CN110323974B - An Active Disturbance Rejection Control Method Based on Proportional Resonant Controller Optimization - Google Patents
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Abstract
一种基于比例谐振控制器优化的自抗扰控制方法，它属于电机控制技术领域。本发明同时解决了传统永磁同步电机驱动系统中外部扰动和内部扰动造成转速波动的问题。本发明对线性自抗扰控制器进行改进，利用含有准谐振调节器的比例谐振控制器取代原线性自抗扰控制器中的比例控制器，不仅保留了传统线性自抗扰控制器能够有效的观测突变扰动和低频扰动并进行前馈补偿的优点，同时抑制了内部扰动造成的转速波动，实现对系统的高性能控制。相对于传统的比例积分控制器，本发明方法可以使得转速跌落减小55％以及转速波动减小到0.5转内。本发明可以应用于电机控制技术领域。
An active disturbance rejection control method optimized based on a proportional resonance controller belongs to the technical field of motor control. The invention simultaneously solves the problem of rotational speed fluctuation caused by external disturbance and internal disturbance in the traditional permanent magnet synchronous motor drive system. The present invention improves the linear active disturbance rejection controller, uses the proportional resonance controller including the quasi-resonant regulator to replace the proportional controller in the original linear active disturbance rejection controller, not only retains the traditional linear active disturbance rejection controller to effectively The advantages of observing sudden disturbances and low-frequency disturbances and performing feedforward compensation, while suppressing the rotational speed fluctuation caused by internal disturbances, realizes high-performance control of the system. Compared with the traditional proportional-integral controller, the method of the present invention can reduce the speed drop by 55% and the speed fluctuation to within 0.5 revolutions. The present invention can be applied to the technical field of motor control.
Description
Technical Field
The invention belongs to the technical field of motor control, and particularly relates to an active disturbance rejection control method based on proportional resonant controller optimization.
Background
The permanent magnet synchronous motor is widely applied and continuously developed in the field of alternating current motor speed regulation systems by virtue of the remarkable advantages of simple structure, reliable operation, small volume, high efficiency and the like. The permanent magnet synchronous motor is remarkably improved in driving capability, control strategy excellence and simplicity or precision, and is gradually used for various industrial application occasions including textile machines, elevator traction, automobile machine tools and the like instead of an asynchronous speed regulating system. In recent years, in particular, in high-performance industrial control occasions, such as the fields of electric automobiles, numerical control machine tool spindle drives, electric locomotives and the like, the requirements of high precision, high efficiency and high quality are put forward for the motor drive variable frequency speed control system. In a circular weaving machine system, a circular weaving machine usually runs under the condition of low rotating speed and large torque, and the stability of the rotating speed directly determines the quality of a product; in the field of electric automobiles, in the face of complex road traffic conditions, the driving of the electric automobiles needs to have the capability of operating under various working conditions, and particularly, the stable operation of the automobiles can be ensured when the automobiles run in a low-speed area in a climbing manner so as to meet the requirements of people on comfort and safety; in the main shaft driving system for the numerical control machine tool, as a core component, the quality of the main shaft driving control performance directly determines the overall level of the numerical control machine tool.
The requirements for the speed regulation of the motor in high-performance control occasions are as follows: the rotating speed is strong in resistance (particularly in a low-speed and high-torque state), and the low-speed stable running capability is realized. However, the permanent magnet synchronous motor based on the traditional control algorithm has the following problems in low-speed and high-torque driving:
the motor drive system has external disturbances (sudden load torque changes), which can cause serious rotation speed drop when a load is suddenly added and can cause rotation speed rise when the load is suddenly reduced. The motor driving system has internal disturbance (cogging torque, motor parameter change and unmodeled dynamic state) at the same time, and the internal disturbance usually generates torque harmonic waves to influence the stability performance of the rotating speed. Especially at low speeds, this causes a periodic fluctuation in the rotational speed. The speed loop control should be time-varying and non-linear as explained above, so that the conventional linear proportional-integral control strategy cannot meet the high-performance speed control requirement.
Disclosure of Invention
The invention aims to solve the problem of rotation speed fluctuation caused by external disturbance and internal disturbance in a traditional permanent magnet synchronous motor driving system, and provides an active disturbance rejection control method based on proportional resonant controller optimization.
