CN104142627B - A kind of networking brshless DC motor delay compensation and control method of employing Auto Disturbances Rejection Control Technique - Google Patents

Abstract

A kind of networking brshless DC motor delay compensation and control method of employing Auto Disturbances Rejection Control Technique, comprises the following steps：1) set up the brushless DC motor control system model containing time-varying network inducing delay.Networking brushless DC motor control system is described as into a discrete-time linear time-varying system with a step input delay, and then the uncertain dynamic part of the system that time-vary delay system is caused is described as the additive noise of system；2) extended state observer design.The present invention is estimated as a part for summation disturbance using the uncertain dynamic that time-vary delay system can be caused by extended state observer；3) compensation process to the time-vary delay system item in networking brushless DC motor control system.The uncertain dynamic extended state observer real-time estimation that effectively time-varying network inducing delay can be caused of the invention is simultaneously compensated, and inside and outside the uncertain and system that the method causes to time delay, disturbance and model uncertainty are respectively provided with very strong rejection ability.

Description

A networked brushless DC motor delay compensation and Control Method

technical field

The present invention is applied in the field of networked motion control, and relates to the problem of brushless DC motor control based on industrial networks, especially how to eliminate the influence of network-induced time delay on the performance of brushless DC motor control system, and realize an effective real-time control method .

Background technique

With the development of power electronics technology and microelectronics technology, a new type of speed-regulating motor, namely brushless DC motor, has been promoted. Due to its low noise, high efficiency, simple structure, long service life, fast response, and large starting torque, it has been widely used in CNC machine tools, robotic arms, and household appliances. With the continuous expansion of industrial production scale and the continuous improvement of the safety requirements of the production process, the traditional motor control system is increasingly unable to meet the actual needs. The development of modern network control technology makes it possible for network control to replace traditional control methods.

A networked control system refers to a closed-loop control system that uses a communication network to connect sensors, controllers, and actuators instead of the traditional point-to-point connection. Compared with traditional control systems, it has many advantages, such as remote control, reduced system connections, easy installation and maintenance, and system information integration and sharing. However, the introduction of the communication network into the control loop also brings some new problems. Due to the time-division multiplexing information transmission method, which is limited to the network's carrying capacity and limited bandwidth, it will inevitably cause information collisions, retransmissions, etc. Occurs, resulting in time delay in the transmission process of information in the control system, and the time delay changes with the change of network load, which is time-varying and uncertain.

Network-induced delays are usually divided into long delays (greater than a system sampling period) and short delays (less than a system sampling period). The frequency of long delays in actual systems is not high. The motion control system will have a great impact. In engineering, the delay is generally reduced as much as possible by improving the network protocol and structure, but the existence of short delays is often unavoidable.

The present invention mainly considers how to reduce or even eliminate the influence of network-induced delay on the performance of the brushless DC motor control system. At present, commonly used processing methods include robust control methods, Smith predictor compensation methods, and artificially extended delay based on time-driven method etc. Among them, the robust control method does not need to accurately know the size of the network delay, and the robust controller has better anti-interference ability, but it is relatively conservative. The Smith predictor method uses a predictive model to compensate for the time delay, but it requires high accuracy of the motor model, which is often difficult to achieve in practice. The method of artificially extending the delay based on the time-driven actuator can convert the time-varying delay into a constant delay, which facilitates the design of the controller, but it will cause the system control input to not be updated in time and reduce the control performance of the system.

Contents of the invention

In order to overcome the shortcomings of the above-mentioned existing control methods that cannot solve the uncertain dynamics caused by time-varying time delays for accurate estimation and weak anti-interference ability, the present invention adopts ADRC technology to design a networked brushless DC motor control system The time-delay compensation and control strategy of the time-varying network can effectively estimate and compensate the uncertain dynamics caused by the time-varying network-induced delay in real time with the extended state observer. Certainty has a strong inhibitory ability.

