A hyperbolic tangent attraction law design method for discrete-time sliding mode controller of direct current motor speed regulation system

Abstract

This invention discloses a design method for a hyperbolic tangent attraction law in a discrete-time sliding mode controller for a DC motor speed control system. Based on the hyperbolic tangent function, a discrete-time hyperbolic tangent attraction law is constructed. Hyperbolic tangent-type adaptive interference compensation measures are embedded into the discrete-time hyperbolic tangent attraction law to construct a discrete-time hyperbolic tangent attraction law with interference compensation capability, thereby designing a discrete-time sliding mode controller. The output signal is then calculated as the control input signal for the DC motor speed control system, enabling the system to follow the given speed signal. The design method for the hyperbolic tangent attraction law in a discrete-time sliding mode controller provided by this invention features fast convergence and chatter-free characteristics, while also improving the tracking accuracy, anti-interference capability, and effectively reducing output speed fluctuations in the DC motor speed control system.

Description

Technical Field

[0001] This invention relates to a design method for a hyperbolic tangent attraction law for a discrete-time sliding mode controller in a DC motor speed control system. This method is applicable to DC motor speed control systems and also to servo drive control systems. Background Technology

[0002] DC motors, due to their excellent controllability, are widely used in applications requiring high control performance, such as rolling mills, double-hull oil tankers, and high-precision CNC equipment. To achieve stepless and smooth speed regulation, armature voltage adjustment is commonly used. Among these methods, pulse width modulation (PWM) technology, which controls the motor input voltage by changing the duty cycle, has become one of the most commonly used DC motor drive methods. However, the inherent hard-switching operation of PWM leads to abrupt changes in voltage and current, resulting in torque ripple and noise, affecting the system's dynamic response performance.

[0003] To overcome the aforementioned problems, a DC / DC power converter is used as the pre-amplifier circuit for the motor drive. This type of converter can dynamically provide smoothly varying armature voltages according to the actual needs of the system (such as tracking target angular velocity or position trajectory), thereby achieving smooth motor start-up and precise control. In particular, Buck-type DC converters, with their inductor and capacitor filtering structure, can significantly reduce output current ripple, effectively suppress voltage spikes and electromagnetic interference caused by PWM hard switching, and improve system operating quality. In practical industrial applications, DC speed control systems often use traditional PI control, but their dynamic and steady-state performance often falls short of expectations. Especially when the load changes drastically over a wide range, the system's regulation capability decreases significantly, resulting in a large amount of energy wasted in ineffective operating states. Improving the system's dynamic regulation performance can effectively reduce ineffective energy consumption and has positive significance for energy conservation.

[0004] Sliding mode control, as a nonlinear control strategy, has advantages such as simple structure, rapid response, and strong robustness. However, its inherent chattering problem can easily lead to significant output speed fluctuations in DC motor speed control systems. Therefore, effectively suppressing chattering has become a key research direction in sliding mode control applications. The sliding mode reaching law converges the system through two stages: reaching and sliding, and its performance depends on the design of the reaching law and the switching function. In contrast, the attraction law method is directly based on the tracking error and can directly drive the error to approach zero within a finite time, eliminating the need to design a sliding surface and resulting in a simpler controller. By embedding disturbance suppression measures into the attraction law, an attraction law with disturbance suppression capabilities can be constructed, thereby improving the system's tracking performance and robustness.

[0005] DC motor speed control systems often encounter various disturbances such as sudden load changes, voltage fluctuations, parameter uncertainties, and frictional nonlinearities, requiring effective compensation and suppression methods to improve control performance. The widely used "one-step delay disturbance estimation" technique can effectively compensate for constant or slow time-varying disturbances; however, this method suffers from response lag due to the delay effect, thus reducing the system's control accuracy and stability. Therefore, in controller design, enhancing disturbance suppression capabilities and reducing output speed fluctuations and steady-state errors have become key challenges for improving system performance and are currently core issues that urgently need to be addressed. Summary of the Invention

[0006] To overcome the poor dynamic and steady-state performance of PI control methods, this invention provides a design method for a hyperbolic tangent attraction law in a discrete-time sliding mode controller for DC motor speed control systems. Hyperbolic tangent adaptive interference compensation measures are embedded into the discrete-time hyperbolic tangent attraction law to construct a discrete-time hyperbolic tangent attraction law with interference compensation capabilities, effectively suppressing various interference signals such as load abrupt changes, voltage fluctuations, parameter uncertainties, and frictional nonlinearities. The digital control technology of the DC motor speed control system employing the hyperbolic tangent adaptive interference compensation strategy can achieve accurate tracking of the given speed signal, and has anti-interference capabilities and effectively reduces output speed fluctuations.

