CN111251288B - Flexible robot cascade control system and method based on time-varying interference compensation - Google Patents

Flexible robot cascade control system and method based on time-varying interference compensation Download PDF

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CN111251288B
CN111251288B CN202010251041.3A CN202010251041A CN111251288B CN 111251288 B CN111251288 B CN 111251288B CN 202010251041 A CN202010251041 A CN 202010251041A CN 111251288 B CN111251288 B CN 111251288B
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direct current
mechanical arm
current motor
estimation
side position
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CN111251288A (en
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王会明
张扬
鲜娟
李清都
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Chongqing University of Post and Telecommunications
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Chongqing University of Post and Telecommunications
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/10—Programme-controlled manipulators characterised by positioning means for manipulator elements
    • B25J9/12—Programme-controlled manipulators characterised by positioning means for manipulator elements electric
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J13/00—Controls for manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1612—Programme controls characterised by the hand, wrist, grip control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1635—Programme controls characterised by the control loop flexible-arm control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis

Abstract

The invention discloses a flexible robot cascade control system and method based on time-varying interference compensation, wherein the system comprises a DC motor side position controller, an extended state observer based on a DC motor model, a mechanical arm side position controller, an extended state observer based on a mechanical arm model, a DC motor side position sensor, a mechanical arm side position sensor, a DC motor, a flexible node and a mechanical arm, wherein the mechanical arm side position controller comprises a flexible node based on interference estimation
Figure DDA0002435494750000011
Feedforward compensation control and state-based estimation
Figure DDA0002435494750000012
The feedback control of (2); the DC motor side position controller includes a controller based on interference estimation
Figure DDA0002435494750000013
Feedforward compensation control and state-based estimation
Figure DDA0002435494750000014
The feedback control of (2). Compared with the traditional cascade proportional-differential control method, the control system and the control method are simple in design and implementation and high in anti-interference capability, and can meet the application requirements of the position tracking system of the single-joint flexible mechanical arm.

Description

Flexible robot cascade control system and method based on time-varying interference compensation
Technical Field
The invention relates to the technical field of control methods based on single-joint flexible mechanical arms, in particular to a flexible robot cascade control system and method based on time-varying interference compensation.
Background
In recent years, the problem of tracking the track of the flexible mechanical arm has attracted great attention, mainly because the problem is complex. To reduce the speed of flexible robotic arms, many robots are equipped with harmonic drives, but such drives introduce elastic torques in the joints. Industrial robots often incorporate resilient elements in the drive train which can exhibit torsional vibrations when the robot needs to respond quickly. For many robotic arms, joint elasticity arises from many aspects, such as the elasticity of gears, belts, tendons, bearings, hydraulic lines, and the like. Most existing method designs assume perfect stiffness at the joint, which may limit the dynamic accuracy of the control method. However, the actual position tracking system of the flexible mechanical arm is a nonlinear system and is affected by various types of time-varying interference. For any control system design, proper selection of the appropriate mathematical model is a critical stage. Experimental evidence shows that in order to achieve a high-performance control effect, the flexibility of the mechanical arm joint needs to be considered in the modeling of the mechanical arm and the design process of a controller, but the introduction of the flexible joint into a mechanical arm model greatly complicates a motion equation.
To solve this complex problem, many feedback control schemes have been proposed. For example, a sliding mode control based design requires that the uncertainty of the system is bounded, while all state variables of the system are required to be known in order to enable control. A control design scheme based on a singular perturbation method requires that position parameters of a mechanical arm and elastic force at a joint can be measured, and meanwhile, a nonlinear sliding mode observer is required to estimate the speed of the mechanical arm and the time derivative of the elastic force at the joint. There are other control methods such as adaptive control, iterative control, etc.
However, most control schemes or industrial implementations are difficult, and have the following defects: for example, the control method is too complex to facilitate engineering implementation, the number of required sensors is too large, the cost is high, and other problems are solved, or various time-varying interferences of the system, including unmodeled dynamics, parameter uncertainty, external interferences, and the like, cannot be effectively observed and immediately suppressed.
Disclosure of Invention
In order to overcome at least one defect in the prior art, the invention provides a flexible robot cascade control system and method based on time-varying interference compensation, which solve the problems, so that the system is simple in structure and good in control performance, and is very important for application and popularization of a flexible mechanical arm.
