical solutions and advantages of the present invention, the present invention will be further explained in the following aspects of model building, design principles, design methods and the like.
A network control system based on event trigger mechanism includes controlled object and controller, the input end of the controlled object is connected with the output end of the controller through the zero order keeper, decoder, encoder and trigger, the input end of the controller is connected with the output end of the controlled object through the zero order keeper, decoder, encoder and trigger, the innovation of the invention is shown in figure 1:
a local controller LCP is arranged between the zero-order keeper at the input end of the controlled object and the decoder2The output end of the controller is connected with one end of a hysteresis quantizer, and the other end of the hysteresis quantizer is connected with a trigger connected with the output end of the controller;
a local controller LCC is arranged between a zero-order retainer at the input end of the controller and the decoder, the output end of a controlled object is connected with one end of another hysteresis quantizer, and the other end of the another hysteresis quantizer is connected with a trigger connected with the output end of the controlled object;
connecting local controllers LCP between encoder and decoder at controller input1The local controller LCP1The other end of the zero-order retainer is connected with one end of a zero-order retainer, and the other end of the zero-order retainer is connected with the input end of the controlled object.
The function of the one lag quantizer and the other lag quantizer is to quantize the input signal and output the quantized signal.
The network control system performance analysis and design based on the event trigger mechanism comprises the following specific steps.
Step 1: establishing the following nonlinear controlled object, controller and networked control system model
Figure BDA0002307373520000063
Figure BDA0002307373520000071
Figure BDA0002307373520000072
Wherein the content of the first and second substances,
Figure BDA0002307373520000073
Figure BDA0002307373520000074
the state of the controlled object (controller), measurement output, and input, respectively.
Figure BDA0002307373520000075
Figure BDA0002307373520000076
Respectively, the reference input, the state and the measurement output of the networked control system. f. ofp(·,·)，hp(·,·)，fc(·,·)，hcThe (H) and f (H) are respectively corresponding nonlinear functions to ensure a nonlinear controlled object HpAnd a controller HcBoth input feed-forward and output feedback are passive.
Assuming that there is disturbance | w (t) | torry at the input of the controller2≤Δw＝δw(t) u (t) (this perturbation and the above equation), where | l | · | | is a Euclid norm,
Figure BDA0002307373520000077
the controlled object and the controller are both passive with input feedforward and output feedback, and the indexes of the input feedforward and the output feedback are ap，bpAnd ac，bc。
Fig. 1 presents a networked control system architecture framework contemplated by the present invention.
Wherein ZOH is zero-order retainer, LCC, LCP1And LCP2Respectively, the proposed local controller. The lag quantizer, the flip-flop and the encoder together form the RIHQBTC strategy proposed in this patent. In the structural framework of the networked control system, the inventionThe new portions are marked with pink and light blue, respectively. The controlled object and the controller form a network control system through a communication channel. Under the combined action of the local controller, the controller and the trigger, the networked control system can realize the limited gain L2And (4) stabilizing.
In the structural framework, up(t) and ypAnd (t) are input and output of the controlled object respectively.
1. Signal yp(t) inputting a hysteresis quantizer and a trigger, the trigger selecting a trigger instant t based on the structure of the hysteresis quantizer and a proposed trigger strategyk. Due to the fact that
Figure BDA0002307373520000078
Figure BDA0002307373520000079
Is encoded into
Figure BDA00023073735200000710
And delivered to the decoder side through a communication channel.
2.