[0007] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a hyperbolic tangent attraction law design method for discrete-time sliding mode controllers of DC motor speed control systems, comprising the following steps:

[0008] Step 1: Establish a discrete-time second-order model of the DC motor speed control system

[0009] The continuous model of the DC motor speed control system is

[0010] (1)

[0011] Where ϑ is the voltage applied to the motor armature terminals, i a For armature current, k e k is the back electromotive force constant. m L is the motor torque constant. a R is the armature inductance. a Let J be the armature resistance, J be the moment of inertia of the rotor and motor load, and b be the viscous friction coefficient of the motor. From equation (1), the following continuous-time second-order model of the DC motor speed control system can be obtained:

[0012] (2)

[0013] The Euler discretization method is used.

[0014] (3)

[0015] Where T is the sampling time; substituting equation (3) into equation (2), we can obtain the discrete-time second-order model of the DC motor speed control system:

[0016] (4)

[0017] Wherein, the system model parameters are

[0018] (5)

[0019] These represent the actual output speed signals of the DC motor speed control system at times k+1, k, and k-1, respectively. This represents the voltage signal applied to the motor armature terminals at time k in the DC motor speed control system. This is the interference signal of the DC motor speed system at time k+1.

[0020] Step 2: Construct the discrete-time hyperbolic tangent attraction law

[0021] Constructing the discrete-time hyperbolic tangent attraction law

[0022] (6)

[0023] in, These are parameters used to adjust the suction speed; Let $\frac{ ... Given the velocity signal at time k, The actual output speed signal of the DC speed control system at time k; hyperbolic tangent function. .when When the value is large, i.e., far from the origin, the value in equation (6) is... tending towards 1 and It tends towards 0, thus accelerating the system's attraction speed; when When it is smaller, that is, near the origin, in equation (6) tending towards 0 and The coefficients of the sign function tend to 0, thus eliminating system chatter.

[0024] Step 3: Hyperbolic Tangent Adaptive Interference Compensation Strategy

[0025] To improve the anti-interference capability of the DC motor speed control system, a hyperbolic tangent adaptive interference compensation measure is embedded into the discrete-time hyperbolic tangent attraction law (6), thus constructing a discrete-time hyperbolic tangent attraction law with interference compensation capability:

[0026] (7)

[0027] in, It is a hyperbolic tangent adaptive interference compensator based on one-step delay interference estimation technique, and satisfies

[0028] (8)

[0029] In equation (8) This is a one-step delay disturbance estimate, and

[0030] (9)

[0031] Hyperbolic tangent adaptive disturbance compensation error satisfy ,in This is the supremum of hyperbolic tangent adaptive interference compensation.

[0032] Step 4: Design of Discrete-Time Sliding Mode Controller

[0033] Based on equations (4) and (7), a discrete-time sliding mode controller is designed as follows:

[0034] (10)

[0035] Will As the control input signal of a DC motor speed control system, the actual output speed signal of the DC motor speed control system can be measured. Follow the given speed signal The dynamic characteristics of the tracking error of the closed-loop system are characterized by equation (7).

[0036] Furthermore, to characterize the convergence and steady-state performance of the discrete-time hyperbolic tangent attraction law (7), this invention provides expressions for two indices: the absolute attraction layer boundary and the steady-state error band boundary. These two indices can be used to guide the tuning of the discrete-time sliding mode controller parameters. The definitions of the absolute attraction layer boundary and the steady-state error band boundary are as follows:

[0037] 1) Absolute attraction layer boundary

[0038] ,when (11)

[0039] 2) Steady-state error band boundary

[0040] ,when (12)

[0041] here, For the boundary of the absolute attraction layer, This represents the boundary of the steady-state error band. The expressions for its various indices are as follows:

