CN106067747B - A kind of design method of sliding formwork disturbance observer for servo system control - Google Patents

Abstract

The invention provides a design method of a sliding mode disturbance observer used for servo system control, aiming at the problem of friction disturbance at low speed of the servo system and considering the error and uncertainty of system modeling. Using the ordinary DC motor model, combining the disturbance observer with the sliding mode variable structure control, a sliding mode disturbance observer is designed. Firstly, the disturbance observer is used to observe the magnitude of the friction torque, and then the sliding mode controller is designed according to the obtained friction torque. The observation of the friction torque can reduce the gain of the switching term of the sliding mode controller and reduce the chattering phenomenon. The low-speed servo system suppresses nonlinear phenomena such as dead zone, crawling, and self-oscillation through the sliding mode disturbance observer, which weakens the requirement for modeling accuracy and has good robustness.

Description

A Design Method of Sliding Mode Disturbance Observer for Servo System Control

technical field

The invention relates to a design method of a sliding mode disturbance observer used for servo system control.

Background technique

In low-speed servo systems, the friction torque has a serious impact on the dynamic performance of the servo system. And it leads to some non-linear phenomena, such as the zero-crossing dead zone of the speed, low-speed crawling phenomenon, stagnation and self-oscillation, etc. In order to eliminate these non-linear phenomena, it is necessary to compensate the friction torque. Generally speaking, there are currently two compensation methods, one is the compensation method based on the friction model, such as the Stribeck model and the LuGre model. The process is to first use the obtained speed and position information to estimate the model parameters, get the real-time friction torque, and then add the corresponding compensation value in the controller. Because this method needs to determine the model parameters through testing or online identification in advance, the control law is more complicated. The other is a non-model-based friction compensation method, which treats friction as a disturbance signal for elimination. Disturbance observer is a common non-model friction compensation method. It is widely used in torque motors to observe and compensate friction force, but there is no application description for DC motors with relatively complex models. In addition, the disturbance observer compensation method has high requirements on the accuracy of system modeling. If there are unmodeled dynamics or modeling errors, the compensation effect will deteriorate.

Sliding mode variable structure control has the characteristics of insensitivity to system parameters and disturbance changes, and has strong robustness. However, if the sliding mode variable structure is used to control the servo system with high friction, the sign function will have a high gain and cause a large chattering phenomenon. Therefore, the friction factor must be considered when designing the sliding mode controller.

Contents of the invention

The invention provides a design method of a sliding mode disturbance observer for servo system control aiming at the problem of frictional disturbance at low speed of the servo system and considering the error and uncertainty of system modeling.

The present invention adopts following technical scheme: a kind of design method for the sliding mode disturbance observer of servo system control, the steps are as follows:

(1) First establish the state equation of the servo system as follows:

Among them, the state variable _x1 represents the rotation angle, _x2 represents the rotational speed, C _e is the back electromotive force coefficient of the motor, u is the control input, K _u is the amplification factor of the PWM driver, K _m is the torque coefficient, J is the moment of inertia, and R is Armature resistance, T _f represents the frictional disturbance torque;

(2) Design sliding mode control rate

r represents the given signal, the tracking errors of angular position and angular velocity are respectively

e=rx ₁ (2)

Design switching function s

Where c represents the parameter of the switching surface, the larger c is, the faster the response speed of the system will be, but the stability will be affected;

Exponential reaching law

Among them, ε>0, k>0, ε is the coefficient of the constant velocity approach term, and k is the coefficient of the exponential approach term, both of which need to be selected manually. Combining formulas (1) and (4), we get

According to the formula (5) (6), the expression of the control rate u is obtained

In the above formula, except for the friction torque T _f , other physical quantities are known, and the disturbance observer is used to observe the friction torque below;

(3) Design the disturbance observer according to the model of the DC motor, and the output value of the disturbance observer is the estimated value of the equivalent friction torque equivalent to the input end of the servo system The following formula expresses its relationship with other physical quantities,

in is the motor speed, Gn ^-1 (s) is the inverse of the nominal transfer function of the controlled object, U(s) is the output of the controller, Q(s) represents a low-pass filter, and its expression is chosen as

The time constant τ is properly selected according to the bandwidth of the system;

Multiply equation (8) by the coefficient Then an estimate of the true friction torque is obtained,

Finally, the control rate obtained by combining formula (7) and formula (10) is used to complete the design of the sliding mode disturbance observer.