Figure BDA00023073735200000711
LCP via local controller1And ZOH zeroth order keeper for converting into segmented continuous signal
Figure BDA00023073735200000712
Decoder receives
Figure BDA00023073735200000713
Then decoding it to obtain
Figure BDA00023073735200000714
Output after passing through a local controller LCC
Figure BDA00023073735200000715
The zero order keeper will
Figure BDA00023073735200000716
Conversion to piecewise continuous
Figure BDA00023073735200000717
The input to the controller is u due to the influence of the disturbance w (t)c(t) of (d). The output of the controller end is yc(t) of (d). Signal yc(t) inputting a hysteresis quantizer and a trigger, the trigger selecting a trigger instant τ based on the structure of the hysteresis quantizer and the proposed trigger strategyj。yc(τj) Is encoded into
Figure BDA00023073735200000718
And delivered to the decoder side through a communication channel. Decoder receives
Figure BDA00023073735200000719
Then decoding it to obtain
Figure BDA00023073735200000720
LCP Via local controller2Rear output
Figure BDA00023073735200000721
The zero order keeper will
Figure BDA00023073735200000722
Conversion to piecewise continuous
Figure BDA00023073735200000723
Figure BDA00023073735200000724
And
Figure BDA00023073735200000725
are formed jointly
Figure BDA00023073735200000726
And the input u (t) of the networked controller forms the input u (t) of the controlled objectp(t)。
Also in this example, the output of the networked control system we are concerned with is yp(t) of (d). Since there may be a delay phenomenon in the channel under consideration, let dp(tk)，dc(τj) Respectively controlled object to controller channel and controller to controlled object channel at trigger time tkAnd τjTime-varying delay of (1) satisfying
Figure BDA0002307373520000081
Wherein the content of the first and second substances,
Figure BDA0002307373520000082
and
Figure BDA0002307373520000083
the maximum delay change rate of the controlled object to the controller channel and the maximum delay change rate of the controller to the controlled object channel are respectively.
Hysteresis quantizer constructed based on uniform quantizer
Figure BDA0002307373520000084
Wherein the content of the first and second substances,
Figure BDA0002307373520000085
non-negative integer, Δ is the maximum quantization error. According to the model of the hysteresis quantizer, the system does not generate buffeting caused by the reciprocating jump of the quantization level under the action of the hysteresis quantizer. By a lag quantizer qh(y (t)) in the model (5), the signal y (t) satisfies | | q before and after quantizationh(y (t)) -y (t)) | | ≦ Δ. And taking the jumping moment of the quantization level as a trigger moment, and designing an event trigger control strategy based on a reference input and a hysteresis quantizer for the controlled object and the output end of the controller.
Step 2: in the networked Control system structure shown in fig. 1, according to the relationship between the controlled object output and the Reference Input and the Hysteresis Quantizer parameter, the jump time of the quantization level is used as the trigger time, and the event trigger Control strategy (Reference Input and hysteris Quantizer Based Triggered Control, RIHQBTC strategy for short) Based on the Reference Input and the Hysteresis Quantizer is designed at the controlled object output end as follows
Figure BDA0002307373520000086
Wherein, tkIs the trigger moment of the output end of the controlled object,
Figure BDA0002307373520000087
for a hysteresis quantizer of the form (5) corresponding to the output of the controlled object, Δp＝δp(t) u (t) is the maximum quantization error,
Figure BDA0002307373520000088
u (t) is the reference input of the networked control system for the lag quantizer parameters. FIG. 2 is a schematic diagram of the triggering of an event-triggered control strategy based on a reference input and a hysteresis quantizer. As can be seen from fig. 2, the signal is triggered only when the quantization level jumps.
Similarly, according to the relationship between the controller output and the Reference Input and the Hysteresis Quantizer parameter, the following event Triggered Control strategy (RIHQBTC strategy for short) Based on the Reference Input and the Hysteresis Quantizer is designed at the controller output end
Figure BDA0002307373520000089
Wherein, taujIs the triggering moment of the output end of the controller,
Figure BDA00023073735200000810
for the hysteresis quantizer at the output of the controller in the form of equation (5), Δc＝δc(t) u (t) is a quantization error,
Figure BDA00023073735200000811
u (t) is the reference input of the networked control system for the lag quantizer parameters.
When the event trigger control strategy (6) is met, the output of the controlled object is sampled, and the value of the sampled output is transmitted through a channel after being coded; otherwise, no information transfer is performed. Similarly, when the event-triggered control strategy (7) is satisfied, the output of the controller is sampled and its value is encoded and passed through the channel; otherwise, no information transfer is performed. In conclusion, the application of the event-triggered control strategy based on the reference input and the hysteresis quantizer reduces the communication times and saves the communication resources.
And step 3: to save channel resources, at the triggering time tkDesign of controlled object output yp(tk) Corresponding transmission code word
Figure BDA0002307373520000091
Wherein the content of the first and second substances,
Figure BDA0002307373520000092
for the first time the required transmission code word is triggered,
Figure BDA0002307373520000093
for triggering a time tk+1The transmission code word is needed as needed.
