Bridge crane flexible falling control method, system and device based on S-shaped curve speed regulation algorithm

Abstract

The invention provides a bridge crane flexible falling control method, system and device based on an S-shaped curve speed regulation algorithm, and belongs to the technical field of engineering machinery, the control method comprises the following steps: 1, analyzing constraint conditions of a bridge crane in a hoisting working process, and establishing a model of the bridge crane at a balance position in the hoisting process; 2, designing an acceleration track, a speed track and a displacement track of load falling based on the model of the bridge crane in the hoisting process, namely finishing S-shaped track planning of load falling; 3, after the S-shaped track is coded into MATLAB, the rotating speed of the three-phase alternating-current asynchronous motor is controlled through a rotating speed closed-loop PI, closed-loop adjustment is achieved under constant-voltage-frequency-ratio open-loop control, the planned S-shaped track is tracked, and flexible falling of the hoisting load is achieved. On the basis of not changing the mechanical structure of the bridge crane, the flexible falling of the three-phase alternating-current asynchronous motor in the crane during hoisting is controlled by designing a control algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of construction machinery, and particularly relates to a flexible falling control method, system and device for a bridge crane based on an S-shaped curve speed regulation algorithm. Background Art

[0002] Bridge cranes are widely used in the field of construction machinery and play a huge role. However, when using traditional control methods to control the lifting and lowering of the load of a bridge crane, a series of problems will occur. In terms of the crane structure, traditional control methods may cause impacts on components such as the hook, wire rope, and drum of the crane, and there may be damage, deformation, cracks, or even destruction; in the transmission system, gears will be impacted due to short-term overload and problems such as tooth breakage, pitting corrosion, and tooth surface wear will occur; for the item being lifted itself, it may be damaged due to hard impacts, and at the same time, it will also cause damage to the carrier. To solve the problems, it is necessary to design a more flexible falling control method that meets the needs of production work to control the motor to reduce the damage to the crane during the work process and reduce the hard impact to protect the lifted object. This is of great significance for improving industrial production efficiency and the service life of engineering equipment.

[0003] For controlling the flexible falling of a bridge crane during the load lifting process, currently, there are mainly two methods. One is to transform by changing the mechanical structure. Wang Gang et al. used triangular wedges to gradually squeeze and brake the remaining wire rope at the inner end of the drum, and the drum can be controlled during falling to achieve the purpose of reducing the falling buffer; Kong Qinghua et al. designed a hoisting system based on a hoisting system including an energy storage device, a hoisting motor, and a rotary drilling rig, and the torque generated by the hoisting generator is used to balance the load value, so that the actual speed of the bridge crane does not exceed the target speed. In summary, using the method of changing the mechanical structure to control the flexible lowering of a bridge crane is indeed a method, but this design-based mechanical structure method cannot be applied to complex and changeable scenarios, has strong limitations in use, high design difficulty and cost, and in addition, the control accuracy is low, and it cannot accurately achieve the flexible falling control of the load of the bridge crane. Summary of the Invention

[0004] To solve the above problems of the prior art, the present invention provides a flexible falling control method, system and device for a bridge crane based on an S-shaped curve speed regulation algorithm. On the basis of not changing the mechanical structure of the bridge crane, the present invention controls the flexible falling of a three-phase AC asynchronous motor in the crane during load lifting by designing a control algorithm.

[0005] The technical solution adopted by the present invention is as follows:

[0006] In the first aspect, the present invention protects a flexible falling control method for a bridge crane based on an S-shaped curve speed regulation algorithm, including the following steps:

[0007] Step 1: Analyze the constraint conditions of the bridge crane during the load lifting process, and establish a model of the bridge crane at the equilibrium position during the load lifting process;

[0008] Step 2: Based on the model of the bridge crane during the load lifting process, design the acceleration trajectory, velocity trajectory, and displacement trajectory of the load falling, that is, complete the S-shaped trajectory planning of the load falling;

[0009] Step 3: After encoding the S-shaped trajectory into MATLAB, use the rotational speed closed-loop PI control to realize the closed-loop adjustment of the speed of the three-phase AC asynchronous motor under the constant voltage-frequency ratio open-loop control, track the planned S-shaped trajectory, and realize the flexible falling of the load.