The invention is realized by the following technical scheme:
a flexible robot cascade control system based on time-varying interference compensation comprises a direct current motor side position controller, an extended state observer based on a direct current motor model, a mechanical arm side position controller, an extended state observer based on a mechanical arm model, a direct current motor side position sensor, a mechanical arm side position sensor, a direct current motor, a flexible node and a mechanical arm, wherein the mechanical arm side position controller is connected with the direct current motor side position controller, the mechanical arm side position controller is connected with the extended state observer based on the mechanical arm model, the direct current motor side position controller is connected with the direct current motor, the direct current motor side position controller is connected with the extended state observer based on the direct current motor model, and the direct current motor is connected with the mechanical arm through the flexible node; the mechanical arm is connected with an extended state observer based on a mechanical arm model, and the extended state observer based on the mechanical arm model is connected with a mechanical arm side position controller; the direct current motor is connected with an extended state observer based on a direct current motor model, and the extended state observer based on the direct current motor model is connected with a direct current motor side position controller;
the direct current motor side position sensor is used for detecting a position sensor signal arranged on the direct current motor; the mechanical arm side position sensor is used for detecting a position sensor signal arranged on the mechanical arm;
the method comprises the following steps that signals of a mechanical arm side position sensor and output control signals of a mechanical arm side position controller are subjected to position estimation, speed estimation and disturbance estimation of a mechanical arm through an extended state observer based on a mechanical arm model; the method comprises the following steps that signals of a position sensor at the side of a direct current motor and output control signals of a position controller at the side of the direct current motor are subjected to position estimation, speed estimation and disturbance estimation of the direct current motor through an extended state observer based on a direct current motor model;
an input signal of the mechanical arm side position controller passes through the mechanical arm side position controller to obtain an input signal of the direct current motor side position controller, and the signal is also a position reference signal of the direct current motor; obtaining a torque control signal of the direct current motor by passing a difference value of a position reference signal of the direct current motor and the obtained position estimation of the direct current motor, a difference value of a differential signal of the position reference signal of the direct current motor and the obtained speed estimation of the direct current motor and the obtained disturbance estimation of the direct current motor through a direct current motor side position controller; the position of the direct current motor is controlled by a torque control signal of the direct current motor, and the position signal output by the direct current motor controls the position of the flexible mechanical arm; wherein:
the input signal of the robot-side position controller includes a difference between a position reference signal of the robot and the obtained position estimate of the robot, a difference between a differential signal of the position reference signal of the robot and the obtained velocity estimate of the robot, and an estimate of a disturbance applied to the robot.
Further, the DC motor side position controller and the mechanical arm side position controller are connected in a cascade manner.
Further, the robot-arm-side position controller includes feedback control and feedforward control, wherein the input signal of the feedback control includes a position estimate and a velocity estimate of the extended state observer based on the robot arm model, and the input signal of the feedforward control includes a disturbance estimate of the extended state observer based on the robot arm model.
Further, the robot-arm-side position controller includes a controller for estimating a position of the robot arm based on the interference
Figure BDA0002435494730000021
Feedforward compensation control and state-based estimation
Figure BDA0002435494730000022
The expression of the robot-side position controller of (1) is:
Figure BDA0002435494730000031
wherein, b 0j ＝1；r m Is a machineThe output signal of the arm side position controller is also a position reference signal of the direct current motor; r is j A position reference signal of the mechanical arm;
Figure BDA0002435494730000032
a differential signal that is a position reference signal of the robot arm;
Figure BDA0002435494730000033
estimating the position of the mechanical arm;
Figure BDA0002435494730000034
estimating the speed of the mechanical arm;
Figure BDA0002435494730000035
estimating the disturbance on the mechanical arm; k is a radical of pj Is a proportional gain; k is a radical of dj Is the differential gain.
Further, the dc motor-side position controller includes feedback control and feedforward control, wherein the input signal of the feedback control includes a position estimation and a speed estimation of the extended state observer based on the dc motor model, and the input signal of the feedforward control includes a disturbance estimation of the extended state observer based on the dc motor model.
Further, the DC motor side position controller includes a controller based on interference estimation
Figure BDA0002435494730000036
Feedforward compensation control and state-based estimation
Figure BDA0002435494730000037
The expression of the dc motor side position controller is:
Figure BDA0002435494730000038
wherein, b 0m 1/J; u is a torque control signal of the direct current motor; r is m Position reference signals of the direct current motor;
Figure BDA0002435494730000039
a differential signal which is a position reference signal of the direct current motor;
Figure BDA00024354947300000310
estimating the position of the direct current motor;
Figure BDA00024354947300000311
estimating the speed of the direct current motor;
Figure BDA00024354947300000312
estimating the disturbance of the direct current motor; k is a radical of pm Proportional gain is obtained; k is a radical of dm Is the differential gain; j is the rotary inertia of the DC motor.
Further, the expression of the extended state observer based on the dc motor model is as follows:
Figure BDA00024354947300000313
wherein, b 0m ＝1/J；
Figure BDA00024354947300000314
Estimating the position of the direct current motor;
Figure BDA00024354947300000315
estimating the speed of the direct current motor;
Figure BDA00024354947300000316
estimating the disturbance of the direct current motor;
Figure BDA00024354947300000317
is based on the gain coefficient of the extended state observer of the DC motor model; y is m Is the position of the DC motor; u is a torque control signal of the direct current motor; j is the moment of inertia of the DC motor.
Further, the expression of the extended state observer based on the mechanical arm model is as follows:
Figure BDA0002435494730000041
wherein, b 0j ＝1；
Figure BDA0002435494730000042
Estimating the position of the mechanical arm;
Figure BDA0002435494730000043
estimating the speed of the mechanical arm;
Figure BDA0002435494730000044
estimating the disturbance on the mechanical arm;
Figure BDA0002435494730000045
is a gain coefficient of an extended state observer based on a mechanical arm model; y is j The position of the mechanical arm; r is m Is an output signal of the robot arm-side position controller, which is also a position reference signal of the dc motor.