Considering the time delay d existing in the channel at the output end of the controlled objectp(t) designing a decoding scheme according to the transmitted codeword (8)
Figure BDA0002307373520000094
Wherein the content of the first and second substances,
Figure BDA0002307373520000095
for the decoding scheme to be decoded for the first time,
Figure BDA0002307373520000096
decoding scheme for decoding the (k + 1) th time.
Similarly, at the trigger time τjDesign controller output yc(τj) Corresponding transmission code word
Figure BDA0002307373520000097
Wherein the content of the first and second substances,
Figure BDA0002307373520000098
for the first time the required transmission code word is triggered,
Figure BDA0002307373520000099
for the triggering time tauj+1The transmission code word is needed as needed.
In view of the time delay d existing in the channel at the output of the controllerc(t) designing a decoding scheme in dependence on the transmitted codeword (10)
Figure BDA00023073735200000910
Wherein the content of the first and second substances,
Figure BDA00023073735200000911
for the decoding scheme to be decoded for the first time,
Figure BDA00023073735200000912
decoding scheme for decoding the j +1 th time. According to the coding and decoding scheme, the receiving end can completely restore the signal sent out at the corresponding sending time.
And 4, step 4: under the action of an event trigger control strategy based on a reference input and a hysteresis quantizer, the Zeno phenomenon of a system can not occur, namely the condition of infinite triggering can not occur in a limited time period. Due to limited output change rates of the controlled object and the controller, the assumption exists
Figure BDA00023073735200000913
Satisfy the requirement of
Figure BDA00023073735200000914
Trigger time interval delta T of controlled objectp[k+1]And the trigger time interval Delta T of the output end of the controllerc[j+1]Are respectively as
Figure BDA00023073735200000915
Wherein, Delta Tp[k+1]And Δ Tc[j+1]The quantizer parameters of the controlled object and the controller output end respectively. As can be seen from equation (12), the triggering time interval between the controlled object and the output end of the controller is constantly greater than zero, and the Zeno phenomenon does not occur in the networked control system under the event triggering control strategy based on the reference input and the hysteresis quantizer.
And 5: as shown in fig. 1, in order to ensure the performance of the networked control system and reduce the influence of the time delay on the networked control system, the following three local controllers are designed
Figure BDA0002307373520000101
Wherein c and p1、p2Respectively local controllers LCC, LCP1、LCP2The control gain of (1).
Step 6: constructed as shown in FIG. 1
Figure BDA0002307373520000102
Storage function of and
Figure BDA0002307373520000103
and reference input u (t). Because the controller (2) meets the passivity of input feedforward and output feedback, and the indexes of the input feedforward and the output feedback are a respectivelycAnd bcIt is known that
Figure BDA0002307373520000104
If there is a constant
Figure BDA0002307373520000105
Satisfy the requirement of
Figure BDA0002307373520000106
Through the calculation, the method has the advantages that,
Figure BDA0002307373520000107
therefore, the local controller parameters c, p1And p2Satisfy the requirement of
Figure BDA0002307373520000108
Then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizer
Figure BDA0002307373520000109
Output is as
Figure BDA00023073735200001010
Is/are as follows
Figure BDA00023073735200001011
Satisfy the requirement of
Figure BDA00023073735200001012
Wherein, Vc(t) as a memory function of the controller, parameters
Figure BDA00023073735200001013
Are respectively as
Figure BDA0002307373520000111
And 7: establishing a network-based control system H with a finite gain L2Sufficient conditions for stability.
Figure BDA0002307373520000112
And controlled object HpIs satisfied by a storage function
Figure BDA0002307373520000113
Figure BDA0002307373520000114
From the inequality characteristics, there are
Figure BDA0002307373520000115
Satisfy the requirement of
Figure BDA0002307373520000116
When in use
Figure BDA0002307373520000117
When the content meets the requirement, the content of the active ingredient,
Figure BDA0002307373520000118
if it is
Figure BDA0002307373520000119
Since the storage function V (t) is greater than or equal to 0, the integration is performed on both sides of the equation (23), and the result is obtained
Figure BDA00023073735200001110
Wherein the content of the first and second substances,
Figure BDA00023073735200001111
is a constant. Therefore, when
Figure BDA00023073735200001112
When the input is u (t) and the output is yp(t) is a finite gain L2And (4) the product is stable.