[0010] Preferably, in Step 1, the constraint conditions include:

[0011] (1) Constraint at the starting moment:

[0012]

[0013] Among them, x(0) is the position of the load at the starting moment of lifting, is the velocity of the load at the starting moment of lifting, is the acceleration of the load at the starting moment of lifting, θ(0) is the swing angle of the load at the starting moment of lifting, is the swing angular velocity of the load at the starting moment of lifting, is the swing angular acceleration of the load at the starting moment of lifting;

[0014] (2) Constraint during the falling process:

[0015]

[0016] |θ(t)| ≤ θ max , 0 < t ≤ t d

[0017] Among them, is the falling velocity of the load at time t, is the falling acceleration of the load at time t, θ(t) is the swing angle of the load at time t, ν max is the upper limit of the velocity of the load during the falling process, a max is the upper limit of the acceleration of the load during the falling process, θ max is the upper limit of the swing angle of the load during the falling process, t d is the total time of the entire falling process of the load;

[0018] (3) Constraint at the end of the work

[0019] When the work is completed, the rotational speed of the three-phase AC asynchronous motor of the overhead crane should be reduced to 0, and the load should land steadily on the platform. The constraint conditions at this time are:

[0020]

[0021] Among them, x(t) is the position of the suspended load at time t, is the falling speed of the suspended load at time t, is the falling acceleration of the suspended load at time t, θ(t) is the swinging angle of the suspended load at time t, is the swinging angular velocity of the suspended load at time t, is the swinging angular acceleration of the suspended load at time t, t d is the total time of the entire falling process of the suspended load.

[0022] More preferably, the model established at the equilibrium position during the load lifting process of the overhead crane in step 1 is:

[0023]

[0024] Among them, m is the load mass; M is the trolley mass; l is the length of the suspension rope.

[0025] More preferably, the specific steps of step 2 are as follows:

[0026] Step 201: First, analyze the motion trajectory of the load from the perspective of acceleration. After analyzing the acceleration, the acceleration trajectory of the load is obtained through integration:

[0027]

[0028] Step 202: During the acceleration change process, introduce a transition link to overcome the sudden impact, and add a sine curve to the acceleration trajectory:

[0029]

[0030] Among them, A is a coefficient to be determined, t d is the total time of the entire falling process of the suspended load;

[0031] Step 203: Integrate the formula in step 202 over time to obtain the velocity trajectory of the load:

[0032]

[0033] Among them, a1, a2 are coefficients to be determined;

[0034] Step 204: Integrate the velocity trajectory of the load over time to obtain the displacement trajectory of the load:

[0035]

[0036] Among them, b1 and b2 are coefficients to be determined;

[0037] Step 205: By using the constraint conditions to eliminate the undetermined coefficients in the above formula, the effective displacement trajectory, velocity trajectory and acceleration trajectory of the load can be obtained:

[0038]

[0039]

[0040] Among them, x d It is the target position for the hanging weight to fall.

[0041] More preferably, the specific implementation of step 4 is:

[0042] The S-shaped trajectory tracking control signal is input into the low-frequency voltage compensation module through the speed closed-loop PI control module, and the frequency-limiting module outputs the frequency-limiting signal to the low-frequency voltage compensation module to keep the voltage-frequency ratio unchanged; the SPWM modulation drive module modulates the voltage and frequency to generate a sinusoidal pulse width modulation wave to send a speed control signal to the inverter, and the output speed is collected by the sensor and fed back to the speed closed-loop PI control module to realize the closed-loop adjustment of the speed of the three-phase AC asynchronous motor.

[0043] In a second aspect, the present invention protects a flexible drop control system for a bridge crane based on an S-curve speed regulation algorithm, comprising:

[0044] An S-curve trajectory planning module, executing step 1-step 2 described in claim 4 to generate an S-curve trajectory of the load falling;

[0045] The speed loop PI control module receives the S-shaped trajectory and combines the control signal to realize closed-loop adjustment of the speed of the three-phase AC asynchronous motor under the voltage-frequency ratio open-loop control, and outputs the speed adjustment signal;

[0046] The frequency-increasing speed-limiting module is used to limit the frequency to avoid the impact of current and torque caused by the speed increasing too fast;

[0047] The low-frequency voltage supplement module receives the input frequency-limiting signal and the speed adjustment signal to keep the ratio of the voltage to the frequency of the three-phase AC asynchronous motor unchanged;

[0048] The SPWM modulation drive module generates a sinusoidal pulse width modulation wave to send a control signal to the inverter, and the control signal is returned to the speed loop PI control module.