In another aspect, the present invention further provides a flexible robot cascade control method based on time-varying interference compensation, including the following steps:
1) the position of the direct current motor is obtained by detecting signals of a position sensor at the side of the direct current motor;
2) the position of the mechanical arm is obtained by detecting a signal of a mechanical arm side position sensor;
3) the method comprises the following steps that signals of a mechanical arm side position sensor and output control signals of a mechanical arm side position controller are subjected to position estimation, speed estimation and disturbance estimation of a mechanical arm through an extended state observer based on a mechanical arm model;
4) the method comprises the following steps that signals of a position sensor at the side of a direct current motor and output control signals of a position controller at the side of the direct current motor are subjected to position estimation, speed estimation and disturbance estimation of the direct current motor through an extended state observer based on a direct current motor model;
5) the input signal of the mechanical arm side position controller comprises a difference value of a position reference signal of the mechanical arm and the position estimation of the mechanical arm obtained in the step 3), a difference value of a differential signal of the position reference signal of the mechanical arm and the speed estimation of the mechanical arm obtained in the step 3), and disturbance estimation of the mechanical arm obtained in the step 3), and the input signal of the direct current motor side position controller is obtained through the mechanical arm side position controller and is also the position reference signal of the direct current motor;
6) the difference value of the position reference signal of the direct current motor obtained in the step 5) and the position estimation of the direct current motor obtained in the step 4), the difference value of the position reference signal of the direct current motor and the speed estimation of the direct current motor obtained in the step 4), and the disturbance estimation of the direct current motor obtained in the step 4) pass through a direct current motor side position controller to obtain a torque control signal of the direct current motor;
7) the position of the direct current motor is controlled by a torque control signal of the direct current motor, and the position signal output by the direct current motor controls the position of the flexible mechanical arm.
Further, the DC motor side position controller and the mechanical arm side position controller are connected in a cascade mode;
the mechanical arm side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a mechanical arm model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the mechanical arm model;
the direct current motor side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a direct current motor model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the direct current motor model.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. compared with the traditional control method, the flexible robot cascade control method based on time-varying interference compensation is simple in control method and easy to realize in structure, and the system can achieve good dynamic performance and steady-state performance;
2. compared with a common cascade proportional-differential control system, the cascade control system of the flexible robot based on time-varying interference compensation comprises feedback control and feedforward control, and the anti-interference capability of the system can be effectively improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a detailed functional block diagram of the control system of the present invention;
FIG. 2 is a functional block diagram of the robotic arm side position controller of the present invention;
FIG. 3 is a functional block diagram of a DC motor side position controller of the present invention;
FIG. 4 is a simulation diagram of the position results of the robot arm under two control modes;
FIG. 5 is a simulation diagram of position results of a DC motor under two control modes;
FIG. 6 is a simulation diagram of the torque control signal results of the DC motor under two control modes;
FIG. 7 is a simulation diagram of the results of disturbance estimation by an observer I and an observer II under the control mode of the invention;
FIG. 8 is a simulation diagram of the position and velocity estimation results of the mechanical arm by the extended state observer based on the mechanical arm model under the control mode of the invention;
FIG. 9 is a simulation diagram of the estimation result of the position and speed of the DC motor by the extended state observer based on the DC motor model under the control mode of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and the accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not used as limiting the present invention.
Example 1
As shown in fig. 1 to 9, the flexible robot cascade control system based on time-varying interference compensation of the present invention, fig. 1 is a detailed schematic block diagram of the control system of the present invention, the system comprises a DC motor side position controller, an extended state observer based on a DC motor model, a mechanical arm side position controller, an extended state observer based on a mechanical arm model, a DC motor side position sensor, a mechanical arm side position sensor, a DC motor, a flexible node and a mechanical arm, the mechanical arm side position controller is connected with the direct current motor side position controller, the mechanical arm side position controller is connected with an extended state observer based on a mechanical arm model, the direct current motor side position controller is connected with the direct current motor, the direct current motor side position controller is connected with the extended state observer based on the direct current motor model, and the direct current motor is connected with the mechanical arm through a flexible node; the mechanical arm is connected with an extended state observer based on a mechanical arm model, and the extended state observer based on the mechanical arm model is connected with a mechanical arm side position controller; the direct current motor is connected with an extended state observer based on a direct current motor model, and the extended state observer based on the direct current motor model is connected with a direct current motor side position controller;
the direct current motor side position sensor is used for detecting a position sensor signal arranged on the direct current motor; the mechanical arm side position sensor is used for detecting a position sensor signal arranged on the mechanical arm;
the method comprises the following steps that signals of a mechanical arm side position sensor and output control signals of a mechanical arm side position controller are subjected to position estimation, speed estimation and disturbance estimation of a mechanical arm through an extended state observer based on a mechanical arm model; the method comprises the following steps that signals of a position sensor at the side of a direct current motor and output control signals of a position controller at the side of the direct current motor are subjected to position estimation, speed estimation and disturbance estimation of the direct current motor through an extended state observer based on a direct current motor model;
an input signal of the mechanical arm side position controller passes through the mechanical arm side position controller to obtain an input signal of the direct current motor side position controller, and the signal is also a position reference signal of the direct current motor; obtaining a torque control signal of the direct current motor by passing a difference value of a position reference signal of the direct current motor and the obtained position estimation of the direct current motor, a difference value of a differential signal of the position reference signal of the direct current motor and the obtained speed estimation of the direct current motor and the obtained disturbance estimation of the direct current motor through a direct current motor side position controller; the position of the direct current motor is controlled by a torque control signal of the direct current motor, and the position signal output by the direct current motor controls the position of the flexible mechanical arm; wherein:
the input signal of the robot-side position controller includes a difference between a position reference signal of the robot and the obtained position estimate of the robot, a difference between a differential signal of the position reference signal of the robot and the obtained velocity estimate of the robot, and an estimate of a disturbance applied to the robot.