The technical solution adopted by the present invention to solve its technical problems:

A networked brushless DC motor time delay compensation and control method using active disturbance rejection control technology, said method comprising the following steps:

Step 1) Establish a BLDC motor control system model with time-varying network-induced delay.

Considering that the network-induced delay is less than one sampling period, the networked brushless DC motor control system is described as a discrete-time linear time-varying system with one-step input delay, and then the uncertain dynamic part of the system caused by the time-varying delay Described as additive noise of the system, the specific process includes:

1.1) Establish the linearized transfer function model of the brushless DC motor control system

The brushless DC motor control system consists of a current loop and a speed loop, and both the current loop and the speed loop can be described by a first-order linear model. After the two are connected in series, the second-order system model of the brushless DC motor control system is obtained. The transfer function for:

in, r is the resistance of the stator phase winding, L is the self-inductance of the winding, M is the mutual inductance between the two-phase windings, K _e is the electromotive force coefficient, J is the moment of inertia of the motor, N(s) is the Laplace transform of the motor speed, U(s) is the Laplace transform of the branch circuit voltage that conducts the two phases. In order to facilitate the design of the controller, the transfer function model shown in formula (1) is transformed into the following state space model:

Among them, x ₁ is the rotational speed of the DC motor, x ₂ is the acceleration of the DC motor, and u is the control quantity, that is, the branch circuit voltage that conducts the two phases.

1.2) Obtain the motor control system model under the influence of time-varying network-induced delay

When data packets are transmitted in the network, there is a delay between the sensor to the controller and the controller to the actuator. with Represent the time delay experienced by the measurement signal from the sensor to the controller and the time delay of the control quantity from the controller to the actuator, then the total network-induced delay of the control loop is Since the time delay is less than one sampling cycle, the control input voltage u(t) of the DC motor in one cycle consists of two parts, one part is the control input voltage u(k-1) calculated in the previous cycle, and the other part is the current The control input voltage u(k) calculated periodically has the following form:

Among them, T is the sampling period, and t _k represents the kth sampling moment. Therefore, according to formulas (2) and (3), the discretized BLDC motor control system model with time-varying network-induced delay is:

After approximating e ^-aT with 1-aT, formula (4) can be transformed into:

The time-varying dynamics caused by the time-varying time delay τ _k in equation (5) is represented by a new state variable x ₃ (k), namely and order Therefore, the networked brushless DC motor control system model represented by equation (5) can be expanded into the following three-order system model:

Among them, x ₁ (k+1), x ₂ (k+1), and x ₃ (k+1) are motor speed x ₁ (k), motor acceleration x ₂ (k), new expansion state quantity x ₃ ( The value of the next sampling moment of k);

Step 2) Design an extended state observer for estimating the uncertainty caused by the network-induced time delay in the BLDC motor control system;

Step 3) Design a networked BLDC motor ADRC controller with an extended state observer to realize real-time compensation of time-varying network-induced delay and real-time control of motor speed.

Further, in the step 2), the extended state observer design process includes:

2.1) Design the extended state observer

The extended state observer for estimating the three state variables in system (6) has the following form:

Among them, e(k) is the difference between the reference value of the motor speed and the estimated value of the actual speed, that is, the error amount of the motor speed, z ₁ (k) is the estimation of the motor speed x ₁ (k), z ₂ (k) is The estimation of motor acceleration x ₂ (k), z ₃ (k) is the estimation of the new expansion state quantity x ₃ (k), and h is the integration step size. fal(e(k),0.25,δ) is a nonlinear function, as shown in formula (8). δ, β ₀₁ , β ₀₂ , and β ₀₃ are a group of parameters to be tuned. In order to ensure a certain estimation accuracy, according to the design principles of high-gain state observers, β ₀₁ , β ₀₂ , and β ₀₃ can be made larger, generally greater than An upper bound on the noise or perturbation.

Among them, a is the power exponent, δ is the interval length of the linear segment, sign() is the sign function, and the specific expression is shown in formula (9).

