Foreword
The robot inertia feedforward technology is a very important technology of B&R. Even in the whole industry, it is a cutting-edge technology that can solve the problem of the robot's jitter during the movement and improve the accuracy and efficiency of the robot system. Currently, this technology is only owned by a few companies in the industry.
I. Inertia matching and torque feedforward
For motion control, inertia matching is a very important feature requirement, and for the driver, good inertia matching can produce better dynamic performance. In the ideal rigid connection, only need to calculate the required torque. Drive the system to operate at high dynamics, however, due to the elastic deformation of the mechanical system connection, such as reducer , belt, coupling, etc., it can not achieve the true high dynamic control characteristics, which brings The problem of inertia matching comes. During the control of the load on the drive, the calculation cycle of the current loop is very fast. In the case of a large inertia matching value, the system needs to give a very large deviation to achieve the output in the PID adjustment. However, this torque The output produces a large vibration.
B&R offers a model of torque feedforward control to solve this problem, and stable control can be achieved by quickly giving inertia. However, for robot systems, the articulation is in multiple dimensions of motion, and the variation of inertia is multi-dimensional. How to apply good inertia matching to ensure high-speed operation of the robot system?
This is a common problem in robot systems. However, the combination of modeling, algorithm design, high-speed torque control and other technologies in B&R's system forms a solution to this problem.
Second, the problem of robot mechanical vibration
The Lagrangian equation describes the dynamic energy problem of the robot during the whole movement. The generation of kinetic energy and potential energy affects the changes of parameters such as torque and position during the movement of the robot. For example, the position of the robot arm changes during the movement of the robot. The potential energy produced changes.
In the robot system, since the mechanical characteristics of the joints of the robot change with the movement process, the inertia also changes. For example, when the arm is elongated in the X-axis direction, the rotation along the Y-axis direction is 0. In the range of ~90 degrees, the inertia also changes from the maximum inertia to the minimum inertia; and when the arm rotates over the range of 90 degrees to 180 degrees, the inertia begins to increase again. Due to the variation caused by this inertia, modulation vibration is generated for the entire control process of the driver, which is a common problem in robot control.
Third, B&R dynamic inertia feedforward technology
The inertia dynamic feedforward technique in B&R's motion control technology can solve this problem very well. For the robot system, the change of inertia is a dynamic process and also a mathematically modelable process. The feedforward variable can be provided for the control of the system by establishing a dynamic inertia model, as shown in Figure 1 below.
In this model, when the set position, set speed and acceleration value are given, the inertia change of the whole motion process is calculated according to the current value and the mechanical constant, and the feedforward value of the torque output is calculated to the motor. This value is superimposed on the control output of the controller setpoint in the current loop, so that the torque output can quickly achieve steady state adjustment, thereby reducing the torque output deviation.
The feedforward output needs to be given before the deviation is generated, and is continuously refreshed every 50uS cycle. Due to its high-speed refresh, the torque output value is ensured to be high speed and high precision, and the mechanical inertia change can be synchronously followed. Good control status.
4. Feedforward model design based on MATLAB/Simulink
MATLAB/Simulink is currently the most popular modeling tool. Due to the cooperation with Mathworks, the B&R control system is interfaced with MATLAB/Simulink modeling and simulation software. The controller model is generated by MATLAB/Simulink simulation tool. The C code of the controller can be generated by the code automatic generation technology, and this code can be imported into the B&R controller without manual rewriting, thereby implementing the loop test.
The robot can be characterized as a space kinematic equation established by the Euler-Lagrange equation. Through MATLAB, the static parameters of the system, such as the length of the arm, the mass, the joint reduction ratio, and other dynamic parameters such as the angle of rotation and acceleration. The start and end positions are input into the model. It provides a dynamic model of the Cartesian joint operation space, which reflects the relationship between the operating force and the joint force, and the relationship between the speed and acceleration of the operating space and the joint space. The relationship between joint input torque and output torque.
This model is a quadratic differential equation that can be resolved by the Euler-Lagrangian method and can be resolved to the following values:
Inertia item; centrifugal and Coriolis terms; gravitational terms
After building the model, we can do the following:
1. Establish identification of unknown parameters
Establish static parameters in the system, define the dynamic parameters by AS torque tracking, and calculate the basic parameters.
2. Activate feedforward control
The calculated basic value is output to B&RPLC, and a motion model is established in the PLC through the AS software. After these basic values ​​are given, the system will calculate an additional torque output value.
The additional torque is output to the driver, and the driver will pre-determine the current value in the calculation of the current loop to realize the feedforward control, and the added value is continuously calculated by the system, and is cycled and provided in a microsecond cycle. Calculated for the current loop of the drive.
Figure 3 shows the model of feedforward control in AutomationStudio. TrqFF is the feedforward cycle write, and 6AxATrqFF is the feedforward implementation code segment written in C code.
Fifth, the control effect
Figure 4 is a torque control process variation curve obtained by actually sampling the entire output through the oscilloscope function of the axis monitoring of B&R Automation Studio. The blue curve is the case of turning off the feedforward control, and it can be seen that the fluctuation of the torque variation is large; The red curve shows the effect of using feedforward control, which significantly improves the stability of the torque output.
This technology represents the highest level of robot control technology. The designed robot system has higher precision, stable running process and less jitter, which is obviously superior to the design of similar robot systems.
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