The mathematical model of the single-joint flexible mechanical arm is as follows:
Figure BDA0002435494730000061
Figure BDA0002435494730000062
wherein q is 1 Position of the arm, q 2 Is the position of the direct current motor,
Figure BDA0002435494730000063
in order to be the speed of the robot arm,
Figure BDA0002435494730000064
is the speed of the direct current motor,
Figure BDA0002435494730000065
in order to accelerate the mechanical arm,
Figure BDA0002435494730000066
the acceleration of the direct current motor is shown, K is the rigidity coefficient of the mechanical arm, J is the rotational inertia of the direct current motor, B is the damping coefficient of the transmission mechanism, and u is the torque control signal of the direct current motor.
Generally, to facilitate control of a position tracking system for a single-joint flexible robot arm, the system may be described as a series of a dynamic model of a dc motor and a dynamic model of the robot arm.
The dynamic model of the mechanical arm can be expressed in the form of:
Figure BDA0002435494730000071
Figure BDA0002435494730000072
wherein x is defined 1 ＝q 1 ，
Figure BDA0002435494730000073
ω＝q 2 。x 1 In order to be the position of the mechanical arm,
Figure BDA0002435494730000074
x 2 in order to be the speed of the robot arm,
Figure BDA0002435494730000075
the acceleration of the mechanical arm is shown, omega is the position of the direct current motor, and d is the disturbance on the mechanical arm. Wherein b is 0j ＝1；
The dynamic model of the direct current motor can be expressed in the following form:
Figure BDA0002435494730000076
Figure BDA0002435494730000077
wherein x is defined 4 ＝q 2 ，
Figure BDA0002435494730000078
x 4 Is the position of the direct current motor,
Figure BDA0002435494730000079
x 5 is the speed of the direct current motor,
Figure BDA00024354947300000710
is the acceleration of the DC motor, u is the torque control signal of the DC motor, f is the disturbance to the DC motor, b 0m 1/J, wherein J is the rotational inertia of the direct current motor;
in this embodiment, the dc motor side position controller and the robot arm side position controller are connected in a cascade manner.
In this embodiment, as shown in fig. 2, the robot-arm-side position controller includes feedback control whose input signals include position estimation and velocity estimation of an extended state observer based on a robot arm model, and feedforward control whose input signals include disturbance estimation of the extended state observer based on the robot arm model; the mechanical arm side position controller includes a controller based on interference estimation
Figure BDA00024354947300000711
Feedforward compensation control and state-based estimation
Figure BDA00024354947300000712
The expression of the robot-side position controller of (1) is:
Figure BDA00024354947300000713
wherein, b 0j ＝1；r m The output signal is the output signal of the mechanical arm side position controller, and the output signal is also the position reference signal of the direct current motor; r is j For position reference of robotic armsNumber;
Figure BDA00024354947300000714
a differential signal that is a position reference signal of the robot arm;
Figure BDA00024354947300000715
estimating the position of the mechanical arm;
Figure BDA00024354947300000716
estimating the speed of the mechanical arm;
Figure BDA00024354947300000717
estimating the disturbance on the mechanical arm; k is a radical of pj Is a proportional gain; k is a radical of dj Is the differential gain.
In this embodiment, as shown in fig. 3, the dc motor-side position controller includes feedback control and feedforward control, where the input signal of the feedback control includes a position estimation and a speed estimation of the extended state observer based on the dc motor model, and the input signal of the feedforward control includes a disturbance estimation of the extended state observer based on the dc motor model; the DC motor side position controller includes a controller based on interference estimation
Figure BDA00024354947300000718
Feedforward compensation control and state-based estimation
Figure BDA00024354947300000719
The expression of the dc motor side position controller is:
Figure BDA0002435494730000081
wherein, b 0m 1/J; u is a torque control signal of the direct current motor; r is m Position reference signals of the direct current motor;
Figure BDA0002435494730000082
position reference signal for DC motorA differential signal of the sign;
Figure BDA0002435494730000083
estimating the position of the direct current motor;
Figure BDA0002435494730000084
estimating the speed of the direct current motor;
Figure BDA0002435494730000085
estimating the disturbance of the direct current motor; k is a radical of formula pm Is a proportional gain; k is a radical of dm Is the differential gain; j is the moment of inertia of the DC motor.
In this embodiment, the expression of the extended state observer based on the dc motor model is as follows:
Figure BDA0002435494730000086
wherein, b 0m ＝1/J；
Figure BDA0002435494730000087
Estimating the position of the direct current motor;
Figure BDA0002435494730000088
estimating the speed of the direct current motor;
Figure BDA0002435494730000089
estimating the disturbance of the direct current motor;
Figure BDA00024354947300000810
is based on the gain coefficient of the extended state observer of the DC motor model; y is m Is the position of the DC motor; u is a torque control signal of the direct current motor; j is the moment of inertia of the DC motor.