[0049] In a third aspect, the present invention protects a flexible falling control device for a bridge crane based on an S-curve speed regulation algorithm. The device includes a memory storing a computer program and a processor for executing the computer program. When the computer program is executed by the processor, the steps of a flexible falling control method for a bridge crane based on an S-curve speed regulation algorithm are implemented.

[0050] Beneficial effects:

[0051] (1) The present invention takes the actual working condition of a variable-frequency bridge crane during the falling of the lifted load as the research object. Through modeling and simulation analysis of the falling working condition, a control method is designed and combined with Simulink simulation analysis to control the three-phase AC asynchronous motor used in the variable-frequency bridge crane, so as to achieve the purpose of flexible falling of the lifted load and reducing the hard impact on the carrier and the crane.

[0052] (2) The flexible falling control method based on the S-curve speed regulation method of the present invention analyzes each constraint condition in the falling state, and plans the S-curve trajectory of the load falling based on this. In the motor speed control, the constant voltage-frequency ratio method is selected, and the motor speed is tracked along the planned trajectory by using the speed PI closed-loop method. It can be seen from the simulation results that this method effectively achieves the purpose of flexible falling of the lifted load, and the effect is good. Description of the drawings

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0054] Figure 1 It is a structural diagram of a wound-rotor asynchronous motor.

[0055] Figure 2 It is a structural diagram of the rotor of a wound-rotor asynchronous motor.

[0056] Figure 3 It is a T-type equivalent circuit diagram of a three-phase AC asynchronous motor.

[0057] Figure 4 It is a schematic diagram of Clarke coordinate transformation.

[0058] Figure 5 It is a Park transformation coordinate conversion diagram.

[0059] Figure 6 It is a speed curve of the trapezoidal speed regulation algorithm.

[0060] Figure 7 It is an acceleration curve of the trapezoidal speed regulation algorithm.

[0061] Figure 8 It is the speed curve diagram of the S-type speed regulation algorithm.

[0062] Figure 9 It is the acceleration curve diagram of the S-type speed regulation algorithm.

[0063] Figure 10 It is the schematic diagram of constant voltage frequency ratio speed regulation.

[0064] Figure 11 It is the structure diagram of the transfer function of the speed loop PI control.

[0065] Figure 12 It is the principle flow chart of the flexible falling control method based on the S-type speed regulation algorithm.

[0066] Figure 13 It is the simulation structure diagram of the S-type trajectory planning module.

[0067] Figure 14 It is the S-type planned trajectory of the load.

[0068] Figure 15 It is the simulation structure diagram of the PWM pulse modulation module.

[0069] Figure 16 It is the simulation model of the flexible falling control method based on the S-type speed regulation algorithm.

[0070] Figure 17 It is the motor speed diagram of the flexible falling control method based on the S-type speed regulation algorithm.

[0071] Figure 18 It is the simulation image of the motor speed when the control method without the design is adopted.

[0072] Figure 19 It is the experimental result of the control group.

[0073] Figure 20 It is the experimental result (1) of the flexible falling control method of the S-type curve speed regulation algorithm.

[0074] Figure 21 It is the experimental result (2) of the flexible falling control method of the S-type curve speed regulation algorithm.

[0075] Figure 22 It is the experimental result (3) of the flexible falling control method of the S-type curve speed regulation algorithm.

[0076] Figure 23 It is the experimental result (4) of the flexible falling control method of the S-type curve speed regulation algorithm. Specific implementation manners

[0077] The various exemplary embodiments of the present invention will be described in detail below. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, characteristics, and implementation manners of the present invention. It should be understood that the terms described in the present invention are only for describing specific embodiments and are not used to limit the present invention.

[0078] 1. Mathematical Model of Three-Phase AC Induction Motor

[0079] 1.1 Structure and Working Principle of Three-Phase AC Induction Motor

[0080] An induction motor is also called an asynchronous motor. As an AC motor, it has a simple internal structure, low production cost, and high working reliability. It is usually used in industry to drive large machinery, fans, pumps and other equipment; in agricultural production, it is usually used in processing machinery, harvesters, threshers and other equipment; it is widely used in daily household appliances such as air conditioners, refrigerators, washing machines, etc.

[0081] During the use of a bridge crane, the motor is often started, braked, and reversed, and it will encounter overload situations. Usually, the motor carried needs to have strong starting performance, a large starting torque multiple, and a mechanical structure with high strength to ensure that the motor can operate normally during the working process. Due to the advantages of large starting torque of the asynchronous motor, it can directly start the load; the adjustable speed range is wide, and the power supply frequency can be adjusted according to the actual working conditions to change the speed; the working adaptability is strong, it can work normally under different voltages and frequencies and has a strong overload capacity, etc., the asynchronous motor is also usually widely used in bridge cranes. Especially in the context of the rapid development of power electronics technology, the speed regulation performance of the asynchronous motor has also been greatly improved.

