CN113325703A - Active disturbance rejection controller for inhibiting resonance and design method thereof - Google Patents
Active disturbance rejection controller for inhibiting resonance and design method thereof Download PDFInfo
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Abstract
The invention provides an active disturbance rejection controller for inhibiting resonance and a design method thereof, which can solve the resonance problem caused by a flexible transmission link. The active disturbance rejection controller comprises a motor speed ring, a motor position ring and a load position ring, and can effectively control the motor and the load position, inhibit the occurrence of resonance phenomenon and enable the output of a system to obtain good dynamic response; in addition, the active disturbance rejection controller is insensitive to the change of the rigidity coefficient of the flexible transmission link, has good robustness and is suitable for engineering application. The active disturbance rejection controller designed by the method of the invention can be used for inhibiting the generation of resonance, can be expanded to other control fields, such as gap nonlinearity inhibition and the like, and has common application effects.
Description
Technical Field
The invention belongs to the field of automatic control with similar flexible links such as high-precision servo control and robot control, and relates to an active disturbance rejection controller for inhibiting resonance and a design method thereof.
Background
Within an automatic control system, the rigidity of any material is limited, so that a flexible transmission link inevitably exists in the system. Taking a servo system as an example, a connecting transmission device between an actuating mechanism and a controlled object is not an ideal rigid link and has certain elasticity. In the system, the flexible transmission link inevitably becomes the most main factor influencing the control of the system, and due to the existence of the flexible link, the dynamic response of the system output is deteriorated, resonance occurs, and even the system becomes divergent, namely unstable. The treatment methods for inducing resonance due to the existence of the flexible link can be roughly divided into two main categories: an active mode and a passive mode. One of the passive methods is to redesign the mechanical structure, and select the more rigid mechanical structure to increase the resonant frequency of the system to be outside the closed-loop bandwidth, so that the mechanical resonance is not induced, but the cost of this method is high; the active mode is to add a compensation device, usually a series-solution notch filter, to the system without changing the mechanical structure and control structure of the system, so as to filter out the fixed resonant frequency component, thereby achieving the purpose of suppressing the mechanical resonance. However, this method has two obvious disadvantages, the first is that it is difficult to obtain an accurate model of the actual controlled object, and thus it is difficult to obtain the resonant frequency of the system; the second is that the robustness to system variations is poor, while the actual system is constantly changing, and these changes can cause the resonant frequency to change. The active mode is realized by applying a control theory and a control method, and mainly comprises resonance suppression based on a motor or load side sensor and resonance suppression based on a state observer method.
The influence of the flexible transmission link on the control performance is mainly because the flexible link introduces a second-order oscillation link with small damping on the basis of the original rigid model, when the resonant frequency of the second-order oscillation link is within the closed-loop bandwidth of the system, resonance can be easily caused, the dynamic response of the system output can be worsened, and the system can even become unstable when the oscillation is serious in the dynamic process.
With the rapid development of control theory in recent years, more and more control algorithms are applied to the suppression of resonance. The traditional control algorithm utilizes the information of the controlled object to perform feedback control, and is divided into full closed loop feedback and semi closed loop feedback according to the difference of the selected and fed back information of the controlled object. The semi-closed loop feedback refers to feedback by using information of the motor, the feedback only can effectively control the position of the motor, and the load position cannot be well controlled; the full closed loop feedback is feedback by using information of a load, and only the position of the load is effectively controlled, but the position of the motor cannot be effectively controlled. In addition to the conventional control algorithms, many advanced control algorithms are also applied to the suppression of resonance, such as advanced control algorithms of optimal control, H infinity, model-based prediction, and the like, but these control algorithms all need to obtain a mathematical model that is accurate to the system to obtain a good control effect, but it is often difficult to obtain a mathematical model that is accurate to the system in an actual system, and the model of the system is also constantly changed due to many factors.
The active disturbance rejection control technology is a nonlinear robust control technology proposed by a Chinese academy of sciences Konjin Qing researchers, can estimate the total disturbance of a system, wherein the total disturbance comprises the disturbance outside the system and the uncertainty caused by the change of the parameters inside the system. The active disturbance rejection control has the advantages of nonlinearity, large time lag and strong uncertainty to control the robustness and the adaptability of an object.