2.2) Estimation of uncertainty caused by time-varying network-induced delay

The designed extended state observer can estimate the speed of the BLDC motor, the acceleration of the motor, and the newly expanded uncertainty caused by the network-induced delay. It can be seen from equation (7) that the designed extended state The observer can estimate the uncertain dynamics of the system with time-varying delay as a sum of disturbances. The key and difficulty in compensating the network-induced delay is to accurately estimate the uncertain dynamics caused by the time-varying delay. At present, there is no effective result for this problem. The present invention uses the extended state observer to convert the time-varying time Uncertain dynamics due to delays are estimated as part of the sum disturbance.

Further, in the step 3), the compensation process of the time-varying time delay item in the networked brushless DC motor control system:

3.1) Arrange the transition process. This process is to use the reference speed v of the motor to obtain the differential signal v ₂ of the approximate speed of the speed v through the tracking differentiator, and at the same time obtain the transition signal v ₁ of the speed v, and smooth the jumping speed signal to prevent overshoot , Equation (10) gives the specific form of the tracking differentiator.

Among them, r is the fast tracking factor, h is the integral step size, h ₀ is the filter factor, fhan(e(k),v ₂ (k),r,h ₀ ) is the comprehensive function of the fastest control, fhan(x ₁ ,x ₂ , r, h) The specific expression is as follows:

3.2) Estimate the uncertainty caused by the network-induced delay with the extended state observer. Obtain the estimate z ₃ (k) of the new expanded state quantity x ₃ (k) through the expanded state observer, the newly expanded quantity x ₃ (k) contains both the uncertain dynamics caused by the time-varying delay and the internal and external disturbances, The extended state observer is estimated together as a sum disturbance.

3.3) Uncertainty compensation and control law design of control system caused by time delay. This process yields two error quantities, e ₁ (k)=v ₁ (k)-z ₁ (k) and e ₂ (k)=v ₂ (k)-z ₂ (k). The control quantity u ₀ (k) can be calculated through the nonlinear combination module, and the calculation process is shown in formula (12).

In order to compensate the uncertainty and internal and external disturbances caused by the time-varying delay in the system, the new control quantity is obtained by subtracting z ₃ (k) from the obtained control quantity u ₀ (k), namely The compensation process can cancel all the sum disturbance items with time-varying delay in the system, so that the system can be transformed into a purely integral linear system, and the influence of time-varying delay on system performance can also be eliminated.

Compared with the prior art, the present invention has the advantages of:

1. It can estimate the uncertain dynamics of the system caused by the network-induced delay more accurately

The extended state observer designed in the present invention can estimate the state quantities of the brushless DC motor control system in real time, that is, z ₁ (k) in the system can estimate the motor speed x ₁ (k), and z ₂ (k) can estimate the motor speed x 1 (k) The estimation of acceleration x ₂ (k), z ₃ (k) is the estimation of the newly expanded state quantity x ₃ (k) containing uncertainty. Therefore, the designed extended state observer can estimate the uncertain dynamics caused by the time-varying network-induced delay in the system as a sum disturbance, which effectively solves the problem of accurately estimating the uncertain dynamics caused by the time-varying delay. a problem.

2. Compensation for uncertain dynamics caused by time-varying network-induced delay

The control law shown in Equation (12) can be reconstructed by using the disturbance sum estimation z ₃ (k) obtained by the extended state observer, which can cancel all the sum disturbances in the system with time-varying network-induced delay dynamics, Therefore, the system is transformed into a purely integral linear system, and the influence of time-varying network-induced delay on system performance is eliminated.

3. Strong anti-interference ability

z ₃ (k), as a newly expanded system state quantity, contains both uncertain dynamics caused by time-varying time delay and internal and external disturbances. The expanded state observer estimates it as a total disturbance, so that in the compensation process, While compensating the uncertain dynamics caused by time-varying network-induced delay, internal and external disturbances are also compensated, eliminating the influence of internal and external disturbances on system performance.

Description of drawings

Figure 1 is a structural diagram of a networked DC motor control system with time delay.

Fig. 2 is a signal sequence diagram of a networked control system with time-varying short delay.