The technical scheme adopted by the invention for solving the technical problems is as follows: an active disturbance rejection control method based on proportional resonant controller optimization, the method includes the following steps:
step one, rewriting a motor motion equation into a state space equation, expanding total disturbance in a motor driving system into a new state variable, and constructing a new state space equation according to the new state variable;
step two, constructing an extended state observer by using the new state space equation in the step one, and performing feedforward compensation by using the total disturbance observed by the extended state observer;
and step three, designing a proportional resonance active disturbance rejection controller to realize unsteady-state static difference tracking reference signals and inhibit the periodic fluctuation of the rotating speed caused by the internal disturbance of the motor driving system.
The invention has the beneficial effects that: the invention relates to an active disturbance rejection control method based on optimization of a proportional resonant controller, which improves a linear active disturbance rejection controller, utilizes the proportional resonant controller containing a quasi-resonant regulator to replace a proportional controller in an original linear active disturbance rejection controller, not only retains the advantage that the traditional linear active disturbance rejection controller can effectively observe sudden disturbance and low-frequency disturbance and carry out feedforward compensation, but also inhibits the rotation speed fluctuation caused by internal disturbance (motor parameter change and unmodeled dynamics), and realizes high-performance control of a system.
Compared with the traditional proportional-integral controller, the method can reduce the rotating speed drop by 55 percent and reduce the rotating speed fluctuation to be within 0.5 revolution.
Drawings
FIG. 1 is a flow chart of an active disturbance rejection control method based on proportional resonant controller optimization according to the present invention;
FIG. 2 is a block diagram of a linear active disturbance rejection controller system;
in the figure:
representing a given rotational speed of the motor,
representing the estimated rotation speed of the extended state observer, LESO representing the linear extended state observer, d (t) representing the disturbance;
FIG. 3 is a Bode diagram of an extended state observer;
FIG. 4 is a Bode diagram of a conventional resonant actuator;
FIG. 5 is a Bode diagram of a quasi-resonant regulator;
FIG. 6 is a bode diagram of a proportional resonant controller;
FIG. 7 is a diagram of a PMSM speed loop control system based on a proportional resonant regulator optimized auto-disturbance rejection controller;
in the figure: u. ofsdRepresenting d-axis voltage of the motor, theta representing motor position angle, ejθRepresents the inverse park (park) transformation, usαRepresents the alpha-axis voltage, usβRepresents the beta axis voltage, uDCWhich represents the voltage of the bus-bar,
representing d-axis reference current, isdRepresenting d-axis current, isαRepresenting the alpha-axis current, isβRepresents beta axis current, 3-Phase Inverter represents a three-Phase Inverter, and Encoder represents an Encoder; PMSM stands for permanent magnet synchronous motor, SVPWM stands for space vector pulse width modulation;
representing the q-axis reference current, usqRepresenting the motor q-axis voltage, isqRepresents the q-axis current;
FIG. 8 is a waveform diagram of a PI control based speed loop operating with a sudden increase and decrease in rated load;
wherein: (a) is a rotating speed waveform diagram, and (b) is a torque waveform diagram;
FIG. 9 is a waveform diagram of a linear-based auto-disturbance-rejection controller and a proportional-resonant-controller-based auto-disturbance-rejection controller controlled speed loop operating under a sudden load increase and decrease condition;
wherein: (a) the rotating speed waveform chart is shown, and the torque waveform chart is shown.
Detailed Description
The first embodiment is as follows: as shown in fig. 1. The active disturbance rejection control method based on the proportional resonant controller optimization in the embodiment includes the following steps:
step one, rewriting a motor motion equation into a state space equation, expanding total disturbance in a motor driving system into a new state variable, and constructing a new state space equation according to the new state variable;
step two, constructing an extended state observer by using the new state space equation in the step one, and observing the total disturbance z by using the extended state observer2Performing feedforward compensation;
firstly, selecting an extended state observer with a proper order, and selecting an extended state observer with the order equal to the order of a state equation according to the extended state observer; secondly, for selecting the gain of the extended state observer, in order to ensure the stability and the excellent performance of the system, the gain determination method adopted by the invention is to ensure that beta is beta1＝2·ωb，
Wherein beta is1，β2Is the gain, ω, of the extended state observerbIs the bandwidth of the extended state observer. And then determining the bandwidth of the extended state observer according to the requirement of the dynamic performance of the system, and further determining the gain of the observer. And (3) selecting proper extended state observer gain, and performing feedforward compensation by using total disturbance (the total disturbance mainly refers to abrupt disturbance and low-frequency disturbance due to limited observer bandwidth) observed by the extended state observer.
And step three, designing a proportional resonant controller to realize unsteady-state static difference tracking reference signals and inhibit the periodic fluctuation of the rotating speed caused by the internal disturbance of the motor driving system.