In this embodiment, the expression of the extended state observer based on the mechanical arm model is as follows:
Figure BDA00024354947300000811
wherein, b 0j ＝1；
Figure BDA00024354947300000812
Estimating the position of the mechanical arm;
Figure BDA00024354947300000813
estimating the speed of the mechanical arm;
Figure BDA00024354947300000814
estimating the disturbance on the mechanical arm;
Figure BDA00024354947300000815
is a gain coefficient of an extended state observer based on a mechanical arm model; y is j The position of the mechanical arm; r is m Is an output signal of the robot arm-side position controller, which is also a position reference signal of the dc motor.
The working principle is as follows: based on the prior art, the traditional feedback control system based on the error automatically corrects only when the controlled quantity of the controlled system has deviation due to the influence of disturbance, and the control system based on the system and the method has poor disturbance rejection capability. In order to solve the problem and further improve the disturbance rejection capability of the control system, on the basis of the feedback control based on the error, the control system of the invention adds the feedforward control based on disturbance compensation, the feedforward control can actively extract disturbance information from the input and output signals of the controlled object and then eliminate the disturbance information by using the control signal as fast as possible, thereby greatly reducing the influence of the disturbance on the controlled quantity of the system. In an ideal situation, the disturbance of the controlled system is offset by the control quantity before the system output is not influenced, so that the control system can greatly improve the disturbance rejection capability of the system.
Specifically, the control system of the present invention includes a robot arm sideThe position controller and the direct current motor side position controller; the mechanical arm side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a mechanical arm model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the mechanical arm model; the DC motor side position controller includes feedback control and feedforward control, wherein the input signals of the feedback control include position estimation and speed estimation of an extended state observer based on a DC motor model, and the input signals of the feedforward control include disturbance estimation of the extended state observer based on the DC motor model. Wherein the robotic arm-side position controller includes estimating based on the interference
Figure BDA0002435494730000091
Feedforward compensation control and state-based estimation
Figure BDA0002435494730000092
The feedback control of (2); the DC motor side position controller includes a controller based on interference estimation
Figure BDA0002435494730000093
Feedforward compensation control and state-based estimation
Figure BDA0002435494730000094
The feedback control of (2).
Compared with the traditional cascade proportional-differential control system or method, the control system has simple design and implementation and strong anti-interference capability, and can meet the application requirements of the position tracking system of the single-joint flexible mechanical arm.
Example 2
As shown in fig. 1 to 9, the present embodiment is different from embodiment 1 in that a flexible robot cascade control method based on time-varying interference compensation, as shown in fig. 1, includes the following steps:
1) the position of the direct current motor is obtained by detecting signals of a position sensor at the side of the direct current motor;
2) the position of the mechanical arm is obtained by detecting a signal of a mechanical arm side position sensor;
3) the position estimation of the mechanical arm is obtained by the signal of the mechanical arm side position sensor and the output control signal of the mechanical arm side position controller through an extended state observer (namely observer I) based on a mechanical arm model
Figure BDA0002435494730000095
Velocity estimation
Figure BDA0002435494730000096
And estimation of the disturbance experienced
Figure BDA0002435494730000097
4) The signal of the DC motor side position sensor and the output control signal of the DC motor side position controller are subjected to an extended state observer (namely, observer II) based on a DC motor model to obtain the position estimation of the DC motor
Figure BDA0002435494730000098
Velocity estimation
Figure BDA0002435494730000099
And estimation of the disturbance experienced
Figure BDA00024354947300000910
5) The input signal of the robot-side position controller includes a position reference signal r of the robot j Estimating the position of the mechanical arm obtained in the step 3)
Figure BDA00024354947300000911
Difference of (d), differential signal of position reference signal of mechanical arm
Figure BDA00024354947300000912
Estimating the speed of the mechanical arm obtained in the step 3)
Figure BDA00024354947300000913
Difference value of (1) and the estimation of the disturbance of the mechanical arm obtained in step 3)
Figure BDA00024354947300000914
Obtaining an input signal r of the direct current motor side position controller through the mechanical arm side position controller m Which is also the position reference signal r of the direct current motor m ；
6) Position reference signal r of the direct current motor obtained in step 5) m And the position estimation of the direct current motor obtained in the step 4)
Figure BDA0002435494730000101
Difference of (d), differential signal of position reference signal of d.c. motor
Figure BDA0002435494730000102
And the speed estimation of the direct current motor obtained in the step 4)
Figure BDA0002435494730000103
Difference value of (4), and estimation of disturbance of the direct current motor obtained in step (4)
Figure BDA0002435494730000104
Obtaining a torque control signal u of the direct current motor through a side position controller of the direct current motor;
7) and a torque control signal u of the direct current motor controls the position of the direct current motor, and a position signal output by the direct current motor controls the position of the flexible mechanical arm.
In this embodiment, the dc motor side position controller and the robot arm side position controller are connected in a cascade manner.