Therefore, there is a need for an auto-disturbance rejection controller capable of suppressing resonance, which can solve the resonance problem caused by the flexible transmission link by applying the auto-disturbance rejection control technology.
Disclosure of Invention
In view of this, the invention provides an auto-disturbance rejection controller for suppressing resonance and a design method thereof, which can solve the resonance problem caused by a flexible transmission link.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the controlled object is a two-inertia system, the driving disk of which is a motor and the driven disk is a load.
The active disturbance rejection controller includes a motor speed loop, a motor position loop, and a load position loop.
And the motor speed ring takes the actual load speed observed by the load position ring ESO as input and is used for controlling the motor speed to track the actual load speed.
The desired input of the load position loop is a desired load position for controlling the actual position of the load to said desired load position; the load position ring simultaneously observes the actual load position and the actual load speed and respectively sends the actual load position and the actual load speed to the motor position ring and the motor speed ring.
The desired input to the motor position loop is the actual load position as observed by the load position loop ESO, which is used to control the motor position to track the position of the load to be consistent with the actual load position.
Further, the motor speed ring comprises a motor speed ring ESO and a speed ring error control law.
Two input signals of the motor speed ring ESO are respectively an input signal of a controlled object and a motor position of the controlled object; the output of the motor speed ring ESO is the observed actual motor speed.
The input signal of the speed loop error control law is the actual load speed observed by the load position loop ESO and the output of the motor speed loop ESO, and the output of the speed loop error control law is the motor speed loop control quantity.
Further, the motor position ring comprises a motor position ring ESO and a motor position ring error control law.
The motor position ring ESO is used to observe the actual motor position and output it.
The input signal of the motor position ring error control law is the actual load position output by the load position ring ESO and the output of the motor position ring ESO, and the motor position ring error control law outputs the motor position ring control quantity.
Further, the load position loop includes a load position loop ESO and a load position loop error control law.
The input signal of the load position loop error control law is the output of the desired load position r and the load position loop ESO, and the load position loop error control law outputs the load position loop control quantity.
A design method of an active disturbance rejection controller for restraining resonance comprises the following steps:
and S01, aiming at the controlled object, modeling according to Newton' S second law, obtaining a differential equation of the controlled object, and designing a motor speed ring comprising a motor speed ring ESO and a speed ring error control law according to the differential equation.
And S02, modeling according to Newton' S second law for the controlled object and the motor speed ring to obtain a new differential equation of the controlled object, and designing a motor position ring including a motor position ring ESO and a motor position ring error control law according to the new differential equation.
And S03, modeling according to Newton' S second law for the controlled object, the motor speed ring and the motor position ring to obtain a re-updated differential equation of the controlled object, and designing the load position ring according to the re-updated differential equation, wherein the load position ring comprises a load position ring ESO and a load position ring error control law.
Has the advantages that: the three-ring active disturbance rejection controller provided by the invention can effectively control the positions of the motor and the load, inhibit the occurrence of resonance phenomenon and ensure that the output of the system obtains good dynamic response; in addition, the invention is insensitive to the change of the rigidity coefficient of the flexible transmission link, has good robustness and is suitable for engineering application. The active disturbance rejection controller designed by the method of the invention can be used for inhibiting the generation of resonance, can be expanded to other control fields, such as gap nonlinearity inhibition and the like, and has common application effects.