[0082] The asynchronous motor is divided into squirrel-cage type and wound-rotor type in structure. The bridge crane studied in this topic uses a wound-rotor asynchronous motor, and its structural schematic diagram is as Figure 1 shown.

[0083] Large asynchronous motors will use insulated copper bars as the stator windings. The number of turns of the coils wound by each winding is the same, and the phase difference between each phase winding is 120°. When three-phase alternating current is passed into the three-phase stator windings, a rotating magnetic field will be generated. According to the specific working requirements, the circuit connection methods of the stator windings usually include star type and bus type.

[0084] The rotor core of the three-phase wound-rotor asynchronous motor is usually stacked with multiple layers of silicon steel sheets to optimize the magnetic circuit and reduce eddy current losses. In the wound-rotor, the winding generally uses copper coils and the ends are led out with slip rings and connected to external control equipment, so that the resistance can be adjusted during the motor starting process, thereby controlling the starting current and torque of the motor.

[0085] When a three - phase asynchronous motor is connected to a three - phase symmetrical alternating current, the three - phase stator windings carry three - phase symmetrical currents, which will generate a rotating magnetic field in the rotor air gap. The rotating magnetic field is the basis for the normal operation of the three - phase asynchronous motor. The generated rotating magnetic field will cut the rotor windings. According to the law of electromagnetic induction, induced electromotive force and induced current will be generated in the conductor. From the structure of the wound - rotor asynchronous motor, it can be seen that its rotor winding is actually a closed circuit. The rotor carrying current will generate an electromagnetic force and an electromagnetic torque under the action of the rotating magnetic field to drive the rotor to rotate. This realizes the conversion of electrical energy to mechanical energy of the asynchronous motor. From the structure of the wound - rotor asynchronous motor, it can be seen that its rotor winding is actually a closed circuit. According to the principle of electromagnetic induction, what actually drives the rotor to rotate is the output electromagnetic torque.

[0086] Assume that the initial phase angle of the voltage applied to phase U at the initial time is 0, then the three - phase currents can be expressed by the following formula:

[0087]

[0088] At the initial moment, i U = 0, then i v is a negative value, and i w is a positive value

[0089] The amplitude of the magnetomotive force can be expressed by the following formula:

[0090]

[0091] Among them, N1 is the number of series turns of one phase of the stator winding, k dp1 is the fundamental - wave winding factor of the stator, and p is the number of pole pairs.

[0092] The angular velocity of the stator winding is

[0093] ω = 2πpn1 / 60 (3)

[0094] When the magnetomotive force of the synthesized rotating magnetic field rotates counter - clockwise relative to the stator winding at ω, the main magnetic flux of each magnetic pole in the air gap is

[0095]

[0096] Among them is the average value of the magnetic - flux density in the air gap, τ is the pole pitch of the stator, and l is the axial length of the motor.

[0097] The maximum value of the magnetic flux linkage of one phase of the stator is

[0098] φ m1 = N1k dp1 φ m (5)

[0099] Then the flux linkage of stator A can be expressed by the following formula

[0100] ψ A1 =φ m1 sin(ωt)=N1k dp1 φ m sin(ω1t) (6)

[0101] From the above formula, the induced electromotive force generated by the flux linkage in the stator winding can be derived as follows:

[0102]

[0103] 1.2 Steady-state model and coordinate transformation principle

[0104] The T-type equivalent circuit diagram of a three-phase AC induction motor is as Figure 3 shown. According to the equivalent circuit diagram, the basic equations during the rotation of the rotor can be written

[0105]

[0106] It can be seen from Equation (2.8) that the slip ratio and I'2 are both 0 at this time, tends to infinity, and the stator current is equal to the excitation current, and the power factor of the motor is relatively low.