Figure 3 is a block diagram of the ADRC controller.

Figure 4 is a motor speed tracking curve with time delay compensation.

Figure 5 is a motor speed tracking curve when external disturbance is added.

detailed description

In order to make the technical scheme and design idea of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings.

Referring to Figures 1 to 5, a networked brushless DC motor delay compensation and control method using active disturbance rejection control technology, the method includes the following steps:

Step 1) Establish a BLDC motor control system model with time-varying network-induced delay.

Considering that the network-induced delay is less than one sampling period, the networked brushless DC motor control system is described as a discrete-time linear time-varying system with one-step input delay, and then the uncertain dynamic part of the system caused by the time-varying delay Described as additive noise of the system, the specific process includes:

1.1) Establish the linearized transfer function model of the brushless DC motor control system

The brushless DC motor control system consists of a current loop and a speed loop, and both the current loop and the speed loop can be described by a first-order linear model. After the two are connected in series, the second-order system model of the brushless DC motor control system is obtained. The transfer function for:

in, r is the resistance of the stator phase winding, L is the self-inductance of the winding, M is the mutual inductance between the two-phase windings, K _e is the electromotive force coefficient, J is the moment of inertia of the motor, N(s) is the Laplace transform of the motor speed, U(s) is the Laplace transform of the branch circuit voltage that conducts the two phases. In order to facilitate the design of the controller, the transfer function model shown in formula (1) is transformed into the following state space model:

Among them, x ₁ is the rotational speed of the DC motor, x ₂ is the acceleration of the DC motor, and u is the control quantity, that is, the branch circuit voltage that conducts the two phases.

1.2) Obtain the motor control system model under the influence of time-varying network-induced delay

When data packets are transmitted in the network, there is a delay between the sensor to the controller and the controller to the actuator. with Represent the time delay experienced by the measurement signal from the sensor to the controller and the time delay of the control quantity from the controller to the actuator, then the total network-induced delay of the control loop is Since the time delay is less than one sampling cycle, the control input voltage u(t) of the DC motor in one cycle consists of two parts, one part is the control input voltage u(k-1) calculated in the previous cycle, and the other part is the current The control input voltage u(k) calculated periodically has the following form:

Among them, T is the sampling period, and t _k represents the kth sampling moment. Therefore, according to formulas (2) and (3), the discretized BLDC motor control system model with time-varying network-induced delay is:

After approximating e ^-aT with 1-aT, formula (4) can be transformed into:

The time-varying dynamics caused by the time-varying time delay τ _k in equation (5) is represented by a new state variable x ₃ (k), namely and order Therefore, the networked brushless DC motor control system model represented by equation (5) can be expanded into the following three-order system model:

Among them, x ₁ (k+1), x ₂ (k+1), and x ₃ (k+1) are motor speed x ₁ (k), motor acceleration x ₂ (k), new expansion state quantity x ₃ ( The value of the next sampling moment of k);

Step 2) Design an extended state observer for estimating the uncertainty caused by the network-induced time delay in the BLDC motor control system;

Step 3) Design a networked BLDC motor ADRC controller with an extended state observer to realize real-time compensation of time-varying network-induced delay and real-time control of motor speed.

Further, in the step 2), the extended state observer design process includes:

2.1) Design the extended state observer

The extended state observer for estimating the three state variables in system (6) has the following form:

Among them, e(k) is the difference between the reference value of the motor speed and the estimated value of the actual speed, that is, the error amount of the motor speed, z ₁ (k) is the estimation of the motor speed x ₁ (k), z ₂ (k) is The estimation of motor acceleration x ₂ (k), z ₃ (k) is the estimation of the new expansion state quantity x ₃ (k), and h is the integration step size. fal(e(k),0.25,δ) is a nonlinear function, as shown in formula (8). δ, β ₀₁ , β ₀₂ , and β ₀₃ are a group of parameters to be tuned. In order to ensure a certain estimation accuracy, according to the design principles of high-gain state observers, β ₀₁ , β ₀₂ , and β ₀₃ can be made larger, generally greater than An upper bound on the noise or perturbation.