[0042] 1) Absolute attraction layer boundary Represented as:

[0043] (13)

[0044] In the formula, , It is a positive real number and satisfies

[0045] (14)

[0046] 2) Steady-state error band boundary Represented as:

[0047] (15)

[0048] In the formula, , It is a positive real number and satisfies

[0049] (16)

[0050] The technical concept of this invention is as follows: a design method for a hyperbolic tangent attraction law in a discrete-time sliding mode controller for a hyperbolic tangent adaptive interference compensation DC motor speed control system. Hyperbolic tangent adaptive interference compensation measures are embedded into the discrete-time hyperbolic tangent attraction law, forming a discrete-time hyperbolic tangent attraction law with interference compensation capability. A discrete-time controller is designed based on the discrete-time hyperbolic tangent attraction law to achieve accurate tracking of a given speed signal and improve the anti-interference capability of the DC motor speed control system.

[0051] The control effects of this invention are mainly manifested in the following aspects: It employs hyperbolic tangent adaptive interference compensation technology to suppress interference signals such as load mutations, voltage fluctuations, parameter uncertainties, and tribolinearity in the DC motor speed control system, thereby improving the system's tracking accuracy. Simultaneously, it utilizes a discrete-time hyperbolic tangent attraction law to achieve rapid convergence and suppress system chattering, resulting in better system control performance and anti-interference capabilities. Attached Figure Description

[0052] Figure 1 This is a flowchart of the design method for the hyperbolic tangent attraction law of the discrete-time sliding mode controller for a DC motor speed control system.

[0053] Figure 2 This is a schematic diagram of the circuit structure of a DC motor speed control system.

[0054] Figure 3 This is a block diagram of the signal flow of a DC motor speed control system.

[0055] Figure 4 This is a block diagram of the Simulink control module of a DC motor speed control system.

[0056] Figure 5 This is the speed curve when starting up to 500 r / min under the action of outer ring SMC + inner ring PI.

[0057] Figure 6 This is the speed curve when starting up to 500 r / min under the action of the outer ring PI and the inner ring PI.

[0058] Figure 7 It refers to the acceleration control performance when accelerating from 500r / min to 600r / min under the action of outer loop SMC + inner loop PI.

[0059] Figure 8 It refers to the acceleration control performance when accelerating from 500 r / min to 600 r / min under the action of outer loop PI + inner loop PI.

[0060] Figure 9 It refers to the acceleration control performance when accelerating from 600 r / min to 500 r / min under the action of outer loop SMC + inner loop PI.

[0061] Figure 10 It refers to the acceleration control performance when accelerating from 600 r / min to 500 r / min under the action of outer loop PI + inner loop PI.

[0062] Figure 11 It is the steady-state error under no-load conditions of 600 r / min, which is the result of the action of the outer ring SMC and the inner ring PI.

[0063] Figure 12 It is the steady-state error under no-load conditions of 600 r / min, under the action of outer loop PI + inner loop PI.

[0064] Figure 13 It is the control performance under the action of outer loop SMC + inner loop PI, from 600r / min with a load of 0.1Nm to unloading.

[0065] Figure 14 It refers to the control performance under the action of outer loop PI + inner loop PI, from 600r / min with a load of 0.1Nm to unloading.

[0066] Figure 15 It is the steady-state error under the action of outer ring SMC + inner ring PI, from 600r / min with a load of 0.1Nm to unloading.

[0067] Figure 16 It is the steady-state error under the action of outer loop PI + inner loop PI, from 600r / min with a load of 0.1Nm to unloading. Detailed Implementation

[0068] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0069] Reference Figure 1-16 A design method for the hyperbolic tangent attraction law of a discrete-time sliding mode controller for a DC motor speed control system is as follows: Figure 1 As shown, it includes the following steps:

[0070] Step 1: Establish a discrete-time second-order model of the DC motor speed control system

[0071] The continuous model of the DC motor speed control system is

[0072] (1)

[0073] Where ϑ is the voltage applied to the motor armature terminals, i a For armature current, k e k is the back electromotive force constant. m L is the motor torque constant. a R is the armature inductance. a Let J be the armature resistance, J be the moment of inertia of the rotor and motor load, and b be the coefficient of viscous friction of the motor. From equation (1), the following continuous-time second-order model of the DC motor speed control system can be obtained:

[0074] (2)

[0075] The Euler discretization method is used.