And 8: when the conditions in step 6 and step 7 are both satisfied, the proposed event-triggered control strategy based on the reference input and the hysteresis quantizer is to ensure that the networked control system satisfies the input feedforward output feedback passivity, that is
Figure BDA00023073735200001113
Need to ensure
Figure BDA0002307373520000121
Formula (26) is equivalent to
Figure BDA0002307373520000122
Wherein the content of the first and second substances,
Figure BDA0002307373520000123
Figure BDA0002307373520000124
order to
Figure BDA0002307373520000125
The input feedforward index a and the output feedback index b need to be satisfied
Figure BDA0002307373520000126
Figure BDA0002307373520000127
Based on the above analysis, the following conclusions can be drawn. Of the three conclusions that follow, conclusion 1 calculation
Figure BDA0002307373520000128
The conditions to be met are laid for conclusion 2 and conclusion 3. Conclusion 2 shows that the networked control system satisfies the finite gain L2And 3, stabilizing the required condition, and giving a condition that the networked control system meets the passive requirement of input feedforward output feedback. The invention hopes to ensure that the networked control system has limited gain L by using the minimum information transfer times, namely the minimum triggering times2Stable and input feed forward output feedback passive. The following three conclusions guide the selection of local controller parameters in practice.
Conclusion 1: controller HcSatisfy the passivity of input feedforward and output feedback, and the indexes of input feedforward and output feedback are acAnd bc. If there is a constant
Figure BDA0002307373520000129
So that
Figure BDA00023073735200001210
And local controller parameters c, p1And p2So that
Figure BDA00023073735200001211
Then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizer
Figure BDA00023073735200001212
Output is as
Figure BDA00023073735200001213
Is/are as follows
Figure BDA00023073735200001214
Satisfy the requirement of
Figure BDA00023073735200001215
Wherein, Vc(t) as a memory function of the controller, parameters
Figure BDA00023073735200001216
Are respectively as
Figure BDA0002307373520000131
Conclusion 2: consider the principle of theorem 1
Figure BDA0002307373520000132
And the input feedforward and output feedback passivity indexes are respectively ap，bpControlled object HpForming a networked control system H, if present
Figure BDA0002307373520000133
Satisfy the requirement of
Figure BDA0002307373520000134
Figure BDA0002307373520000135
Figure BDA0002307373520000136
The proposed event-triggered control strategy based on the reference input and the hysteresis quantizer can ensure that the networked control system H has a finite gain L2And (4) the product is stable.
Conclusion 3: consider that
Figure BDA0002307373520000137
And the indexes of input feedforward and output feedback are a respectivelyp，bpControlled object HpWhen theorem 1 and theorem 2 are both established, the event trigger control strategy based on the reference input and the hysteresis quantizer can ensure that the networked control system has the passivity of input feedforward output feedback, namely the networked control system meets the requirement
Figure BDA0002307373520000138
Wherein, it is made
Figure BDA0002307373520000139
The input feedforward index a and the output feedback index b satisfy
Figure BDA00023073735200001310
Figure BDA00023073735200001311
Application examples
The invention is applied to a double-wheel differential wheel type mobile robot Qbot 2, and the finite gain L of a networked control system (shown in figure 3) formed by the double-wheel differential wheel type mobile robot and an upper computer is verified through experiments2Stability and input feed-forward output feedback passivity.
The system communication structure of QBot 2 is shown in figure 4. The IP address of the upper computer is 192.168.2.12, and the IP address of the wheeled mobile robot is 192.168.2.113.
The networked control system formed by Qbot 2 comprises a double-wheel differential wheel type mobile robot, a computer and six positioning cameras (only three cameras in the six cameras are shown in figure 3, and the other three cameras are arranged on the wall opposite to the three cameras on the wall in the figure).
The program written by Simulink can be written into a wheeled mobile robot by QUARC embedded in Matlab/Simulink module. The computer calculates a control signal through coordinate positioning of the current wheeled mobile robot and transmits control information to the wheeled mobile robot through wifi.
The aim of the experiment is to control the wheeled mobile robot to make circular rotation under the RIHQBTC strategy.