In the present embodiment, as shown in fig. 2, the robot-arm-side position controller includes feedback control and feedforward control, in which an input signal of the feedback control includes a position estimate and a velocity estimate of the extended state observer based on the robot arm model, and an input signal of the feedforward control includes a disturbance estimate of the extended state observer based on the robot arm model; the mechanical arm side position controller includes a controller based on interference estimation
Figure BDA0002435494730000105
Feedforward compensation control and state-based estimation
Figure BDA0002435494730000106
The expression of the robot-side position controller of (1) is:
Figure BDA0002435494730000107
wherein, b 0j ＝1；r m The output signal is the output signal of the mechanical arm side position controller, and the output signal is also the position reference signal of the direct current motor; r is j A position reference signal of the mechanical arm;
Figure BDA0002435494730000108
a differential signal that is a position reference signal of the robot arm;
Figure BDA0002435494730000109
estimating the position of the mechanical arm;
Figure BDA00024354947300001010
estimating the speed of the mechanical arm;
Figure BDA00024354947300001011
estimating the disturbance on the mechanical arm; k is a radical of pj Is a proportional gain; k is a radical of formula dj Is the differential gain.
In this embodiment, as shown in fig. 3, the dc motor-side position controller includes feedback control and feedforward control, where the input signal of the feedback control includes a position estimation and a speed estimation of the extended state observer based on the dc motor model, and the input signal of the feedforward control includes a disturbance estimation of the extended state observer based on the dc motor model; the DC motor side position controller includes a controller based on interference estimation
Figure BDA00024354947300001012
Feedforward compensation control and state-based estimation
Figure BDA00024354947300001013
The expression of the dc motor side position controller is:
Figure BDA00024354947300001014
wherein, b 0m 1/J; u is a torque control signal of the direct current motor; r is m Position reference signals of the direct current motor;
Figure BDA00024354947300001015
a differential signal which is a position reference signal of the direct current motor;
Figure BDA00024354947300001016
estimating the position of the direct current motor;
Figure BDA00024354947300001017
estimating the speed of the direct current motor;
Figure BDA0002435494730000111
estimating the disturbance borne by the direct current motor; k is a radical of pm Is a proportional gain; k is a radical of dm Is the differential gain; j is the moment of inertia of the DC motor.
In this embodiment, the expression of the extended state observer based on the dc motor model is as follows:
Figure BDA0002435494730000112
wherein, b 0m ＝1/J；
Figure BDA0002435494730000113
Estimating the position of the direct current motor;
Figure BDA0002435494730000114
estimating the speed of the direct current motor;
Figure BDA0002435494730000115
estimating the disturbance of the direct current motor;
Figure BDA0002435494730000116
is based on the gain coefficient of the extended state observer of the DC motor model; y is m Is the position of the DC motor; u is a torque control signal of the direct current motor; j is the moment of inertia of the DC motor.
In this embodiment, the expression of the extended state observer based on the mechanical arm model is as follows:
Figure BDA0002435494730000117
wherein, b 0j ＝1；
Figure BDA0002435494730000118
Estimating the position of the mechanical arm;
Figure BDA0002435494730000119
estimating the speed of the mechanical arm;
Figure BDA00024354947300001110
estimating the disturbance on the mechanical arm;
Figure BDA00024354947300001111
is a gain coefficient of an extended state observer based on a mechanical arm model; y is j The position of the mechanical arm; r is m Is an output signal of the robot arm-side position controller, which is also a position reference signal of the dc motor.
As shown in fig. 4, compared with the conventional control method (cascade proportional-differential control method), the control method of the present invention can be known to enable the position tracking system of the single-joint flexible mechanical arm to rapidly reach a stable value after being started, and has the advantages of small overshoot and short adjustment time; when disturbance is applied to the system at t-10 s, the system is less affected by the disturbance, and the traditional cascade proportional-derivative control method has poor interference suppression capability.
As shown in fig. 5, it is a simulation diagram of position results of the dc motor under two control modes, and it can be seen from the diagram that compared with the conventional control method (cascade proportional-derivative control method), the control method of the present invention can make the system reach a steady state quickly after starting. The overshoot of the system is small, and the adjusting time is short; when the system is disturbed when t is 10s, the system is slightly influenced by disturbance, the adjusting time is short, and the steady-state error is small.
As shown in fig. 6, the result simulation diagrams of the torque control signal curves of the dc motor under the control mode of the present invention and the traditional cascade proportional-differential control mode are shown respectively, and it can be seen from the diagram that the torque control signal curve of the dc motor under the control mode of the present invention is smoother; when the system is disturbed when t is 10s, the direct current motor torque control signal curve in the control mode of the invention does not have large fluctuation, and the adjusting time is short.
As shown in fig. 7, the disturbance estimation output curves of the extended state observer based on the dc motor model and the disturbance estimation output curve of the extended state observer based on the mechanical arm model are respectively shown, and after the system is disturbed when t is 10s, the disturbance can be observed well by both the extended state observer based on the dc motor model and the extended state observer based on the mechanical arm model.
As shown in fig. 8, for the estimation of the position and the speed of the robot arm by the extended state observer based on the robot arm model in the control method of the present invention, the extended observer based on the robot arm model can well observe the position and the speed of the robot arm, and after the disturbance is applied to the system at t equal to 10s, the extended observer based on the robot arm model can well observe the position and the speed of the robot arm.