The invention has the advantages that the disturbance observer can observe the friction disturbance of the common DC motor, not just the torque motor, through the structure transformation. The observation of the friction torque by the disturbance observer can reduce the jitter problem of the sliding mode control, and the use of the sliding mode controller can effectively improve the shortcomings of the disturbance observer, weaken the requirements for modeling accuracy, and improve the robustness and stability of the system. Anti-interference ability, the two complement each other.

Description of drawings

Figure 1 is a sliding mode control diagram of a friction servo system;

Fig. 2 is the schematic diagram of disturbance observer;

Fig. 3 is the structural diagram of sliding mode disturbance observer;

Fig. 4 is the speed curve diagram of PID control under sinusoidal input;

Fig. 5 is the rotating speed curve figure that sine input sliding mode disturbance observer controls;

Fig. 6 is the position error graph of two kinds of control strategies under step position input;

Figure 7 shows the response curves of the two control strategies under low-speed ramp input.

Detailed ways

The present invention will be further explained below by way of example according to the accompanying drawings of the description:

Example 1

A method for designing a sliding mode disturbance observer for servo system control, the steps are as follows:

1. Design of sliding mode controller

As shown in Figure 1, a sliding mode controller is used to control a servo system affected by friction. First, the state equation of the servo system is established as shown in equation (1):

where r(t) is the command signal, u is the control input, C _e is the back EMF coefficient of the motor, K _u is the amplification factor of the PWM driver, R is the armature resistance, K _m is the torque coefficient, J is the moment of inertia, T _f represents the frictional disturbance torque. The state variable _x1 represents the angle of rotation, and _x2 represents the rotational speed.

The tracking errors of angular position and angular velocity are respectively

e=rx ₁ (2)

Design switching function

Exponential reaching law

Where ε>0, k>0. Combining formulas (1) and (4) can get

According to the formula (5) (6), the expression of the control rate u can be obtained

In the above formula, except the friction torque _Tf , other physical quantities are known. Next, we use the disturbance observer method to observe the friction torque.

2. The principle of the disturbance observer

The schematic diagram of the disturbance observer is shown in Figure 2, where n in the figure represents the disturbance signal, Represents the observed value of the disturbance, G _p (s) represents the transfer function of the controlled object, G _n ^-1 (s) represents the inverse of the nominal model of the controlled object, ξ represents the noise at the output end, Q(s) is a low-pass filter . Usually Q(s) can be chosen

For the DC motor shown in Figure 1, since the frictional disturbance it receives is located inside the controlled object, certain mathematical processing is required. If the disturbance observer is still designed according to the structure in Figure 2, then the output value of the disturbance observer is not the real friction torque, but its equivalent value T _eq at the input end of the servo system. The relationship between the equivalent friction torque T _eq and the original friction torque T _f is

Neglecting the effect of inductance, approximately

3. Design of the sliding mode disturbance observer

Combining the method of sliding mode variable structure control and disturbance observer, the control block diagram of the servo system is shown in Figure 3. First, the estimated value of the friction torque is obtained by the disturbance observer Since the output value of the disturbance observer is an estimate of the equivalent friction torque According to formula (10), multiply by the coefficient Then get an estimate of the true friction torque

Finally, the sliding mode control rate of the controller is designed according to formula (7).

Example 2

The parameters of the servo system of the controlled motor are known: R＝14.7Ω, K _m ＝1.134N·m/A, C _e ＝0.119V/(r/min), J＝1.79*10 ^-6 kg*m ² , K _u =12.

The transfer function of the motor is

Select the parameter τ=0.001ms of the low-pass filter Q(s), then

Then according to Q(s) and G _p (s), build a disturbance observer to get the estimated value of friction torque Choose c=30, k=1, ε=1 as the control parameter design control rate u.