In order to ensure the practicability and stability of the control method of the invention, a quasi-resonance regulator is selected to be used instead of a traditional resonance regulator. Because the rotation speed fluctuation caused by the internal disturbance of the motor has strong periodicity and the maximum influence on the rotation speed is 6 th-order torque harmonic and 12 th-order torque harmonic, two resonance regulators are used in parallel to respectively compensate the 6 th-order torque harmonic and the 12 th-order torque harmonic. Finally, the parameters of the resonance regulators are set, and the resonance frequencies of the two resonance regulators are respectively set to be 6 omegarAnd 12. omegar。
The method of the invention reserves the advantages that the traditional linear active disturbance rejection controller can effectively observe sudden disturbance and low-frequency disturbance and carry out feedforward compensation, and simultaneously realizes the compensation of torque harmonic wave and sine disturbance caused in the system, namely, the high-performance control of the system is realized.
The invention further improves the traditional linear active disturbance rejection control strategy to obtain stronger disturbance rejection performance, and the following explanation and analysis are carried out on the linear active disturbance rejection controller by combining with a figure 2:
the extended state observer is the core unit of the auto-disturbance-rejection controller, and can be used to approximate the sum of all disturbances of the system except the control quantity. By means of the idea of the extended state observer, the disturbance which can affect the controlled output is synthesized into a state quantity called the 'extended state' of the system, and the part of the disturbance is input into the system in a certain form through the control quantity, so that the influence of the disturbance on the system is eliminated. The basic principle is as follows:
for a first order system equation of state
In the formula: x is the number of1Is the state variable of the system, f is the uncertain quantity of the system except the control input, u is the control input of the system, b is the control gain, and y is the output of the system.
Let x2F, the state equation of the system can be written as
In the formula: x is the number of2Is an expansion state variable.
Establishing a corresponding extended state observer for the first order system according to equation (8):
in the formula: beta is a1、β2Is the gain of the extended state observer, z1，z2Are respectively a state variable x1，x2An estimate of (a).
The control rate can be written as follows:
in the formula: kpIs a proportionality coefficient of u0Is an uncompensated control quantity.
Selecting the appropriate beta1、β2The state observer can track the uncertain state of the system at a very fast speed, z1→x1，z2→ f. After the indeterminate quantity f is obtained, the control quantity is set as u-u0And f/b, the system becomes a relatively ideal pure integral link and is not influenced by uncertain disturbance any more.
From (8) and (9), an estimated disturbance z can be obtained2And the actual disturbance f
From (8), (9) and (10), the following expression can be obtained
In the formula: v is a reference signal.
From (13), the transfer function between the reference signal v and the output y can be deduced:
at the same time, the transfer function between the disturbance f and the output y can be derived:
as can be seen from equation (11), the estimated total disturbance is an integral of the error between the estimated output and the actual output. As can be seen from equation (12), the extended state observer resembles a low-pass filter, whose bode diagram is shown in fig. 3. Although the control rate (14) is only a proportional link, the auto-disturbance rejection controller can realize the control without steady and static differences. From the above discussion, the following conclusions can be drawn:
because the bandwidth of the extended state observer cannot be infinite, high-frequency disturbance cannot be observed, but low-frequency and abrupt disturbance can be well observed.
The extended state observer can help the controller to achieve steady-state-free error control.
Therefore, the linear active-disturbance-rejection controller can well inhibit disturbance with lower frequency and sudden change, because sinusoidal disturbance often exists in a motion system, in order to inhibit the sinusoidal disturbance, the invention introduces a resonance regulator into the active-disturbance-rejection controller, and the theory of the resonance regulator is briefly introduced below.
According to the internal model control principle, if a sinusoidal signal is to be accurately tracked without error, a mathematical model of the sinusoidal signal needs to be established in the controller. Resonant regulators are often used to suppress sinusoidal disturbances in moving systems. The transfer function of a conventional resonant regulator is as follows:
in the formula: k is a radical ofrTo amplify the coefficient, ω0Is the resonant frequency.
The bode diagram of the conventional resonant regulator is shown in fig. 4, and it can be seen that the resonant bandwidth is very narrow, which causes instability of the system. In order to increase the stability and the practicability of the device, the invention adopts a quasi-resonance regulator with a transfer function of
In the formula: omegacIs the cut-off frequency.