Drawings
FIG. 1 is a model diagram of a two-inertia system;
FIG. 2 is a diagram of a three-ring active disturbance rejection controller;
FIG. 3 is a motor and load position response (double loop) diagram;
FIG. 4 is a motor and load position response (three-loop) diagram;
FIG. 5 shows the motor and load position response (three-ring, 2J)L) A drawing;
FIG. 6 shows the motor and load speed responseShould (tricyclic, 2J)L) A drawing;
FIG. 7 shows motor and load position response (double ring, 2J)L) A drawing;
FIG. 8 is a partial enlarged view of the motor and load position response (double ring, 2J)L) A drawing;
FIG. 9 shows motor and load speed response (double loop, 2J)L) A drawing;
FIG. 10 shows the motor versus load position response (three rings, 0.5 k)s) A drawing;
FIG. 11 shows motor and load speed response (three-ring, 0.5 k)s) A drawing;
FIG. 12 is a graph of a three-ring ADRC position response experiment;
FIG. 13 is a three-ring ADRC position response experimental curve (1.5J)L) A drawing;
FIG. 14 is a three-ring ADRC position response experimental curve (0.5 k)s) Figure (a).
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The design principle of the invention is as follows: a system in which a motor indirectly drives a load through a flexible drive is considered to be a two-inertia system. For the problem of resonance suppression of the two-inertia system connected by the flexible link, the suppression is to ensure that the position and the speed between the two inertias are consistent essentially, so that the elastic link is prevented from being twisted to generate deformation to further cause resonance. For the problems, the invention is regarded as a single-input multi-output problem, and when flexible links exist between inertias, the flexible links can be caused to twist to generate elastic deformation when the position difference or the speed difference exists between the connected inertias. As previously mentioned, the output response of the system can be made worse or even diffuse when the bandwidth of the system is relatively high or the resonant frequency of the system is low. Due to the existence of the elastic link, the control of the two-inertia system becomes complicated, so that the control of the system cannot simply input a single-input single-output system for controlling the position or the speed of the last inertia in a single mode, and the control is performed by regarding the system as a single-input multi-output system, so that the position of the last inertia and the position and the speed of the first inertia are controlled, and if the control is performed by simply adopting the position of the load (driven disc), the position of the motor (driving disc) is not effectively controlled at the moment, and the flexible link connecting the motor and the load still generates elastic deformation to further cause mechanical resonance.
Through the above analysis, it can be inferred that: when the position and the speed of the known motor can be consistent with the position or the speed of a load, the flexible link does not have torsion, and elastic deformation does not occur, so that the flexible link can be regarded as an ideal rigid body, and the system with the transmission device as the ideal rigid body does not have resonance. For such a two-inertia system, it should be considered as an under-actuated system for which a three-loop control system is designed to control motor speed, position and load position. First, the position of the driven disk (load) should be controlled at the outer ring, then the position and speed of the driven disk and the disturbance are estimated using the ESO, then the position of the driven disk is used as an input to control the design position of the driving disk (motor) to track control the position of the driven disk, and the speed of the driving disk is used as a desired input of the speed of the driving disk. The invention designs the three-ring active disturbance rejection controller based on the above, so that the speed and the position of the driving disk can quickly track the driven disk, and the elastic link is prevented from generating torsion to cause resonance.
The present invention will be described in detail below by taking a motor servo system as an example.
First, algorithm design and simulation
Fig. 1 is a System model of a Two-Inertia System (Two Inertia System) having a flexible transmission link between a driving disk (motor) and a driven disk (load). Wherein, TEFor an input torque JmIs the moment of inertia of the motor, JlTo load moment of inertia, ksA coefficient of rigidity of a flexible link, bsDamping coefficient of flexible link, thetam、ωm、αmIs the position and speed of the motor shaftDegree, acceleration, thetal、ωl、αlLoad shaft position, velocity, acceleration.
Firstly, a differential equation is established by a model of the two-inertia system through Newton's law to obtain a related transfer function as follows:
next, for the two-inertia system, a three-closed-loop active disturbance rejection controller is designed to achieve resonance suppression of the two-inertia system. The controller structure is shown in fig. 2.
The three-ring active disturbance rejection controller consists of a speed ring and two position control rings, wherein the three rings are a motor speed ring, a motor position ring and a load position ring in sequence.
The motor speed ring comprises a motor speed ring ESO and a speed ring error control law. Two input signals of the motor speed ring ESO are respectively an input signal of a controlled object and a motor position of the controlled object; the input signals of the speed ring error control law are the actual load speed observed by the load position ring ESO and the output of the motor speed ring ESO, and the output of the motor speed ring ESO is the actual motor speed observed.