Fig. 5 shows a model structure of the wheeled mobile robot. Modeling a wheeled mobile robot as
Figure BDA0002307373520000141
Wherein, (x), (t), z (t)) are coordinates of a center point of the wheeled mobile robot. θ (t), v (t), w (t) and w (t) are the direction, linear velocity and angular velocity of the wheeled mobile robot, respectively.
In view of equation (37) being a non-linear model, coordinates are introduced
Figure BDA0002307373520000142
And corresponding coordinate transformation
Figure BDA0002307373520000143
Definition of
Figure BDA0002307373520000144
Wherein the content of the first and second substances,
Figure BDA0002307373520000145
and
Figure BDA0002307373520000146
is a control signal.
To realize
Figure BDA0002307373520000147
Tracking ux(t) ═ 0.7+0.6cos (0.3t) and
Figure BDA0002307373520000148
tracking uz(t) 0.7+0.6sin (0.3t), and through coordinate transformation, the event-triggered control strategy based on the reference input and the hysteresis quantizer can be respectively selected for determination
Figure BDA0002307373520000149
And
Figure BDA00023073735200001410
the triggering time of (c). That is to say will
Figure BDA00023073735200001411
Is regarded as a networked control process, will
Figure BDA00023073735200001412
Is considered another networked control process.
Figure BDA00023073735200001413
Is dynamic in that
Figure BDA00023073735200001414
Wherein the initial value of the controlled object is
Figure BDA00023073735200001415
In order to be an input, the user can select,
Figure BDA00023073735200001416
to output ux(t) ═ 0.7+0.6cos (0.3t) as a reference signal, and the function is stored
Figure BDA00023073735200001417
The indexes of input feedforward and output feedback of the controlled object are respectively
Figure BDA00023073735200001418
The controlled object in the corresponding model is the formula (1).
The controller is designed as
Figure BDA00023073735200001419
Wherein the controller inputs
Figure BDA00023073735200001420
The memory function of the controller is
Figure BDA00023073735200001421
The indexes of input feedforward and output feedback of the controller are respectively
Figure BDA00023073735200001422
Corresponding to the controller in the model, i.e., equation (2). The model abstracted by the experiment meets the requirements of the system models (1) and (2) through verification.
The other parameters are selected as follows
1) Time delay parameters: initial network induced latency
Figure BDA0002307373520000151
Maximum rate of change of delay
Figure BDA0002307373520000152
Figure BDA0002307373520000153
2) Local controller parameters: c. Cx＝1，
Figure BDA0002307373520000154
3) Inequality weight coefficients:
Figure BDA0002307373520000155
4) lag quantizer parameters:
Figure BDA0002307373520000156
therefore, the temperature of the molten metal is controlled,
Figure BDA0002307373520000157
Figure BDA0002307373520000158
due to possible delay phenomena in the considered channel, let
Figure BDA0002307373520000159
Respectively controlled object to controller channel and controller to controlled object channel at trigger time
Figure BDA00023073735200001510
And
Figure BDA00023073735200001511
time-varying delay of (1) satisfying
Figure BDA00023073735200001512
Hysteresis quantizer constructed based on uniform quantizer
Figure BDA00023073735200001513
The following event-triggered control strategy based on reference input and hysteresis quantizer is designed
Figure BDA00023073735200001514
Similarly, an event Triggered Control strategy (RIHQBTC strategy for short) Based on Reference Input and hysteresis Quantizer is designed at the output end of the controller as follows
Figure BDA00023073735200001515
At the moment of triggering
Figure BDA00023073735200001516
Design controlled object output
Figure BDA00023073735200001517
Corresponding transmission code word
Figure BDA00023073735200001518
The following decoding scheme is designed according to the transmitted code word
Figure BDA00023073735200001519
Corresponding transmission code word
Figure BDA0002307373520000161
Designing a decoding scheme
Figure BDA0002307373520000162
Calculating the trigger time interval of the controlled object
Figure BDA0002307373520000163
And the trigger time interval of the output end of the controller
Figure BDA0002307373520000164
And ensuring that the Zeno phenomenon does not occur in the networked control system under the event trigger control strategy based on the reference input and the hysteresis quantizer.