The bode diagram of the quasi-resonant regulator is shown in fig. 5, and compared with the conventional resonant regulator, the quasi-resonant regulator has the advantages that the resonance bandwidth is increased, the gain is larger near the resonance frequency, and the stability of the system is ensured. Although the resonance regulator can accurately track a sinusoidal signal, the dynamic performance of the resonance regulator is poor, the resonance regulator is usually used in parallel with a proportional link to form a proportional resonance controller, and the transfer function of the proportional resonance controller is as follows:
fig. 6 is a bode diagram of a proportional resonant controller, which can be found to have a larger bandwidth and a larger gain at the resonant frequency, and to achieve the tracking of the unsteady static error of the sinusoidal signal.
Based on the above description of the active disturbance rejection control strategy and the resonant regulator, the following description details the application of the present invention to the speed loop of the driving system of the permanent magnet synchronous motor.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the specific process of the step one is as follows:
the expression of the motor motion equation is shown in formula (1):
in the formula: omegarIs the rotational speed of the motor and is,
is omegarJ is the moment of inertia of the machine, pnIs the number of pole pairs, T, of the motorLIs the load torque of the motor, B is the viscosity coefficient of the motor, isqFor q-axis current, i.e. the control variable of the velocity loop,. phifIs the permanent magnet flux linkage of the motor;
the motor equation of motion (1) is rewritten in the form of state space equations (2) and (3):
f1is an unknown disturbance in the motor drive system, and f is a total disturbance in the motor drive system;
extending total disturbances in a motor drive system to a new state variable x2The expression for constructing the new state space equation is shown in equation (4):
in the formula: x is the number of1Is the state variable of the motor drive system, b is the control gain,
x1→ωr,x2→ f, y is the output of the motor drive system, u is the control quantity of the speed loop of the motor drive system, x2Is the new state variable into which the total disturbance in the motor drive system expands,
is x1The first derivative of (a) is,
is x2The first derivative of (a) is,
the first derivative of f.
The third concrete implementation mode: the second embodiment is different from the first embodiment in that: the expression of the extended state observer constructed in the second step is as follows:
wherein: z is a radical of1And z2Are respectively a state variable x1And x2Is detected by the measured values of (a) and (b),
and
are each z1And z2First derivative of, beta1、β2Are the gains of the extended state observer and e is the intermediate variable.
With reference to FIG. 7, the extended state observer operates by selecting the appropriate gain β1And beta2For the observed rotational speed z1And the actual rotational speed omegarTo obtain the total disturbance z2The observed total disturbance is then used for feed forward compensation to reduce fluctuations in rotational speed. Because of the limited bandwidth of the extended state observer, only low-frequency and abrupt disturbances (abrupt torque changes) can be compensated effectively.
The fourth concrete implementation mode: the third difference between the present embodiment and the specific embodiment is that: the specific process of the third step is as follows:
introducing quasi-resonance regulators into the control rate of the active disturbance rejection controller to modify the control rate of the active disturbance rejection controller, namely, in the control rate of the active disturbance rejection controller, after utilizing the parallel connection of the two quasi-resonance regulators, the parallel connection structure of the two quasi-resonance regulators is connected in parallel with a proportion link for use; the active disturbance rejection controller which introduces two quasi-resonance regulators is called a proportional resonance active disturbance rejection controller;
when the rotating speed of the speed ring is greater than or equal to a given threshold value, the two quasi-resonance regulators and the proportional link work together, and only the proportional link acts independently during a transient state period (the rotating speed is less than the given threshold value);
the design of the proportional resonance active disturbance rejection controller is used for realizing unsteady state static difference control, so that the gain is larger at the periodic fluctuation position of the rotating speed, the torque harmonic wave caused by the internal disturbance of the motor driving system is compensated, and the periodic fluctuation of the rotating speed caused by the internal disturbance of the motor driving system is inhibited;
and in order to further simplify the structure, the actual rotation speed of the motor is used as a feedback rotation speed instead of the estimated rotation speed. For the torque harmonics caused by internal disturbance, of which the 6 th and 12 th torque harmonics have the largest influence on the rotational speed, two quasi-resonant regulators are connected in parallel here to compensate the 6 th and 12 th torque harmonics, respectively. Thus:
the control rate of the modified proportional resonant active-disturbance-rejection controller is as follows:
wherein:
for a given speed of rotation, ω, of the motorcTo cut-off frequency, kpIs a proportionality coefficient, krFor amplification factors, s is a time domain variable, u0Is an uncompensated control quantity, ω6And ω12The resonant frequencies, omega, of two quasi-resonant regulators, respectively6＝6·ωrFor compensating for 6 th order torque harmonics, omega12＝12·ωrFor compensating for the 12 th order torque harmonics.