The motor speed ring is used to control the speed of the driving disc, i.e. the motor, to be consistent with the speed of the driven disc, i.e. the load, and the input to the speed ring is the actual load speed as observed by the load position ring ESO, which is used to control the motor speed to track the actual load speed.
The two position rings are respectively a motor position ring and a load position ring, and the motor position ring and the load position ring are structurally equivalent to be connected in parallel. The motor position ring comprises a motor position ring ESO and a motor position ring error control law. The desired input to the motor position loop is the actual load position as observed by the load position loop ESO, which is used to control the motor position to track the position of the load to be consistent with the actual load position. The motor position ring ESO is used for observing and outputting the actual motor position, the input signals of the motor position ring error control law are the actual load position output by the load position ring ESO and the output of the motor position ring ESO, and the motor position ring error control law outputs the motor position ring control quantity.
The load position loop includes a load position loop ESO and a load position loop error control law. The desired input to the load position loop is a desired load position for controlling the actual position of the load to the desired load position; the load position ring simultaneously observes the actual load position and the actual load speed and respectively sends the actual load position and the actual load speed to the motor position ring and the motor speed ring. And the load position ring error control law outputs a load position ring control quantity. The input signal of the load position loop error control law is the output of the desired load position r and the load position loop ESO, and the load position loop error control law outputs the load position loop control quantity.
Aiming at the design of the active disturbance rejection controller, the design method comprises the following steps:
and aiming at the controlled object, modeling according to Newton's second law, obtaining a differential equation of the controlled object, and designing a motor speed ring aiming at the differential equation, wherein the motor speed ring comprises a motor speed ring ESO and a speed ring error control law.
The motor speed loop is designed to keep the speed of the motor and the speed of the load consistent so that the speed of the motor can track the speed of the load, and therefore the reference input of the speed loop is the load speed observed by the load position loop ESO.
The differential equation of the controlled object is as follows:
TE＝u3+uz (3)
wherein u iszIs input of a two-position loop, and the input of the controlled object is TE。
Get x1＝θm,
x3F and from this the state equation is constructed as follows:
wherein the content of the first and second substances,
extended state observer, ESO: because the motor speed loop is designed, the invention only needs to estimate the two states of the speed and the disturbance at the motor end. The reduced-order ESO was constructed as follows:
the inner loop control rate is designed as follows:
in the intermediate state, the state of the system is,
ω02the state observer bandwidth is extended for the speed loop.
Where r is the speed inner loop reference input, and r is taken from the load speed observed by the load extended state observer. Omegac2The rate bandwidth is controlled for the inner loop. And modeling according to Newton's second law for a controlled object and a motor speed ring to obtain a new differential equation, and designing a motor position ring including a motor position ring ESO and a motor position ring error control law for the new differential equation.
The design of motor position ring is in order to make the motor position can track the load position, and both can keep unanimous, and motor position is 0 with the load position difference this moment, and the flexible link just also can not take place to twist reverse and lead to deformation and cause the resonance.
The controlled object changes for the outer ring of positions due to the introduction of the speed ring. Firstly, the original controlled object is changed by increasing the speed loop control quantity u3And the second change is that the input of the controlled object at the moment is changed into uz。
T in (3)E＝u3+uzThe finishing in the step (4) can obtain:
wherein u is3For the speed loop control quantity, will
And (7) finishing to obtain:
wherein e ═ θm-θl,uz＝u1+u2。
Designing a motor position ring extended state observer:
get x1m＝θm,
x3m＝fmThe equation of state is thus constructed as follows:
wherein the content of the first and second substances,
the extended state observer is constructed in this way as follows:
wherein the content of the first and second substances,
are respectively x1m,x2m,x3mThe observed value of (1). Omega01Is the motor position loop observer bandwidth.
The motor position loop control law is designed as follows:
wherein, ω isc1Rate bandwidth is controlled for the motor position loop. And modeling according to Newton's second law for a controlled object, a motor speed ring and the motor position ring to obtain a new differential equation, and designing a load position ring according to the new differential equation, wherein the load position ring comprises a load position ring ESO and a load position ring error control law.