As shown in fig. 9, for the estimation of the position and the speed of the dc motor by the extended state observer based on the dc motor model in the control method of the present invention, the extended state observer based on the dc motor model can well observe the position and the speed of the dc motor, and after applying disturbance to the system when t is 10s, the extended state observer based on the dc motor model can well observe the position and the speed of the dc motor.
Therefore, compared with the traditional control method, the flexible robot cascade control method based on time-varying interference compensation is simple in control method and easy to achieve in structure, and the system can achieve good dynamic performance and steady-state performance.
The working principle is as follows: based on the prior art, the traditional feedback control system based on errors can automatically correct only when the controlled quantity of the controlled system has deviation due to the influence of disturbance, and the control system based on the system and the method has poor disturbance rejection capability. In order to solve the problem and further improve the disturbance rejection capability of the control method, on the basis of the feedback control based on the error, the control method of the invention adds the feedforward control based on disturbance compensation, the feedforward control can actively extract disturbance information from the input and output signals of the controlled object and then eliminate the disturbance information by using the control signal as fast as possible, thereby greatly reducing the influence of the disturbance on the controlled quantity of the system. In an ideal situation, the disturbance of the controlled system is offset by the control quantity before the system output is not influenced, so that the control method can greatly improve the disturbance rejection capability of the system.
Compared with the traditional cascade proportional-differential control method, the control method has strong anti-interference capability and can meet the application requirement of the position tracking system of the single-joint flexible mechanical arm.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. A flexible robot cascade control system based on time-varying interference compensation is characterized by comprising a direct current motor side position controller, an extended state observer based on a direct current motor model, a mechanical arm side position controller, an extended state observer based on a mechanical arm model, a direct current motor side position sensor, a mechanical arm side position sensor, a direct current motor, a flexible node and a mechanical arm, wherein the mechanical arm side position controller is connected with the direct current motor side position controller; the mechanical arm is connected with an extended state observer based on a mechanical arm model, and the extended state observer based on the mechanical arm model is connected with a mechanical arm side position controller; the direct current motor is connected with an extended state observer based on a direct current motor model, and the extended state observer based on the direct current motor model is connected with a direct current motor side position controller;
the direct current motor side position sensor is used for detecting a position sensor signal arranged on the direct current motor; the mechanical arm side position sensor is used for detecting a position sensor signal arranged on the mechanical arm;
the method comprises the following steps that signals of a mechanical arm side position sensor and output control signals of a mechanical arm side position controller are subjected to position estimation, speed estimation and disturbance estimation of a mechanical arm through an extended state observer based on a mechanical arm model; the method comprises the following steps that signals of a position sensor at the side of a direct current motor and output control signals of a position controller at the side of the direct current motor are subjected to position estimation, speed estimation and disturbance estimation of the direct current motor through an extended state observer based on a direct current motor model;
an input signal of the mechanical arm side position controller passes through the mechanical arm side position controller to obtain an input signal of the direct current motor side position controller, and the signal is also a position reference signal of the direct current motor; obtaining a torque control signal of the direct current motor by passing a difference value of a position reference signal of the direct current motor and the obtained position estimation of the direct current motor, a difference value of a differential signal of the position reference signal of the direct current motor and the obtained speed estimation of the direct current motor and the obtained disturbance estimation of the direct current motor through a direct current motor side position controller; the position of the direct current motor is controlled by a torque control signal of the direct current motor, and the position signal output by the direct current motor controls the position of the flexible mechanical arm; wherein:
the input signal of the mechanical arm side position controller comprises a difference value between a position reference signal of the mechanical arm and the obtained position estimation of the mechanical arm, a difference value between a differential signal of the position reference signal of the mechanical arm and the obtained speed estimation of the mechanical arm, and the obtained disturbance estimation of the mechanical arm;
the mechanical arm side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a mechanical arm model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the mechanical arm model;
the direct current motor side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a direct current motor model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the direct current motor model;
the expression of the extended state observer based on the direct current motor model is as follows:
Figure FDA0003694939450000021
wherein, b 0m ＝1/J；
Figure FDA0003694939450000022
Estimating the position of the direct current motor;
Figure FDA0003694939450000023
estimating the speed of the direct current motor;
Figure FDA0003694939450000024
estimating the disturbance of the direct current motor;
Figure FDA0003694939450000025
is based on the gain coefficient of the extended state observer of the DC motor model; y is m Is the position of the DC motor; u is a torque control signal of the direct current motor; j is the rotational inertia of the direct current motor;
the expression of the extended state observer based on the mechanical arm model is as follows:
Figure FDA0003694939450000026
wherein, b 0j ＝1；
Figure FDA0003694939450000027
Estimating the position of the mechanical arm;
Figure FDA0003694939450000028
estimating the speed of the mechanical arm;
Figure FDA0003694939450000029
estimating the disturbance on the mechanical arm;
Figure FDA00036949394500000210
is a gain coefficient of an extended state observer based on a mechanical arm model; y is j The position of the mechanical arm; r is m Is an output signal of the robot arm-side position controller, which is also a position reference signal of the dc motor.
2. The flexible robot cascade control system based on time-varying interference compensation of claim 1, wherein the DC motor side position controller and the mechanical arm side position controller are connected in cascade.