Among them, a is the power exponent, δ is the interval length of the linear segment, sign() is the sign function, and the specific expression is shown in formula (9).

2.2) Estimation of uncertainty caused by time-varying network-induced delay

The designed extended state observer can estimate the speed of the brushless DC motor, the acceleration of the motor, and the newly expanded uncertainty caused by the network-induced delay. It can be seen from equation (7) that the designed extended state The observer can estimate the uncertain dynamics of the system with time-varying delay as a sum of disturbances. The key and difficulty in compensating the network-induced delay is to accurately estimate the uncertain dynamics caused by the time-varying delay. At present, there is no effective result for this problem. The present invention adopts the extended state observer to make the time-varying time Uncertain dynamics due to delays are estimated as part of the sum disturbance.

Further, in the step 3), the compensation process of the time-varying time delay item in the networked brushless DC motor control system:

3.1) Arrange the transition process. This process is to use the reference speed v of the motor to obtain the differential signal v ₂ of the approximate speed of the speed v through the tracking differentiator, and at the same time obtain the transition signal v ₁ of the speed v, and smooth the jumping speed signal to prevent overshoot , Equation (10) gives the specific form of the tracking differentiator.

Among them, r is the fast tracking factor, h is the integral step size, h ₀ is the filter factor, fhan(e(k),v ₂ (k),r,h ₀ ) is the comprehensive function of the fastest control, fhan(x ₁ ,x ₂ , r, h) The specific expression is as follows:

3.2) Estimate the uncertainty caused by the network-induced delay with the extended state observer. Obtain the estimate z ₃ (k) of the new expanded state quantity x ₃ (k) through the expanded state observer, the newly expanded quantity x ₃ (k) contains both the uncertain dynamics caused by the time-varying delay and the internal and external disturbances, The extended state observer is estimated together as a sum disturbance.

3.3) Uncertainty compensation and control law design of control system caused by time delay. This process yields two error quantities, e ₁ (k)=v ₁ (k)-z ₁ (k) and e ₂ (k)=v ₂ (k)-z ₂ (k). The control quantity u ₀ (k) can be calculated through the nonlinear combination module, and the calculation process is shown in formula (12).

In order to compensate the uncertainty and internal and external disturbances caused by the time-varying delay in the system, the new control quantity is obtained by subtracting z ₃ (k) from the obtained control quantity u ₀ (k), namely The compensation process can cancel all the sum disturbance items with time-varying delay in the system, so that the system can be transformed into a purely integral linear system, and the influence of time-varying delay on system performance can also be eliminated.

As shown in Figure 1, due to the introduction of the network, there is a delay in the data transmission process, mainly including the delay between the sensor and the controller and the delay between the controller and the actuator The total delay of the control loop The sensor nodes are driven by time and sample the output speed of the DC motor with a fixed sampling period T. Both the controller node and the actuator (brushless DC motor) node are event-driven, and when the data reaches the controller, the control quantity is calculated and transmitted to the BLDC motor system.

As shown in Figure 2, when the data is transmitted through the wireless network, there is a time delay between the sensor and the controller and the controller and the actuator. When the brushless DC motor outputs data, since the sensor is driven by time, no The rotational speed of the brushed DC motor is sampled by the sensor at a period T to obtain a discrete rotational speed value sequence. When the sampled speed data reaches the controller, there will be a certain time delay between them, and this time delay is time-varying and uncertain, but its size is limited within one sampling period; when the controller calculates When the control amount is output, and then the control amount data is transmitted to the brushless DC motor, there is still a delay between them, and this delay is time-varying and uncertain; when the data reaches the brushless DC motor, the data delay The size is the sum of the two delays mentioned above, and the sum of the delays is also limited within one sampling period, so the control amount applied to the object is actually composed of two parts, one part is the control calculated in the previous cycle The other part is the control quantity calculated in the current cycle.