The load position ring is designed to control the load position of the motor. The input of the load position loop of the three-loop active disturbance rejection controller is u as well as the input of the motor position loopz＝u1+u2In this case, the controlled object designed for the load position loop is shown as (11):
aiming at a load position ring of the three-ring active disturbance rejection controller, the invention designs the state observer thereof.
Get x1l＝θl,
x4l＝flFrom this, the equation of state is constructed:
wherein the content of the first and second substances,
the extended state observer is constructed in this way as follows:
wherein the content of the first and second substances,
are respectively x1l,x2l,x3l,x4lThe observed value of (1).
The load position loop control law is designed as follows:
wherein, ω iscFor the motor position loop control rate bandwidth, r is the desired input to the system. Therefore, the design of the three-ring active disturbance rejection controller is completed.
In an actual servo system, there are the following situations: the load in the servo system is changed frequently, so that the load inertia is changed; some servo system stiffness coefficient ksWill be continuously variable. But coefficient of rigidity ksThe resonance of the system is affected by the change of the load inertia, the resonance frequency is reduced due to the fact that the rigidity coefficient is reduced and the load inertia is increased, and low-frequency resonance can occur even if the bandwidth of the system is not large. Therefore, a good controller cannot only control a system with constant load inertia and constant elastic link, and has good robustness to continuous changes of the load inertia and the rigidity coefficient.
In order to verify the effectiveness of the invention, the parameter of the controlled object is taken as JM＝0.0014kg·m2、JL＝0.0084kg·m2、ksThe ability of the three-loop controller to suppress resonance is verified below by simulation and comparison with the dual-loop active disturbance rejection controller, 8.45N/m, c 0.17N/(m/s).
The simulation result under the control of the double-ring active disturbance rejection controller is shown in fig. 3, the simulation result under the control of the three-ring active disturbance rejection controller is shown in fig. 4, and the three-ring active disturbance rejection controller and the double-ring active disturbance rejection controller can obtain a good control effect no matter at a motor end or a load end and have no resonance phenomenon.
In a real servo system, the stiffness coefficient ksThe resonance of the system is affected by the change of the load inertia, the resonance frequency is reduced due to the fact that the rigidity coefficient is reduced and the load inertia is increased, and low-frequency resonance can occur even if the bandwidth of the system is not large. Therefore, the capability of the three-ring active disturbance rejection controller for inhibiting resonance under the condition that the rigidity coefficient and the load inertia of the transmission link are changed is verified through simulation.
Firstly, the capability of the three-ring active disturbance rejection controller for inhibiting resonance under the condition of load inertia change is verified, so that the load inertia J is enabledL＝0.0168kg·m2At this time, the response of the load position and the motor position of the three-loop active-disturbance-rejection controller is shown in fig. 5, and the response of the load speed and the motor speed of the three-loop active-disturbance-rejection controller is shown in fig. 6, so that the motor position and speed can quickly track the load position and speed, and no resonance phenomenon occurs at either the motor end or the load end. Compared with a three-ring active disturbance rejection controller, the speed simulation response of the double-ring active disturbance rejection controller is shown in fig. 9, and the motor position and speed of the double-ring active disturbance rejection controller are difficult to quickly follow the load position and speed, so that the flexible transmission link is twisted, and the dynamic response of the system is poor.
Next, the capability of the three-ring active disturbance rejection controller for inhibiting resonance under the condition of rigidity coefficient change is verified, so that the rigidity coefficient is changed to 0.5ksAt this time, the response of the load position and the motor position of the three-ring active disturbance rejection controller is shown in fig. 10, and the load speed and the motor speed of the three-ring active disturbance rejection controllerThe response of the motor is shown in fig. 11, the position and the speed of the motor can quickly track the position and the speed of the load, and no resonance phenomenon occurs at the motor end or the load end.