Figure BDA0002307373520000165
Designing three local controllers
Figure BDA0002307373520000166
And
Figure BDA0002307373520000167
in a similar manner to that described above,
Figure BDA0002307373520000168
is dynamic in that
Figure BDA0002307373520000169
Wherein the initial value of the controlled object is
Figure BDA00023073735200001610
Input device
Figure BDA00023073735200001611
Output of
Figure BDA00023073735200001612
Reference signal uz(t) of (d). Storing functions
Figure BDA00023073735200001613
The indexes of input feedforward and output feedback of the controlled object are respectively
Figure BDA00023073735200001614
Figure BDA00023073735200001615
The controlled object in the corresponding model is the formula (1).
Figure BDA00023073735200001616
The corresponding controller is
Figure BDA00023073735200001617
Wherein the controller inputs
Figure BDA00023073735200001618
The memory function of the controller is
Figure BDA00023073735200001619
The indexes of input feedforward and output feedback of the controller are respectively
Figure BDA00023073735200001620
Corresponding to the controller in the model, i.e., equation (2). The model abstracted by the experiment meets the requirements of the system models (1) and (2) through verification.
The other parameters are selected as follows
1) Time delay parameters: initial network induced latency
Figure BDA00023073735200001621
Maximum rate of change of delay
Figure BDA00023073735200001622
Figure BDA00023073735200001623
2) Local controller parameters: c. Cz＝1，
Figure BDA00023073735200001624
3) Inequality weight coefficients:
Figure BDA0002307373520000171
4) lag quantizer parameters:
Figure BDA0002307373520000172
therefore, the temperature of the molten metal is controlled,
Figure BDA0002307373520000173
Figure BDA0002307373520000174
due to possible delay phenomena in the considered channel, let
Figure BDA0002307373520000175
Respectively controlled object to controller channel and controller to controlled object channel at trigger time
Figure BDA0002307373520000176
And
Figure BDA0002307373520000177
time-varying delay of (1) satisfying
Figure BDA0002307373520000178
Hysteresis quantizer constructed based on uniform quantizer
Figure BDA0002307373520000179
The following event-triggered control strategy based on reference input and hysteresis quantizer is designed
Figure BDA00023073735200001710
Similarly, an event Triggered Control strategy (RIHQBTC strategy for short) Based on Reference Input and hysteresis Quantizer is designed at the output end of the controller as follows
Figure BDA00023073735200001711
At the moment of triggering
Figure BDA00023073735200001712
Design controlled object output
Figure BDA00023073735200001713
Corresponding transmission code word
Figure BDA00023073735200001714
The following decoding scheme is designed according to the transmitted code word
Figure BDA00023073735200001715
Corresponding transmission code word
Figure BDA00023073735200001716
Designing a decoding scheme
Figure BDA00023073735200001717
Calculating the trigger time interval of the controlled object
Figure BDA0002307373520000181
And the trigger time interval of the output end of the controller
Figure BDA0002307373520000182
And ensuring that the Zeno phenomenon does not occur in the networked control system under the event trigger control strategy based on the reference input and the hysteresis quantizer.
Figure BDA0002307373520000183
Designing three local controllers
Figure BDA0002307373520000184
FIG. 6 depicts controlled object output
Figure BDA0002307373520000185
(blue solid line) and reference trajectory ux(t)，uz(t) (red dotted line). As can be seen, the networked control system has a finite gain L2Stable and has input feedforward and output feedback passivity.
FIG. 7 shows
Figure BDA0002307373520000186
ux(t) and trigger time
Figure BDA0002307373520000187
The relationship between them. The dashed blue line represents the reference input ux(t), the red solid line indicates the actual position of the wheeled mobile robot
Figure BDA0002307373520000188
Black five-pointed star represents the moment of trigger
Figure BDA0002307373520000189
FIG. 8 shows
Figure BDA00023073735200001810
uz(t) and trigger time
Figure BDA00023073735200001811
The relationship between them. The dashed blue line represents the reference input uz(t) of (d). Red solid line is the actual position of the wheeled mobile robot
Figure BDA00023073735200001812
The black five-pointed star stands for touchTime of day
Figure BDA00023073735200001813
Comparing FIG. 7 with FIG. 8, the output was obtained during the experiment
Figure BDA00023073735200001814
Trigger 465 times in total and output
Figure BDA00023073735200001815
A total of 443 triggers. And in the case of time-triggered control, outputs
Figure BDA00023073735200001816
Need to trigger 22500 times and output
Figure BDA00023073735200001817
Need to trigger 22500 times. Therefore, the event trigger control strategy based on the reference input and the hysteresis quantizer can greatly reduce the trigger times and save communication resources.

