Closed-loop controller and control method based on improved sigmoid function

Abstract

The invention discloses a closed-loop controller based on an improved sigmoid function and a control method. The input of the controller is an error. The controller can be used for replacing a position ring and a speed ring in traditional motor three-closed-loop control. The input of the position ring controller is the current position error of the control mechanism, the controller calculates the output according to the maximum speed and the position error of the mechanism, and the output is the reference speed of the speed ring at the next moment. The input of a speed ring controller is a speed error, the controller calculates the output according to the maximum current of the mechanism and the speed error, and the output of the speed ring is the reference current of the next moment. Compared with a traditional proportional differential integral (PID) controller, the method has the advantages that only one parameter needs to be adjusted, the adjusted parameter can be calculated according to actual control requirements, the parameter adjustment is simpler, simpler and more effective, meanwhile, the steady-state precision is higher, and the controller is suitable for occasions with high requirements for motion precision and stability and has wide application prospects. And a good effect is achieved in control and application of a high-precision mechanism of a photoelectric telescope.

Description

Technical Field

[0001] The invention belongs to the technical field of motor control, and in particular relates to a closed-loop controller and a control method based on an improved sigmoid function, which can be used for motor control. Background Art

[0002] At present, most closed-loop control methods use PID control, which is simple, has a small amount of calculation, and does not require an accurate model of the control object. However, for PID control, three parameters need to be adjusted. However, currently the parameters can only be adjusted based on experience, and there is a lack of quantitative and controllable adjustment methods for parameter adjustment, which makes parameter adjustment inconvenient. Summary of the invention

[0003] The present invention provides a closed-loop controller and a control method based on an improved sigmoid function. Compared with traditional PID control, an accurate model of a controlled object is not required, only one parameter needs to be adjusted, and the parameter to be adjusted can be calculated according to actual control requirements. Compared with PID control, parameter adjustment is simpler.

[0004] The technical solution provided by the present invention is as follows:

[0005] A closed-loop controller based on an improved sigmoid function includes: after improving the sigmoid function, its mathematical expression is:

[0006] ,

[0007] in, For maximum output, To adjust the parameters, is the input error, is the natural logarithm;

[0008] The closed-loop controller comprises:

[0009] Position loop controller, the expression is:

[0010] ,

[0011] is the maximum speed, is the current position error, , is the expected position at the current moment, is the actual position value measured at the current moment, is the calculated position loop controller output, Adjust the parameters for the position loop controller, where To ensure control stability, ,in is the position loop sampling time;

[0012] The speed loop controller is used to adjust the reference speed according to the output of the position loop controller. , further based on the measured speed value , calculate the speed loop output, the speed loop controller expression is:

[0013] ,

[0014] is the maximum current, is the speed error, , is the expected speed at the current moment, is the actual speed value measured at the current moment, is the calculated speed loop controller output, Adjust the parameters for the speed loop controller, where To ensure control stability, ,in It is the speed loop sampling time.

[0015] A closed-loop control method based on an improved sigmoid function includes: after improving the sigmoid function, its mathematical expression is:

[0016] ,

[0017] in, For maximum output, To adjust the parameters, is the input error, is the natural logarithm;

[0018] The closed-loop control method comprises the following steps:

[0019] Step 1: First, the position loop is calculated through the position loop controller. The expression of the position loop controller is:

[0020] ,

[0021] is the maximum speed, is the current position error, , is the expected position at the current moment, is the actual position value measured at the current moment, is the calculated position loop controller output, Adjust the parameters for the position loop controller, where To ensure control stability, ,in is the position loop sampling time;

[0022] Step 2: Use the speed loop controller to calculate the reference speed according to the output of the position loop controller , further based on the measured speed value , calculate the speed loop output, the speed loop controller expression is:

[0023] ,

[0024] is the maximum current, is the speed error, , is the expected speed at the current moment, is the actual speed value measured at the current moment, is the calculated speed loop controller output, Adjust the parameters for the speed loop controller, where To ensure control stability, ,in It is the speed loop sampling time.