[0076] (3)

[0077] Where T is the sampling time; substituting equation (3) into equation (2), we can obtain the discrete-time second-order model of the DC motor speed control system:

[0078] (4)

[0079] Wherein, the system model parameters are

[0080] (5)

[0081] These represent the actual output speed signals of the DC motor speed control system at times k+1, k, and k-1, respectively. This represents the voltage signal applied to the motor armature terminals at time k in the DC motor speed control system. This is the interference signal of the DC motor speed system at time k+1.

[0082] Step 2: Construct the discrete-time hyperbolic tangent attraction law

[0083] Constructing the discrete-time hyperbolic tangent attraction law

[0084] (6)

[0085] in, These are parameters used to adjust the suction speed; Let $\frac{ ... Given the velocity signal at time k, The actual output speed signal of the DC speed control system at time k; hyperbolic tangent function. .when When the value is large, i.e., far from the origin, the value in equation (6) is... tending towards 1 and It tends towards 0, thus accelerating the system's attraction speed; when When it is smaller, that is, near the origin, in equation (6) tending towards 0 and The coefficients of the sign function tend to 0, thus eliminating system chatter.

[0086] Step 3: Hyperbolic Tangent Adaptive Interference Compensation Strategy

[0087] To improve the anti-interference capability of the DC motor speed control system, a hyperbolic tangent adaptive interference compensation measure is embedded into the discrete-time hyperbolic tangent attraction law (6), thus constructing a discrete-time hyperbolic tangent attraction law with interference compensation capability:

[0088] (7)

[0089] in, It is a hyperbolic tangent adaptive interference compensator based on one-step delay interference estimation technique, and satisfies

[0090] (8)

[0091] In equation (8) This is a one-step delay disturbance estimate, and

[0092] (9)

[0093] Hyperbolic tangent adaptive disturbance compensation error satisfy ,in This is the supremum of hyperbolic tangent adaptive interference compensation.

[0094] Step 4: Design of Discrete-Time Sliding Mode Controller

[0095] Based on equations (4) and (7), we can obtain

[0096] (10)

[0097] Depend on Know

[0098] (11)

[0099] Combining equations (8) and (9), the discrete-time sliding mode controller can be obtained as follows:

[0100] (12)

[0101] Will As the control input signal of a DC motor speed control system, the actual output speed signal of the DC motor speed control system can be measured. Follow the given speed signal The dynamic characteristics of the tracking error of the closed-loop system are characterized by equation (7).

[0102] Furthermore, to characterize the convergence and steady-state performance of the discrete-time hyperbolic tangent attraction law (7), this invention provides expressions for two indices: the absolute attraction layer boundary and the steady-state error band boundary. These two indices can be used to guide the tuning of discrete-time controller parameters, wherein the absolute attraction layer boundary and the steady-state error band boundary are defined as follows:

[0103] 1) Absolute attraction layer boundary

[0104] ,when (13)

[0105] 2) Steady-state error band boundary

[0106] ,when (14)

[0107] here, For the boundary of the absolute attraction layer, This represents the boundary of the steady-state error band. The expressions for its various indices are as follows:

[0108] 1) Absolute attraction layer boundary Represented as:

[0109] (15)

[0110] In the formula, , It is a positive real number and satisfies

[0111] (16)

[0112] 2) Steady-state error band boundary Represented as:

[0113] (17)

[0114] In the formula, , It is a positive real number and satisfies

[0115] (18)

[0116] Furthermore, after the discrete-time sliding mode controller of the DC motor speed control system is designed, its controller parameters need to be tuned. Adjustable parameters... The tuning is performed based on two indices characterizing the convergence process of the discrete-time hyperbolic tangent attraction law.