The fifth concrete implementation mode: the fourth difference between this embodiment and the specific embodiment is that: the torque harmonics caused by the internal disturbance of the compensation motor driving system comprise 6 th order torque harmonics and 12 th order torque harmonics.
The invention adopts the quasi-resonance regulator to compensate the internal disturbance, but the quasi-resonance regulator has serious overshoot problem when the rotating speed is started in step, in order to overcome the problem, a judgment statement is added in front of the quasi-resonance regulator, the quasi-resonance regulator can be put into use only when the rotating speed is close to the given rotating speed, and only a proportion link plays a role in the transient state period. The selection of the threshold value is determined according to the actual situation, and multiple times of simulation test verification show that the rotating speed periodic wave is selectedPreferably 1.5 times the peak value of the dynamic peak. The threshold value here is chosen to be 294 because the peak value of the speed fluctuation for the proportional-integral-controller-based speed loop is 4rpm, given a frequency of 10Hz (300 rpm). When the motor operates in a steady state, the quasi-resonance regulator is connected into the system and is ensured to be at 6 omegarAnd 12. omegarThe motor has larger gain, realizes the unsteady static error control of the rotating speed, compensates the internal disturbance of a motor system, and inhibits the periodic fluctuation of the rotating speed.
The experimental effect is as follows: FIG. 8 is a waveform of speed and torque at a sudden rated torque based on a proportional-integral controller controlled speed loop. From fig. 8(a), it can be found that in the case of a sudden change in the rated torque, the maximum drop speed is 76 rpm; in a steady state situation, the peak to peak value of the periodic rotational speed fluctuations caused by the motor drive system interior is 4 rpm. As can be seen from fig. 8(b), the speed loop based on the proportional-integral controller control has a very slow convergence to the rated load after the rated torque is abruptly changed and the rated torque is converged to the rated load after the abrupt change of the torque is reached after about 0.12 s; after sudden load shedding, it also takes 0.12s before converging to zero. This verifies the reason why the rotational speed drops more and converges to a given rotational speed slower. The torque ripple peak to peak value was 1.75Nm when operating at rated load, but the torque ripple was small at 0 load. This indicates that the speed fluctuations are caused by torque harmonics, and also indicates that the speed fluctuations are severe when the motor is operated at a low speed and a high torque.
As can be seen from fig. 9, the method of the present invention can obtain a relatively smooth rotation speed waveform, and at the same time, when the rated torque is running, the torque fluctuation is also small, which indicates that the method of the present invention can effectively suppress abrupt disturbance, low frequency disturbance and sinusoidal disturbance in the motor system at the same time. Fig. 9(a) can verify that the inventive method retains the advantages of the linear active disturbance rejection control strategy, and effectively suppresses abrupt disturbance and low-frequency disturbance. In case of sudden rated torque changes, the speed drop is the same, i.e. 35rpm, based on the speed loops of the linear and optimized active disturbance rejection controllers. Compared with the traditional proportional-integral controller, the rotating speed drop is reduced by 55 percent.
But is different in that the fluctuation of the rotation speed caused by the disturbance inside the system is suppressed when the motor is in steady operation. The peak value of the periodic fluctuation of the rotating speed of the speed ring based on the linear active disturbance rejection controller is 2.3rpm, and the speed ring is improved compared with the speed ring of the traditional proportional-integral control. The speed loop based on the optimized active disturbance rejection control of the invention has small and basically negligible fluctuation of the rotating speed. From fig. 9(b) it can be seen that the method of the invention can compensate the torque harmonics to the extent that the torque fluctuations no longer affect the rotational speed. The effectiveness of replacing the linear active disturbance rejection controller with the proportional resonant controller is further verified.
Compared with the traditional active disturbance rejection control strategy which can only effectively suppress external disturbance (torque sudden change), the improved control strategy can achieve simultaneous suppression of internal disturbance and external disturbance.
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.
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| CN115622464A (en) * | 2022-11-03 | 2023-01-17 | 中国科学院国家空间科学中心 | A Control Method of Space Low Speed Servo System Based on Quasi-Proportional Resonant Controller |
| CN116032170B (en) * | 2023-02-17 | 2025-02-11 | 中国科学院长春光学精密机械与物理研究所 | A motor speed control method for suppressing disturbance, storage medium and processor |
| CN116300476B (en) * | 2023-05-16 | 2023-09-05 | 成都微精电机股份公司 | Resonance suppression method based on rotating speed loop LADRC controller |
| CN118088463A (en) * | 2024-02-02 | 2024-05-28 | 浙江大学 | A speed control method suitable for magnetic suspension pump at low speed |
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