And (3) experimental verification:
the experimental environment consisted of: PC, PCI-1716, PCI-QUAD04, ECP Model205a experiment platform. The PC needs to install Matlab Real-time Workshop to construct a semi-physical simulation experiment environment. The Model205A is composed of a machine body and a control box, the control box is a power driving device of the Model205A, the input voltage is-10V, and the corresponding output is-15A current. PCI-QUAD04 is used to count the pulse signal of the encoder, the encoder outputs A, B two-phase pulse signal, and the rotation direction can be determined according to the relationship between the phases of the two-phase signal. The machine body mainly comprises a motor, a load and a transmission mechanism.
Fig. 12 is a diagram showing the control effect of the motor position and the load position of the three-ring active disturbance rejection controller in a semi-physical simulation experiment, and fig. 13 is a diagram showing the control effect of the motor position inner ring and the load position when the load inertia is increased to 1.5 times of the original load inertia. FIG. 14 shows the change of the stiffness coefficient of the flexible link to 0.5ksThe control effect diagram of the inner ring of the motor position and the load position. As shown in fig. 12, 13, and 14, the three-ring active disturbance rejection controller has a good control effect on the two-inertia servo system, and even if the load inertia becomes large or the rigidity coefficient of the flexible transmission link becomes small, both the motor side and the load side can be well controlled, and the three-ring active disturbance rejection controller has a good resonance suppression capability.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. An active disturbance rejection controller for inhibiting resonance is characterized in that a controlled object is a two-inertia system, a driving disk of the controlled object is a motor, and a driven disk of the controlled object is a load;
the active disturbance rejection controller comprises a motor speed ring, a motor position ring and a load position ring;
the motor speed loop takes the actual load speed observed by the load position loop ESO as input and is used for controlling the motor speed to track the actual load speed;
a desired input to the load position loop is a desired load position for controlling an actual position of a load to the desired load position; the load position ring simultaneously observes the actual load position and the actual load speed and respectively sends the actual load position and the actual load speed to the motor position ring and the motor speed ring;
the expected input to the motor position loop is the actual load position as observed by the load position loop ESO, which is used to control the motor position to track the position of the load to stay consistent with the actual load position.
2. The controller of claim 1, wherein the motor speed loop comprises a motor speed loop ESO and a speed loop error control law;
two input signals of the motor speed ring ESO are respectively an input signal of a controlled object and a motor position of the controlled object; the output of the motor speed ring ESO is the observed actual motor speed;
the input signal of the speed loop error control law is the actual load speed observed by the load position loop ESO and the output of the motor speed loop ESO, and the output of the speed loop error control law is the motor speed loop control quantity.
3. The controller of claim 1, wherein the motor position loop comprises a motor position loop (ESO) and a motor position loop error control law;
the motor position ring ESO is used for observing and outputting the actual motor position;
the input signal of the motor position ring error control law is the actual load position output by the load position ring ESO and the output of the motor position ring ESO, and the motor position ring error control law outputs the motor position ring control quantity.
4. The controller of claim 1, wherein the load position loop comprises a load position loop ESO and a load position loop error control law;
the input signals of the load position loop error control law are the outputs of the expected load position r and the load position loop ESO, and the load position loop error control law outputs a load position loop control quantity.
5. A design method of an active disturbance rejection controller for suppressing resonance, which is designed for the active disturbance rejection controller according to any one of claims 1 to 4, and comprises the following steps:
s01, aiming at a controlled object, modeling according to Newton' S second law to obtain a differential equation of the controlled object, and designing a motor speed ring aiming at the differential equation, wherein the motor speed ring comprises a motor speed ring ESO and a speed ring error control law;
s02, aiming at the controlled object and the motor speed ring, modeling is carried out according to Newton' S second law to obtain a new differential equation of the controlled object, and a motor position ring is designed according to the new differential equation, wherein the new differential equation comprises a motor position ring ESO and a motor position ring error control law;
and S03, modeling according to Newton' S second law for the controlled object, the motor speed ring and the motor position ring to obtain a re-updated differential equation of the controlled object, and designing the load position ring according to the re-updated differential equation, wherein the load position ring comprises a load position ring ESO and a load position ring error control law.
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