[0117] Example

[0118] Closed-loop control is implemented for the output speed of a DC motor speed control system. The circuit diagram and signal flow block diagram of the DC motor speed control system are shown below. Figure 2 and Figure 3 As shown. The DC motor speed control system is based on the Speedgoat real-time target machine platform, with control hardware built upon it. The control module design is completed in the Simulink environment on the host computer. The Simulink control module is as follows: Figure 4 As shown, the system comprises modules for calculating speed error, armature voltage error, a PI algorithm module, a discrete-time sliding mode control algorithm module, a real-time PWM signal generation and output module, and a real-time data acquisition module. The control system uses a solver with a fixed step size of 0.0001s and maintains a sampling frequency of 1kHz to synchronize control commands with the sampling process. In the experiment, Simulink's Signal Data Inspector (SDI) was used to monitor the motor's armature voltage, steady-state error, and speed variation curves in real time.

[0119] The overall process of the DC motor speed control system is as follows: (1) After setting the target speed in Simulink, it is compared with the sampled motor speed to obtain the speed error signal. The speed error signal is input to the outer loop discrete-time sliding mode controller (12) or PI controller to obtain the reference voltage. This is the speed outer loop. (2) The obtained reference voltage is compared with the sampled motor armature voltage to obtain the voltage error signal. The voltage error signal is input to the PI controller. This is the voltage inner loop. (3) The PWM duty cycle command is output through the real-time PWM signal output module. After PWM modulation, it is fed back to the Buck converter to adjust the DC motor armature voltage and realize the dual closed-loop DC motor speed control. (4) The Speedgoat real-time target machine is responsible for transmitting the PWM signal generated in Simulink to the Buck circuit through the IO module. At the same time, it samples the motor speed signal and armature voltage signal and sends them back to the host computer for recording and analysis.

[0120] The following describes the design process of a discrete-time sliding mode controller for a DC motor speed control system: First, a discrete-time second-order model of the DC motor speed control system is established. Figure 2 The Buck main control circuit and DC motor are used as objects for mechanism modeling, and the switching cycle of the Buck circuit switching transistor is analyzed. , capacitor is Inductance is Armature inductance of a DC motor Armature resistance viscous friction coefficient Moment of inertia Torque constant back electromotive force constant Based on the above electrical parameters and the discrete-time second-order model of the DC motor speed control system, we can obtain:

[0121] (19)

[0122] In Simulink, the rotation speed is set to... The actual rotational speed is Define the speed error as The target value for the inner voltage loop is set to the output value of the outer speed controller. The proportional link is The points system is as follows The PI controller is:

[0123] (20)

[0124] The controller parameters of the outer-loop discrete-time sliding mode controller (12) SMC are set as follows: The outer loop PI controller is selected as: The parameters of the inner-loop PI controller are: .

[0125] The response time and steady-state error under the outer loop PI controller or the outer loop discrete-time sliding mode controller (SMC) are used to verify the effectiveness and superiority of the discrete-time sliding mode controller design method given in this invention during the startup process, the given speed change process, and the load change process of the DC motor speed control system.

[0126] (1) Startup process

[0127] Figure 5 and Figure 6 The speed curves from start-up to 500 r / min are shown for two control scenarios: outer loop SMC + inner loop PI and outer loop PI + inner loop PI. Figure 5 and Figure 6 It can be seen that the response time of the outer-loop discrete-time sliding mode controller is much longer than that of the outer-loop PI controller, and the start-up curve is also smoother with the outer-loop discrete sliding mode controller.

[0128] (2) Given the sudden change in rotational speed

[0129] Figure 7 and Figure 8 The acceleration control performance from 500 r / min to 600 r / min is shown under two control conditions: outer loop SMC + inner loop PI and outer loop PI + inner loop PI. Figure 7 and Figure 8 It can be seen that the outer-loop discrete-time sliding mode controller (SMC) responds much faster than the outer-loop PI controller under sudden speed changes.

[0130] Figure 9 and Figure 10 The acceleration control performance from 600 r / min to 500 r / min is shown under two control conditions: outer loop SMC + inner loop PI and outer loop PI + inner loop PI. Figure 9 and Figure 10 It can be seen that the outer-loop discrete-time sliding mode controller (SMC) responds faster than the outer-loop PI controller under sudden speed changes.