Claims (2)

1. A networked control system based on an event trigger mechanism is characterized in that: the control system comprises a controlled object and a controller, wherein the input end of the controlled object is connected with the output end of the controller through a zero-order retainer, a decoder, an encoder and a trigger, the input end of the controller is connected with the output end of the controlled object through the zero-order retainer, the decoder, the encoder and the trigger, and the control system is characterized in that:
a local controller LCP is arranged between the first zeroth order keeper at the controlled object input end and the decoder2The output end of the controller is connected with one end of a hysteresis quantizer, and the other end of the hysteresis quantizer is connected with a trigger connected with the output end of the controller;
a local controller LCC is arranged between a second zeroth-order retainer at the input end of the controller and the decoder, the output end of a controlled object is connected with one end of another hysteresis quantizer, and the other end of the another hysteresis quantizer is connected with a trigger connected with the output end of the controlled object;
connecting local controller LCP between encoder at controller input end and trigger at controlled object output1The local controller LCP1The other end of the first zero-order retainer is connected with one end of a third zero-order retainer, and the other end of the first zero-order retainer is connected with the input end of the controlled object;
the control method of the control system comprises the following steps:
first setting
Firstly, establishing a nonlinear controlled object, a controller and a networked control system model
Hp:
Figure FDA0003514009100000011
Hc:
Figure FDA0003514009100000012
H:
Figure FDA0003514009100000013
Wherein the content of the first and second substances,
Figure FDA0003514009100000014
state, measurement output and input of a controlled object;
Figure DEST_PATH_IMAGE002
is the state, measurement output, input of the controller;
Figure FDA0003514009100000016
respectively a reference input, a state and a measurement output of the networked control system;
fp(·,·)，hp(·,·)，fc(·,·)，hc(-) f (-) h) are respectively corresponding nonlinear functions;
② there is disturbance at the controller input
||w(t)||2≤Δw＝δw(t)u(t)
Wherein, | | · | | is a Euclid norm,
Figure FDA0003514009100000017
the controlled object and the controller are both input feedforward output feedback passive, and the indexes of the input feedforward and the output feedback are ap，bpAnd ac，bc；
④dp(tk)，dc(τj) Respectively controlled object to controller channel and controller to controlled object channel at trigger time tkAnd τjThe time-varying delay of (2) satisfies:
Figure FDA0003514009100000021
wherein the content of the first and second substances,
Figure FDA0003514009100000022
and
Figure FDA0003514009100000023
the maximum time delay change rate from the controlled object to the controller channel and the maximum time delay change rate from the controller to the controlled object channel are respectively;
constructing a hysteresis quantizer based on the uniform quantizer
Figure FDA0003514009100000024
（ 5 ）
Wherein the content of the first and second substances,
Figure FDA0003514009100000025
non-negative integer, Δ is the maximum quantization error;
and taking the jumping moment of the quantization level as a trigger moment, and triggering a control strategy by the controlled object output end based on the reference input and the event of the hysteresis quantizer:
Figure FDA0003514009100000026
（ 6 ）
wherein, tkThe trigger time of the output end of the controlled object is the trigger time of the output end of the controlled object;
Figure FDA0003514009100000027
a lag quantizer in the form of step (v) corresponding to the output end of the controlled object; deltap＝δp(t) u (t) is the maximum quantization error;
Figure FDA0003514009100000028
is the lag quantizer parameter; u (t) is a reference input of the networked control system;
the controller output triggers a control strategy based on the reference input and the event of the hysteresis quantizer:
Figure FDA0003514009100000029
（ 7 ）
wherein, taujThe trigger time of the output end of the controller;
Figure FDA00035140091000000210
a hysteresis quantizer having the form of equation (5) for the controller output; deltac＝δc(t) u (t) is the quantization error;
Figure FDA00035140091000000211
is the lag quantizer parameter; u (t) is a reference input of the networked control system;