[0107] When the three-phase AC induction motor operates at a speed of n, the input power of the motor at this time is

[0108]

[0109] The copper loss and iron loss of the stator can be expressed respectively as

[0110]

[0111] The copper loss on the rotor winding is

[0112]

[0113] The electromagnetic power of the motor is

[0114]

[0115] The mechanical power output by the motor is

[0116]

[0117] The output shaft power of the motor can be obtained by subtracting the mechanical loss power and additional loss power from the output mechanical power and can be expressed as

[0118] P2=P m -P m -P a(15)

[0119] The mechanical power can also be obtained by multiplying the output torque by the mechanical angular velocity, i.e.,

[0120] P m = TΩ (16)

[0121] It can be derived that

[0122] P m = (1 - s)P M (17)

[0123] The relationship expression between the electromagnetic power and the electromagnetic torque can be expressed as

[0124]

[0125] Substituting the expression of the electromagnetic power, the expression of the electromagnetic torque can be obtained as

[0126]

[0127] where, m2 is the number of rotor windings, N2 is the number of turns of each phase of the rotor winding, k dp2 is the fundamental winding factor of the rotor, I2 is the phase current, C T represents the torque factor of the rotor

[0128] The following relationship exists between the electromagnetic torque of the motor and the rotor current

[0129]

[0130] In the T-type equivalent circuit, the leakage impedance of the stator and the leakage impedance of the rotor can be ignored. Therefore, the current of the motor rotor can be expressed as

[0131]

[0132] Substituting the rotor current expression into the electromagnetic torque expression, we can get

[0133]

[0134] Through derivation, in the actual control process, the output variables of the motor in the three-phase stationary coordinate system usually have many variables and strong coupling of mathematical equations. In order to reduce the order of the system and the difficulty of control, the mathematical model of the asynchronous motor in the three-phase stationary coordinate system is usually subjected to a coordinate transformation, converting the mathematical model on the three-phase stationary coordinate system to the two-phase stationary coordinate system, and then further converting the mathematical model from the two-phase stationary coordinate system to the two-phase rotating coordinate system through a coordinate transformation.

[0135] First, a three-phase rotating coordinate system needs to be transformed into a two-phase stationary coordinate system. According to the basic principle of Clarke transformation, it is known from the working principle of an asynchronous motor that the three phase sequences of the motor differ by 120° respectively. The transformed coordinate system is as Figure 4 shown:

[0136]

[0137] According to the phase angle relationship, u A , u B , u c are transformed into the two-phase stationary coordinate system

[0138]

[0139] The above formula is expressed by the transformation matrix as

[0140]

[0141] Then the transformation matrix is

[0142]

[0143] From the above, the transformation from the three-phase stationary coordinate system to the two-phase stationary coordinate system can be realized. The coordinate transformation from the two-phase stationary coordinate system to the two-phase rotating coordinate system is also called Park transformation, as Figure 5 shown.

[0144] The transformation from the two-phase stationary coordinate system to the two-phase rotating coordinate system can be realized by making the d-axis of the rotating coordinate system coincide with the rotating vector in the two-phase stationary coordinate system. Taking the phase angle of phase A as an example, the voltage conversion relationship is

[0145]

[0146] The transformation matrix of Park transformation can be obtained as

[0147]

[0148] From the above, the transformation from the two-phase stationary coordinate system to the two-phase rotating coordinate system can be realized.

[0149] 1.3 Mathematical Models in Stationary and Rotating Coordinate Systems

[0150] The matrix form of the voltage equation in the mathematical model is:

[0151]

[0152] R s and R r are the stator resistance and the rotor resistance referred to the stator side respectively; i sa , i sb , isc is the three-phase stator current; i ra , i rb , i rc are the three-phase rotor currents referred to the stator side; p is the differential operator; ψ sa , ψ sb , ψ sc are the three-phase stator fluxes; ψ ra , ψ rb , ψ rc are the three-phase rotor fluxes referred to the stator side.

[0153] Flux linkage equations:

[0154]

[0155] where L sl , L rl are the stator leakage inductance and the rotor leakage inductance referred to the rotor side, L 1m is the stator inductance corresponding to the main flux, and θ is the space angle between the stator A-axis and the rotor A-axis.

[0156] Torque equation:

[0157]

[0158] where n p is the number of pole pairs of the motor. It can be seen from the equation that the motor torque is a function of the stator currents i sa , i sb , i sc , the rotor currents i ra , i rb , i rc and θ.

[0159] Motion equation:

[0160]

[0161] where T e is the electromagnetic torque output by the motor, and ω r is the electrical angular velocity of the rotor rotation.

[0162] According to the conversion state equation, the mathematical model in the two-phase stationary coordinate system can be obtained

[0163] Voltage equation

[0164]

[0165] Flux linkage equation

[0166]

[0167] Torque equation

[0168]

[0169] Similarly, according to the transformation state equation, the mathematical model voltage equation in the two-phase rotating coordinate system can be obtained.