[0131] Figure 11 and Figure 12The figures show the steady-state errors of the two control methods under no-load conditions at 600 r / min. It can be seen that under the control of the outer-loop PI controller, the upper and lower limits of the steady-state error can be stabilized within ±9 r / min; while under the control of the outer-loop discrete-time sliding mode controller (SMC), the upper and lower limits of the steady-state error can be stabilized within ±6 r / min. Therefore, the outer-loop discrete-time sliding mode controller (SMC) has a better steady-state error under no-load conditions than the outer-loop PI controller, meeting the design requirements and demonstrating good stability.

[0132] (3) Load mutation process

[0133] Figure 13 and Figure 14 This test examines the control performance of two control methods: outer-loop SMC + inner-loop PI and outer-loop PI + inner-loop PI, under conditions of 0.1 Nm load at 600 r / min and unload conditions. Figure 13 and Figure 14 It can be seen that under the control of the outer loop discrete-time sliding mode controller (SMC), the DC motor has a faster response speed and better control performance than the outer loop PI algorithm. Figure 15 and Figure 16 The figures show the steady-state errors of two control methods at 600 r / min under a load of 0.1 Nm. The outer-loop discrete-time sliding mode controller (SMC) exhibits better steady-state error under load than the outer-loop PI controller, with the upper and lower speed limits stabilized within ±5 r / min. In contrast, the steady-state error under the control of the outer-loop PI controller is only stable within ±6 r / min, with significant fluctuations. This demonstrates that the system's anti-interference capability is significantly improved under the control of the outer-loop discrete-time sliding mode controller (SMC), meeting design requirements and exhibiting good stability.

Claims

1. A method for designing a hyperbolic tangent attraction law for a discrete-time sliding mode controller in a DC motor speed control system, characterized in that, Includes the following steps: Step 1: Establish a discrete-time second-order model of the DC motor speed control system The continuous model of the DC motor speed control system is (1) Where ϑ is the voltage applied to the motor armature terminals, i a For armature current, k e k is the back electromotive force constant. m L is the motor torque constant. a R is the armature inductance. a Let J be the armature resistance, J be the moment of inertia of the rotor and motor load, and b be the viscous friction coefficient of the motor; from equation (1), the following continuous-time second-order model of the DC motor speed control system can be obtained: (2) The Euler discretization method is used. (3) Where T is the sampling time; substituting equation (3) into equation (2), we can obtain the discrete-time second-order model of the DC motor speed control system: (4) Wherein, the system model parameters are (5) These represent the actual output speed signals of the DC motor speed control system at times k+1, k, and k-1, respectively. This represents the voltage signal applied to the motor armature terminals at time k in the DC motor speed control system. This is the interference signal of the DC motor speed system at time k+1. Step 2: Construct the discrete-time hyperbolic tangent attraction law Constructing the discrete-time hyperbolic tangent attraction law (6) in, These are parameters used to adjust the suction speed; Let $\frac{ ... Given the velocity signal at time k, The actual output speed signal of the DC speed control system at time k; hyperbolic tangent function. ;when When the value is large, i.e., far from the origin, the value in equation (6) is... tending towards 1 and It tends towards 0, thus accelerating the system's attraction speed; when When it is smaller, that is, near the origin, in equation (6) tending towards 0 and The coefficients of the sign function tend to 0 as the coefficients approach 1, thus eliminating system chatter. Step 3: Hyperbolic Tangent Adaptive Interference Compensation Strategy To improve the anti-interference capability of the DC motor speed control system, a hyperbolic tangent adaptive interference compensation measure is embedded into the discrete-time hyperbolic tangent attraction law (6), thus constructing a discrete-time hyperbolic tangent attraction law with interference compensation capability: (7) in, It is a hyperbolic tangent adaptive interference compensator based on one-step delay interference estimation technique, and satisfies (8) In equation (8) This is a one-step delay disturbance estimate, and (9) Hyperbolic tangent adaptive disturbance compensation error satisfy ,in This is the upper bound of hyperbolic tangent adaptive disturbance compensation; Step 4: Design of Discrete-Time Sliding Mode Controller Based on equations (4) and (7), a discrete-time sliding mode controller is designed as follows: (10) Will As the control input signal of a DC motor speed control system, the actual output speed signal of the DC motor speed control system can be measured. Follow the given speed signal The dynamic characteristics of the tracking error of the closed-loop system are characterized by equation (7).

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