when the event trigger control strategy (6) is met, the output of the controlled object is sampled, and the value of the sampled output is transmitted through a channel after being coded; otherwise, not transmitting information;
when the event-triggered control strategy (7) is satisfied, the output of the controller is sampled, and the value of the sampled output is transmitted through a channel after being encoded; otherwise, not transmitting information;
decoding scheme
At triggering time tkDesign of controlled object output yp(tk) Corresponding transmission code word
Figure FDA00035140091000000212
Wherein the content of the first and second substances,
Figure FDA00035140091000000213
triggering the needed transmission code word for the first time;
Figure FDA00035140091000000214
for triggering a time tk+1A transmission codeword as needed;
considering the time delay d existing in the channel at the output end of the controlled objectp(t) designing a decoding scheme according to the transmitted codeword
Figure FDA00035140091000000215
Wherein the content of the first and second substances,
Figure FDA0003514009100000031
a decoding scheme for first decoding;
Figure FDA0003514009100000032
a decoding scheme for decoding the (k + 1) th time;
② at the triggering time τjDesign controller output yc(τj) Corresponding transmission code word
Figure FDA0003514009100000033
Wherein the content of the first and second substances,
Figure FDA0003514009100000034
triggering the needed transmission code word for the first time;
Figure FDA0003514009100000035
for the triggering time tauj+1A transmission codeword as needed;
in view of the time delay d existing in the channel at the output of the controllerc(t) designing a decoding scheme according to the transmitted codeword
Figure FDA0003514009100000036
Wherein the content of the first and second substances,
Figure FDA0003514009100000037
a decoding scheme for first decoding;
Figure FDA0003514009100000038
a decoding scheme for decoding the j +1 th time;
the controlled object and the controller have limited output change rate and are set to exist
Figure FDA0003514009100000039
Satisfy the requirement of
Figure FDA00035140091000000310
Figure FDA00035140091000000311
Due to yp(t) and yc(T) has a finite rate of change, and the trigger interval Δ T of the controlled objectp[k+1]And the trigger time interval Delta T of the output end of the controllerc[j+1]Are respectively as
Figure FDA00035140091000000312
Wherein, Delta Tp[k+1]And Δ Tc[j+1]Quantizer parameters of the controlled object and the controller output end respectively;
partial controller
Figure FDA00035140091000000313
Wherein c and p1、p2Respectively local controllers LCC, LCP1、LCP2The control gain of (1);
sixth, a method for constructing
Figure FDA00035140091000000314
Storage function of and
Figure FDA00035140091000000315
and reference input u (t)
The controller satisfies the passivity of input feedforward and output feedback, and the indexes of the input feedforward and the output feedback are acAnd bcIf there is a constant b1，
Figure FDA00035140091000000316
So that
Figure FDA00035140091000000317
And local controller parameters c, p1And p2Satisfies the following conditions:
Figure FDA00035140091000000318
then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizer
Figure FDA00035140091000000319
Output is as
Figure FDA00035140091000000320
Is/are as follows
Figure FDA00035140091000000321
Satisfy the requirement of
Figure FDA00035140091000000322
Wherein, Vc(t) is a memory function of the controller; parameter(s)
Figure FDA0003514009100000041
Are respectively as
Figure FDA0003514009100000042
Figure FDA0003514009100000043
Figure FDA0003514009100000044
The killed control system H has a limited gain L2Sufficient condition for stability
If a exists1，
Figure FDA0003514009100000045
When it is satisfied with
Figure FDA0003514009100000046
And is
Figure FDA0003514009100000047
And is
Figure FDA0003514009100000048
When the input is u (t), the output isyp(t) is a finite gain L2Is stable;
and when the conditions in the step sixteenth and the step fourth are both satisfied, the control system satisfies
Figure FDA0003514009100000049
Wherein, it is made
Figure FDA00035140091000000412
The input feedforward index a and the output feedback index b satisfy
Figure FDA00035140091000000410
Figure FDA00035140091000000411
2. The method for controlling the networked control system based on the event trigger mechanism according to claim 1, wherein: the function of the one lag quantizer and the other lag quantizer is to quantize the input signal and output the quantized signal.
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