CN110989347B - Networked control system and control method based on event trigger mechanism - Google Patents
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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
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
is the state, measurement output, input of the controller;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)
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:
wherein,andthe 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
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:
wherein, tkThe trigger time of the output end of the controlled object is the trigger time of the output end of the controlled object;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;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:
wherein, taujThe trigger time of the output end of the controller;a hysteresis quantizer having the form of equation (5) for the controller output; deltac=δc(t) u (t) is the quantization error;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
Wherein,triggering the needed transmission code word for the first time;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
② at the triggering time τjDesign controller output yc(τj) Corresponding transmission code word
Wherein,triggering the needed transmission code word for the first time;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
the controlled object and the controller have limited output change rate and are set to existSatisfy the requirement of
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
Wherein, Delta Tp[k+1]And Δ Tc[j+1]Quantizer parameters of the controlled object and the controller output end respectively;
partial controller
Wherein c and p1、p2Respectively local controllers LCC, LCP1、LCP2The control gain of (1);
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 constantSo thatAnd local controller parameters c, p1And p2Satisfies the following conditions:then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizerOutput is asIs/are as followsSatisfy the requirement ofWherein, Vc(t) is a memory function of the controller; parameter(s)Are respectively as
The killed control system H has a limited gain L2Sufficient condition for stability
If present, isWhen it is satisfied withAnd isAnd isWhen 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
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. 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
Wherein, the state of the controlled object (controller), measurement output, and input, respectively. 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,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 Is encoded intoAnd delivered to the decoder side through a communication channel.
2.LCP via local controller1And ZOH zeroth order keeper for converting into segmented continuous signalDecoder receivesThen decoding it to obtainOutput after passing through a local controller LCCThe zero order keeper willConversion to piecewise continuous
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 intoAnd delivered to the decoder side through a communication channel. Decoder receivesThen decoding it to obtainLCP Via local controller2Rear outputThe zero order keeper willConversion to piecewise continuous Andare formed jointlyAnd 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
Wherein,andthe 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
Wherein,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
Wherein, tkIs the trigger moment of the output end of the controlled object,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,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
Wherein, taujIs the triggering moment of the output end of the controller,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,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
Wherein,for the first time the required transmission code word is triggered,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)
Wherein,for the decoding scheme to be decoded for the first time,decoding scheme for decoding the (k + 1) th time.
Similarly, at the trigger time τjDesign controller output yc(τj) Corresponding transmission code word
Wherein,for the first time the required transmission code word is triggered,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)
Wherein,for the decoding scheme to be decoded for the first time,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 existsSatisfy the requirement ofTrigger 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
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
Wherein c and p1、p2Respectively local controllers LCC, LCP1、LCP2The control gain of (1).
Step 6: constructed as shown in FIG. 1Storage function of andand 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
Through the calculation, the method has the advantages that,
therefore, the local controller parameters c, p1And p2Satisfy the requirement of
Then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizerOutput is asIs/are as followsSatisfy the requirement of
And 7: establishing a network-based control system H with a finite gain L2Sufficient conditions for stability.And controlled object HpIs satisfied by a storage function
if it isSince 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
Wherein,is a constant. Therefore, whenWhen 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
Need to ensure
Formula (26) is equivalent to
Based on the above analysis, the following conclusions can be drawn. Of the three conclusions that follow, conclusion 1 calculationThe 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 constantSo thatAnd local controller parameters c, p1And p2So that
Then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizerOutput is asIs/are as followsSatisfy the requirement of
Conclusion 2: consider the principle of theorem 1And the input feedforward and output feedback passivity indexes are respectively ap,bpControlled object HpForming a networked control system H, if presentSatisfy the requirement of
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 thatAnd 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
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
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 introducedAnd corresponding coordinate transformation
Definition of
To realizeTracking ux(t) ═ 0.7+0.6cos (0.3t) andtracking 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 determinationAndthe triggering time of (c). That is to say willIs regarded as a networked control process, willIs considered another networked control process.
Wherein the initial value of the controlled object isIn order to be an input, the user can select,to output ux(t) ═ 0.7+0.6cos (0.3t) as a reference signal, and the function is storedThe indexes of input feedforward and output feedback of the controlled object are respectivelyThe controlled object in the corresponding model is the formula (1).
The controller is designed as
Wherein the controller inputsThe memory function of the controller isThe indexes of input feedforward and output feedback of the controller are respectivelyCorresponding 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
due to possible delay phenomena in the considered channel, letRespectively controlled object to controller channel and controller to controlled object channel at trigger timeAndtime-varying delay of (1) satisfying
Hysteresis quantizer constructed based on uniform quantizer
The following event-triggered control strategy based on reference input and hysteresis quantizer is designed
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
The following decoding scheme is designed according to the transmitted code word
Corresponding transmission code word
Designing a decoding scheme
Calculating the trigger time interval of the controlled objectAnd the trigger time interval of the output end of the controllerAnd 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.
Designing three local controllers
Wherein the initial value of the controlled object isInput deviceOutput ofReference signal uz(t) of (d). Storing functionsThe indexes of input feedforward and output feedback of the controlled object are respectively The controlled object in the corresponding model is the formula (1).
Wherein the controller inputsThe memory function of the controller isThe indexes of input feedforward and output feedback of the controller are respectivelyCorresponding 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
due to possible delay phenomena in the considered channel, letRespectively controlled object to controller channel and controller to controlled object channel at trigger timeAndtime-varying delay of (1) satisfying
Hysteresis quantizer constructed based on uniform quantizer
The following event-triggered control strategy based on reference input and hysteresis quantizer is designed
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
The following decoding scheme is designed according to the transmitted code word
Corresponding transmission code word
Designing a decoding scheme
Calculating the trigger time interval of the controlled objectAnd the trigger time interval of the output end of the controllerAnd 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.
Designing three local controllers
FIG. 6 depicts controlled object output(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 showsux(t) and trigger timeThe 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 robotBlack five-pointed star represents the moment of triggerFIG. 8 showsuz(t) and trigger timeThe 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 robotThe black five-pointed star stands for touchTime of day
Comparing FIG. 7 with FIG. 8, the output was obtained during the experimentTrigger 465 times in total and outputA total of 443 triggers. And in the case of time-triggered control, outputsNeed to trigger 22500 times and outputNeed 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
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)
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:
wherein,andthe 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
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:
wherein, tkThe trigger time of the output end of the controlled object is the trigger time of the output end of the controlled object;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;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:
wherein, taujThe trigger time of the output end of the controller;a hysteresis quantizer having the form of equation (5) for the controller output; deltac=δc(t) u (t) is the quantization error;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
Wherein,triggering the needed transmission code word for the first time;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
② at the triggering time τjDesign controller output yc(τj) Corresponding transmission code word
Wherein,triggering the needed transmission code word for the first time;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
the controlled object and the controller have limited output change rate and are set to existSatisfy the requirement of
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
Wherein, Delta Tp[k+1]And Δ Tc[j+1]Quantizer parameters of the controlled object and the controller output end respectively;
partial controller
Wherein c and p1、p2Respectively local controllers LCC, LCP1、LCP2The control gain of (1);
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,So thatAnd local controller parameters c, p1And p2Satisfies the following conditions:then the input is as follows under the action of an event-triggered control strategy based on the reference input and the hysteresis quantizerOutput is asIs/are as followsSatisfy the requirement ofWherein, Vc(t) is a memory function of the controller; parameter(s)Are respectively as
The killed control system H has a limited gain L2Sufficient condition for stability
If a exists1,When it is satisfied withAnd isAnd isWhen 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
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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