As shown in Figure 3, the research object of this patent is a brushless DC motor. When testing the effectiveness of the ADRR method, the reference value of the motor speed can be given, and two quantities will be obtained after the transition process arranged, one is the transition signal v ₁ (k) of the motor speed reference value, and the other is the differential signal v ₂ (k) of the motor speed reference value. The rotational speed value output by the motor and the control quantity are used as the input of the extended state observer, so that the extended state observer can separately analyze the three states of the motor speed x ₁ (k), the motor acceleration x ₂ (k) and the disturbance sum x ₃ (k) The corresponding three estimated values are z ₁ (k), z ₂ (k), and z ₃ (k). Based on this, the error of the motor speed and the differential of the error can be calculated, namely e ₁ (k)=v ₁ (k)-z ₁ (k) and e ₂ (k)=v ₂ (k)-z ₂ (k) . The control variable u ₀ (k) can be calculated through the nonlinear combination of the two error signals obtained as shown in formula (12). In order to eliminate the uncertain dynamics caused by the time-varying delay in the system, the obtained control Subtract z ₃ (k) from u ₀ (k) to get the new control voltage When this control quantity acts on the object, it can offset all uncertain dynamics caused by time-varying delay in the system, and transform the system into a purely integral linear system.

As shown in Figure 4, it can be seen from the figure that the output speed of the brushless DC motor control system still has a fast response time and the tracking curve is stable even if there is a time-varying network-induced delay when the ADRC method is applied. , There is no overshoot and steady-state error, indicating that the uncertain dynamics caused by the network-induced delay are effectively compensated, and the motor control system is basically not affected by the time-varying delay on its performance.

As shown in Figure 5, it can be seen from the figure that even in the case of external disturbances, the motor speed can still quickly track the given reference value, and there is no obvious jitter after reaching the reference value. It can still effectively compensate the uncertain dynamics caused by the time-varying network-induced delay. It can be seen that the designed ADRC algorithm not only has a good compensation effect on the network-induced delay, but also has a good ability to suppress external noise. .

Claims (3)

1. A networked brushless direct current motor time delay compensation and control method adopting an active disturbance rejection control technology is characterized in that: the method comprises the following steps:

step 1) establishing a brushless direct current motor control system model containing time-varying network induced time delay, describing a networked brushless direct current motor control system as a discrete time linear time varying system with one-step input time delay, and further describing a system uncertain dynamic part caused by the time-varying time delay as additive noise of the system, wherein the method comprises the following processes:

1.1) establishing a linear transfer function model of a brushless direct current motor control system

The transfer function of the second-order system model of the brushless direct current motor control system is as follows:

wherein,r is the resistance of the stator phase winding, L is the self inductance of the winding, M is the mutual inductance between the two phase windings, K_eIs an electromotive force coefficient, J is the rotational inertia of the motor, N(s) is the Laplace transform of the motor rotation speed, and U(s) is the Laplace transform of the branch voltage for conducting two phases; converting the transfer function model shown in the formula (1) into a state space model as follows:

wherein x is₁Is the rotational speed, x, of the DC motor₂The acceleration of the direct current motor is used, u is a control quantity, namely, the branch voltage of two phases is conducted;

1.2) obtaining a motor control system model under the influence of time-varying network induced time delay

When data packets are transmitted in the network, there is a time delay from the sensor to the controller and from the controller to the actuatorAndrespectively representing the time delay experienced by the transmission of the measurement signal from the sensor to the controller and the time delay experienced by the transmission of the control quantity from the controller to the actuator, the total network-induced time delay of the control loop is thenBecause the time delay is less than one sampling period, the control input voltage u (t) of the direct current motor in one period is composed of two parts, one part is the control input voltage u (k-1) calculated in the previous period, the other part is the control input voltage u (k) calculated in the current period, and the control input voltage u (k) has the following form:

where T is the sampling period, T_kRepresents the kth sampling instant; therefore, according to the equations (2) and (3), the discretized model of the brushless direct current motor control system containing the time-varying network induced time delay is as follows:

e is to be^-aTAfter approximation by 1-aT, equation (4) is converted to:

delay tau by time variation in equation (5)_kThe resulting time-varying dynamics use a new state variable x₃(k) Is shown, i.e.And make an orderThe networked brushless dc motor control system model represented by equation (5) is thus expanded to a third order system model as follows:

wherein x is₁(k+1)、x₂(k+1)、x₃(k +1) is the motor rotation speed x₁(k) Motor acceleration x₂(k)、New expansion state quantity x₃(k) The value of the next sampling instant of (a);

step 2) designing an extended state observer for estimating uncertainty caused by network-induced time delay in a brushless direct current motor control system;

and 3) designing a networked brushless direct current motor active disturbance rejection controller with an extended state observer to realize real-time compensation of time-varying network induced time delay and real-time control of motor rotating speed.

2. The networked brushless direct current motor delay compensation and control method adopting the active disturbance rejection control technology according to claim 1, wherein in the step 2), the extended state observer designing process includes:

2.1) design extended State observer

The extended state observer for estimating three state variables in a system (6) has the form:

wherein e (k) is the difference between the reference value of the motor rotation speed and the estimated value of the actual rotation speed, i.e. the error of the motor rotation speed, z₁(k) Is to the motor speed x₁(k) Estimate of (b), z₂(k) Is to the motor acceleration x₂(k) Estimate of (b), z₃(k) Is to the new expansion state quantity x₃(k) H is the integration step, fal (e (k),0.25,) is a non-linear function, as shown in equation (8), β₀₁、β₀₂、β₀₃A group of parameters to be set;

wherein a is a power exponent and is an interval length of a linear segment, sign () is a sign function, and a specific expression is shown as formula (9):

2.2) estimation of uncertainty caused by time-varying network-induced delay

The designed extended state observer can estimate the rotating speed and the acceleration of the brushless direct current motor and the newly expanded uncertain quantity caused by network-induced time delay, and as can be seen from the formula (7), the designed extended state observer can estimate the uncertain dynamics containing time-varying time delay in the system as sum disturbance; the key and difficulty in compensating the network induced delay lies in accurately estimating the uncertain dynamics caused by the time-varying delay, and the uncertain dynamics caused by the time-varying delay can be estimated as a part of the total disturbance by adopting the extended state observer.

3. The networked brushless direct current motor time delay compensation and control method adopting the active disturbance rejection control technology according to claim 1 or 2, wherein in the step 3), the compensation process for the time-varying time delay term in the networked brushless direct current motor control system is as follows:

3.1) arranging a transition process: the process is that the motor is referenced to the rotating speed v, and a differential signal v of the approximate rotating speed of the rotating speed v is obtained through a tracking differentiator₂While obtaining a transition signal v of the rotating speed v₁Smoothing the jump speed signal to prevent overshoot, wherein the following differentiator is given by the formula (10):

wherein r is a fast tracking factor, h is an integration step length, h₀As filter factor, fhan (e (k), v₂(k),r,h₀) For the steepest control synthesis function, fhan (x)₁,x₂R, h) the specific expression is as follows:

3.2) by dilationThe state observer estimates uncertainty caused by network induced delay; obtaining a new extended state quantity x by an extended state observer₃(k) Is estimated z₃(k)，x₃(k) The system comprises uncertain dynamics caused by time-varying time delay and internal and external disturbances, and an extended state observer estimates the dynamic disturbance as a sum disturbance;

3.3) control system uncertainty compensation and control law design caused by time delay, and two error quantities are obtained in the process, namely e₁(k)＝v₁(k)-z₁(k) And e₂(k)＝v₂(k)-z₂(k) (ii) a The control quantity u can be calculated through nonlinear combination₀(k) The calculation process is shown as formula (12):

at the obtained control quantity u₀(k) Minus z₃(k) Obtaining new control quantities, i.e.The compensation process can offset all the total disturbance terms containing time-varying time delay in the system, so that the system is converted into a pure integral linear system.