[0025] Beneficial effects:

[0026] Compared with the traditional proportional differential integral (PID) controller, this method only needs to adjust one parameter, and the adjustment parameter can be calculated according to the actual control requirements. The adjustment parameter is simpler, simple and effective, and the steady-state accuracy is higher. This controller is suitable for occasions with high requirements on motion accuracy and stability, and has achieved good results in the application of high-precision mechanism control of optoelectronic telescopes. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Output, first-order derivative, and second-order derivative graphs of the improved sigmoid function;

[0028] Figure 2 A control block diagram of a closed-loop control method based on an improved sigmoid function of the present invention;

[0029] Figure 3 It is a simulation control block diagram of a closed-loop control method based on an improved sigmoid function of the present invention;

[0030] Figure 4 The control simulation result comparison curve of the method of the present invention and the PID control method when the input is a step;

[0031] Figure 5 The control measured results comparison curve of the method of the present invention and the integral separation PI control method when the input is a step. DETAILED DESCRIPTION

[0032] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0033] The present invention proposes a closed-loop control method based on an improved sigmoid function. The control object of the method is a motor or other closed-loop controllable object, and the motor drives a mechanism to operate. The method performs position loop closed-loop control, and a reference speed is calculated through a position error and a maximum speed of a current cycle of the mechanism. The method performs speed loop closed-loop control, and a given reference current is calculated for a current loop through a maximum current and a speed error of the mechanism, thereby controlling the operation of the mechanism.

[0034] A control method based on an improved sigmoid function. After the sigmoid function is improved, its mathematical expression is:

[0035] ,

[0036] in For maximum output, To adjust the parameters, is the input error, is the natural logarithm.

[0037] Figure 1 is the output curve of the controller. , ,from Figure 1 It can be seen is an odd function, and its maximum output is , the output is bounded. Therefore, when using When it is a controller, there is no need to limit the output, which is simpler than PID and the adjustment parameters are only Compared with the three adjustment parameters of PID, the number is smaller and it is convenient for engineering use.

[0038] Figure 2 This is a control block diagram of a closed-loop control method based on an improved sigmoid function of the present invention. Figure 2 As shown, the method specifically comprises the following steps:

[0039] Step 1: First, the position loop is calculated through the position loop controller. The expression of the position loop controller is:

[0040] ,

[0041] is the maximum speed, is the current position error, , is the expected position at the current moment, is the actual position value measured at the current moment, is the calculated position loop controller output. Adjust the parameters for the position loop controller, where To ensure control stability, ,in is the position loop sampling time, usually less than 0.001s, The larger the value, the shorter the adjustment time. Since the controller output is bounded, the maximum value is Therefore, the position loop controller output does not need to add a limiting function.

[0042] In actual use, a discretized position loop controller is used, and the expression is as follows:

[0043] ,

[0044] is the maximum speed, is the current position error, , is the expected position at the current moment, is the actual position value measured at the current moment, It is the calculated output of the position loop controller, that is, the given reference speed of the speed loop at the next moment. Adjust parameters for the position loop controller.

[0045] Step 2: Use the speed loop controller to calculate the reference speed according to the output of the position loop controller , further based on the measured speed value , calculate the speed loop output, the speed loop controller expression is:

[0046] ,

[0047] is the maximum current, is the speed error, , is the expected speed at the current moment, is the actual speed value measured at the current moment, is the calculated speed loop controller output. Adjust the parameters for the speed loop controller, where To ensure control stability, ,in is the speed loop sampling time, usually the control system is 0.001s, The larger the value, the greater the acceleration and the shorter the adjustment time. Since the output of the speed loop controller is bounded, the maximum output value is Therefore, there is no need to add a limiting function to the output of the speed loop controller.

[0048] In actual use, a discrete controller is used, and the expression of the speed loop controller after discretization is:

[0049] ,

[0050] is the maximum current, is the speed error at the current moment, , is the given reference speed calculated by the position loop, that is, the expected speed at the current moment, is the actual speed value measured at the current moment, By differentiation, we get , to ensure To stabilize the For filtering calculation, a low-pass filter is generally used, and the filter frequency domain expression is: ,in is the circumference of a circle, is the filtering frequency, is the velocity value after filtering, is the speed value before filtering, is the Laplace operator. It is the calculated output of the speed loop controller, that is, the given reference current of the current loop at the next moment. Tune parameters for the speed loop controller.

[0051] Specific control process such as Figure 2 As shown, Figure 2 The position loop and speed loop use the above controllers, and the current loop uses a PI controller.