3. The flexible robot cascade control system based on time-varying interference compensation of claim 1, wherein the robotic arm side position controller comprises an interference estimation based flexible robot cascade control system
Figure FDA00036949394500000211
Feedforward compensation control and state-based estimation
Figure FDA00036949394500000212
The expression of the robot-side position controller of (1) is:
Figure FDA00036949394500000213
wherein, b 0j ＝1；r m The output signal is the output signal of the mechanical arm side position controller, and the output signal is also the position reference signal of the direct current motor; r is j A position reference signal of the mechanical arm;
Figure FDA00036949394500000214
a differential signal that is a position reference signal of the robot arm;
Figure FDA00036949394500000215
estimating the position of the mechanical arm;
Figure FDA00036949394500000216
estimating the speed of the mechanical arm;
Figure FDA00036949394500000217
estimating the disturbance on the mechanical arm; k is a radical of pj Proportional gain is obtained; k is a radical of dj Is the differential gain.
4. The flexible robot cascade control system based on time-varying interference compensation of claim 1, wherein the DC motor side position controller comprises a system based on interference estimation
Figure FDA0003694939450000031
Feedforward compensation control and state-based estimation
Figure FDA0003694939450000032
Figure FDA0003694939450000033
The expression of the dc motor side position controller is:
Figure FDA0003694939450000034
wherein, b 0m 1/J; u is a torque control signal of the direct current motor; r is m Position reference signals of the direct current motor;
Figure FDA0003694939450000035
a differential signal which is a position reference signal of the direct current motor;
Figure FDA0003694939450000036
estimating the position of the direct current motor;
Figure FDA0003694939450000037
estimating the speed of the direct current motor;
Figure FDA0003694939450000038
estimating the disturbance borne by the direct current motor; k is a radical of pm Is a proportional gain; k is a radical of dm Is the differential gain; j is the rotary inertia of the DC motor.
5. A flexible robot cascade control method based on time-varying interference compensation is characterized by comprising the following steps:
1) the position of the direct current motor is obtained by detecting signals of a position sensor at the side of the direct current motor;
2) the position of the mechanical arm is obtained by detecting a signal of a mechanical arm side position sensor;
3) the method comprises the following steps that signals of a mechanical arm side position sensor and output control signals of a mechanical arm side position controller are subjected to position estimation, speed estimation and disturbance estimation of a mechanical arm through an extended state observer based on a mechanical arm model;
4) the method comprises the following steps that signals of a position sensor at the side of a direct current motor and output control signals of a position controller at the side of the direct current motor are subjected to position estimation, speed estimation and disturbance estimation of the direct current motor through an extended state observer based on a direct current motor model;
5) the input signal of the mechanical arm side position controller comprises a difference value of a position reference signal of the mechanical arm and the position estimation of the mechanical arm obtained in the step 3), a difference value of a differential signal of the position reference signal of the mechanical arm and the speed estimation of the mechanical arm obtained in the step 3), and disturbance estimation of the mechanical arm obtained in the step 3), and the input signal of the direct current motor side position controller is obtained through the mechanical arm side position controller and is also the position reference signal of the direct current motor;
6) the difference value of the position reference signal of the direct current motor obtained in the step 5) and the position estimation of the direct current motor obtained in the step 4), the difference value of the position reference signal of the direct current motor and the speed estimation of the direct current motor obtained in the step 4), and the disturbance estimation of the direct current motor obtained in the step 4) pass through a direct current motor side position controller to obtain a torque control signal of the direct current motor;
7) the position of the direct current motor is controlled by a torque control signal of the direct current motor, and the position signal output by the direct current motor controls the position of the flexible mechanical arm;
the direct current motor side position controller is connected with the mechanical arm side position controller in a cascade mode;
the mechanical arm side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a mechanical arm model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the mechanical arm model;
the direct current motor side position controller comprises feedback control and feedforward control, wherein input signals of the feedback control comprise position estimation and speed estimation of an extended state observer based on a direct current motor model, and input signals of the feedforward control comprise disturbance estimation of the extended state observer based on the direct current motor model;
the expression of the extended state observer based on the direct current motor model is as follows:
Figure FDA0003694939450000041
wherein, b 0m ＝1/J；
Figure FDA0003694939450000042
Estimating the position of the direct current motor;
Figure FDA0003694939450000043
estimating the speed of the direct current motor;
Figure FDA0003694939450000044
estimating the disturbance of the direct current motor;
Figure FDA0003694939450000045
is based on the gain coefficient of the extended state observer of the DC motor model; y is m Position of the dc motor; u is a torque control signal of the direct current motor; j is the rotational inertia of the direct current motor;
the expression of the extended state observer based on the mechanical arm model is as follows:
Figure FDA0003694939450000046
wherein, b 0j ＝1；
Figure FDA0003694939450000047
Estimating the position of the mechanical arm;
Figure FDA0003694939450000048
estimating the speed of the mechanical arm;
Figure FDA0003694939450000049
estimating the disturbance on the mechanical arm;
Figure FDA00036949394500000410
is a gain coefficient of an extended state observer based on a mechanical arm model; y is j The position of the mechanical arm; r is m Is an output signal of the robot arm-side position controller, which is also a position reference signal of the dc motor.
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