Through computer simulink simulation, compare the quality of PID control and sliding mode disturbance observer control.

Firstly, double-closed-loop PID control of speed loop and position loop is used. The rules for selecting PID parameters are as follows: Firstly, regardless of the nonlinear friction part of the motor, the PID coefficients of the speed loop and position loop are determined sequentially by the critical proportionality method, and then the coefficients Fine-tune for near-optimal tracking performance. Finally, the proportional coefficient of the speed loop is 0.021, and the integral coefficient is 1.6. Due to the frictional interference, the output end has a large noise, and the differential term is zero; the proportional coefficient of the position loop is 6, the integral coefficient is 1.8, and the differential term is zero.

Given a sinusoidal position input signal θ=6sin2t( ^o ) whose amplitude is 6° and frequency is 2rad/s, its velocity expression is theoretically ω=2cos2t(r/min). Figure 4 shows the angular velocity change curve under PID control. The speed curve shows a dead zone phenomenon at the zero crossing point. The dead zone time is about 0.15s, accounting for 4.8% of a cycle, which is mainly caused by friction nonlinearity. Figure 5 shows the change curve of the speed after using the sliding mode disturbance observer. The dead time is about 0.02s, accounting for 0.64% of the cycle, which shows that the use of the sliding mode disturbance observer can effectively suppress the dead zone phenomenon.

Given a step position input signal of 6°, Fig. 6 shows the position error curves of the two control strategies when the steady state is reached. The position error curve of PID control shows the phenomenon of stagnation and self-oscillation when the position tracking reaches a steady state, and the maximum position deviation is 0.012°. Using the position error curve of the sliding mode disturbance observer (SMDOB), the oscillation value is significantly reduced, the maximum position deviation is 0.001°, and the oscillation amplitude is 8% of the PID control.

Given a low-speed ramp position input with a slope of 0.01°, the dotted line in Figure 7 shows the curve of the output position changing with time under PID control, showing an obvious creeping phenomenon; the solid line is the sliding mode disturbance observer (SMDOB ) controlled position response curve, the crawling phenomenon is basically eliminated. It shows that the SMDOB control scheme can well suppress the creeping phenomenon that occurs when the motor is running at low speed.

Claims (1)

1. a method for designing a sliding mode disturbance observer for servo system control, characterized in that, the steps are as follows: (1) First establish the state equation of the servo system as follows: Among them, the state variable _x1 represents the rotation angle, _x2 represents the rotational speed, C _e is the back electromotive force coefficient of the motor, u is the control input, K _u is the amplification factor of the PWM driver, K _m is the torque coefficient, J is the moment of inertia, and R is Armature resistance, T _f represents the frictional disturbance torque; (2) Design sliding mode control rate r represents the given signal, the tracking errors of angular position and angular velocity are respectively e=rx ₁ (2) Design switching function s Where c represents the parameter of the switching surface, the larger c is, the faster the response speed of the system will be, but the stability will be affected; Exponential reaching law Among them, ε>0, k>0, ε is the coefficient of the constant velocity approach term, and k is the coefficient of the exponential approach term, both of which need to be selected manually. Combining formulas (1) and (4), we get According to the formula (5) (6), the expression of the control rate u is obtained In the above formula, except for the friction torque T _f , other physical quantities are known, and the disturbance observer is used to observe the friction torque below; (3) Design the disturbance observer according to the model of the DC motor, and the output value of the disturbance observer is the estimated value of the equivalent friction torque equivalent to the input end of the servo system The following formula expresses its relationship with other physical quantities, in is the motor speed, Gn ^-1 (s) is the inverse of the nominal transfer function of the controlled object, U(s) is the output of the controller, Q(s) represents a low-pass filter, and its expression is chosen as The time constant τ is properly selected according to the bandwidth of the system; Multiply equation (8) by the coefficient Then an estimate of the true friction torque is obtained, Finally, the control rate obtained by combining formula (7) and formula (10) is used to complete the design of the sliding mode disturbance observer.