[0052] Example:

[0053] In order to specifically illustrate the effectiveness of the invention, firstly, the simulation is used to verify the specific simulation control object. Figure 3 As shown, the Coulomb friction coefficient in the friction model is 0.05, the viscous friction coefficient is 0.05, and the maximum speed value of the motor of the control mechanism is assumed to be , maximum motor current According to the motor control requirement parameters, the position loop controller is:

[0054] ,

[0055] Among them, the adjustment parameters , is the current position error, It is the output of the position loop, i.e. the reference speed.

[0056] The speed loop controller is:

[0057] ,

[0058] Among them, the adjustment parameters , is the speed error at the current moment, It is the speed loop output. Figure 4 When the input is a step, the control simulation results comparison curve of the method of the present invention and the PID control method is shown. From the simulation results, it can be seen that compared with the PID control, the controller has no overshoot in the step response and has higher steady-state accuracy.

[0059] This method is actually used in the three-mirror rotation mechanism of a telescope. The 15° step response result is as follows: Figure 5 As shown in the figure, in order to reduce overshoot, the integral separation PI (IS-PI) control is used in the comparison. From the step response results, it can be seen that the controller based on the improved sigmoid function effectively reduces the adjustment time and can recover faster when encountering disturbances.

[0060] In summary, the use of the controller based on the improved sigmoid function of the present invention effectively improves the steady-state accuracy and reduces the overshoot in the dynamic adjustment process. Compared with the traditional PID control algorithm, there is only one adjustment parameter, which makes parameter adjustment easier and convenient for engineering use.

[0061] The above-mentioned embodiment is only one embodiment of the present invention. The application scope of the present invention is not limited to motor control, but can also be used in other control occasions. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A closed-loop controller based on an improved sigmoid function, characterized in that: include: After improving the sigmoid function, its mathematical expression is: ， in, For maximum output, To adjust the parameters, is the input error, is the natural logarithm; The closed-loop controller comprises: Position loop controller, the expression is: ， is the maximum speed, is the current position error, , is the expected position at the current moment, is the actual position value measured at the current moment, is the calculated position loop controller output, Adjust the parameters for the position loop controller, where To ensure control stability, ,in is the position loop sampling time; The speed loop controller is used to adjust the reference speed according to the output of the position loop controller. , further based on the measured speed value , calculate the speed loop output, the speed loop controller expression is: ， is the maximum current, is the speed error, , is the expected speed at the current moment, is the actual speed value measured at the current moment, is the calculated speed loop controller output, Adjust the parameters for the speed loop controller, where To ensure control stability, ,in It is the speed loop sampling time.

2. A closed-loop control method based on an improved sigmoid function, characterized in that: include: After improving the sigmoid function, its mathematical expression is: ， in, For maximum output, To adjust the parameters, is the input error, is the natural logarithm; The closed-loop control method comprises the following steps: Step 1: First, the position loop is calculated through the position loop controller. The expression of the position loop controller is: ， is the maximum speed, is the current position error, , is the expected position at the current moment, is the actual position value measured at the current moment, is the calculated position loop controller output, Adjust the parameters for the position loop controller, where To ensure control stability, ,in is the position loop sampling time; Step 2: Use the speed loop controller to calculate the reference speed according to the output of the position loop controller , further based on the measured speed value , calculate the speed loop output, the speed loop controller expression is: ， is the maximum current, is the speed error, , is the expected speed at the current moment, is the actual speed value measured at the current moment, is the calculated speed loop controller output, Adjust the parameters for the speed loop controller, where To ensure control stability, ,in It is the speed loop sampling time.

3. The closed-loop control method based on the improved sigmoid function according to claim 2, characterized in that: Using a discretized speed loop controller, the expression is: ， is the maximum current, Adjust parameters for the speed loop controller, is the speed error at the current moment, , is the given reference speed calculated by the position loop controller, that is, the expected speed at the current moment, is the actual speed value measured at the current moment, It is the calculated output of the speed loop controller, that is, the given reference current of the current loop at the next moment.

4. The closed-loop control method based on the improved sigmoid function according to claim 3, characterized in that: By differentiation, we get , using filter pair Perform filtering calculation, the filter frequency domain expression is ,in is the circumference of a circle, is the filtering frequency, is the velocity value after filtering, is the speed value before filtering, is the Laplace operator.

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