[0170]

[0171] Flux linkage equation

[0172]

[0173] Torque equation

[0174]

[0175] 2. Design of Flexible Falling Control Method Based on S-shaped Curve Speed Regulation Algorithm

[0176] 2.1 Principle of S-shaped Curve Speed Regulation Algorithm

[0177] The S-shaped curve speed regulation method for AC asynchronous motors is an advanced motor speed control technology, which can achieve smooth acceleration and deceleration of the motor during startup, operation and stop, thus improving the operation efficiency and stability of the motor.

[0178] The core of the S-shaped curve speed regulation method lies in controlling the input voltage and frequency of the motor. By segmenting the motion process, it realizes continuous speed connection in different stages, and the change rate of acceleration is controllable. The tightness of connection in each stage enables the acceleration to be controlled simultaneously.

[0179] In the acceleration section, the acceleration of the motor gradually increases, enabling the motor to smoothly transition from the stationary state to the acceleration state; in the constant acceleration section, the motor runs at a constant acceleration to achieve a stable acceleration process; in the constant speed section, the motor runs at a constant speed to meet the load demand; in the subsequent deceleration section, the motor smoothly reduces its speed by decreasing the acceleration until it stops completely.

[0180] The S-shaped curve speed regulation method is improved from the trapezoidal curve speed regulation method. As Figure 6 shown, in the trapezoidal algorithm, the rotational speed of the motor is divided into three stages. The 0 - t0 stage is the acceleration section, t0 - t1 is the constant speed section, and t1 - t2 is the deceleration section.

[0181] The control principle of the trapezoidal algorithm is very simple and easy to implement. The total displacement can be represented by the area of the trapezoid

[0182]

[0183] From the acceleration curve of the trapezoidal algorithm ( Figure 7) It can be seen that the trapezoidal algorithm has a serious defect, that is, the acceleration is discontinuous, and thus jerk will be generated in the system at the moment of change. Jerk means that under specific load conditions, the increase in jerk often leads to an unnecessary increase in vibration energy, and further makes the vibration spectrum wider. When the change rate of acceleration increases, the intensity of vibration will also increase accordingly, and the number of excited vibration modes will also increase correspondingly. Since these vibration energies will be absorbed by the mechanical system, if the vibration frequency happens to coincide with the resonance frequency in the mechanical and control systems, the stabilization time of the system may be prolonged, and its accuracy may also be affected. The S-shaped algorithm optimizes the jerk problem based on the trapezoidal algorithm.

[0184] To solve the jerk problem of the trapezoidal curve, ideally, the velocity curve can be planned as Figure 8 shown.

[0185] As Figure 8 shown in the ideal S-shaped curve speed regulation, on the basis of the trapezoidal curve, the velocity is first normalized, and

[0186] v(0) = 0, v(1) = 1, v′(0) = 0, v′(1) = 0

[0187] It is known that

[0188] a = v′(t) (40)

[0189] From the velocity curve function and its derivative of the formula,

[0190] v(t) = at 3 + bt 2 (41)

[0191] v′(t) = 3at 2 + 2bt (42)

[0192] We get the equations

[0193]

[0194] Solving, we get a = -2, b = 3. According to the solved values of the undetermined coefficients, the velocity and acceleration curves can be obtained,

[0195] v(t) = -2t 3 + 3t 2 (44)

[0196] v′(t) = -6t 2 + 6t (45)

[0197] At this time, the acceleration curve becomes as follows Figure 9 shown.

[0198] By solving the values of a and b from the system of equations, the speed regulation curve can be obtained. The principle of normalization is relatively simple and easy to understand, and it has universality. In the actual motor speed regulation process, sine or cosine functions are often embedded according to the motor characteristics to optimize the algorithm in detail.

[0199] 2.2 Controller Design

[0200] During the hoisting operation of the bridge crane, various constraints it is subjected to should be considered. When planning the trajectory of the load, the constraint conditions should be taken into account. According to the working process, the constraints can be classified as follows:

[0201] (1) Starting moment constraint

[0202]

[0203] (2) Constraints during the falling process

[0204] While achieving the goal of flexible falling control, factors such as safety, working efficiency, and feasibility should be considered. Not only should the operating parameters of the bridge crane such as speed and acceleration be within the output range, but it is also necessary to make the falling as smooth as possible, and the swing angle of the load should also be within a certain range.

[0205]

[0206] (3) Constraints at the end of the work

[0207] According to the control goal, when the work is over, the motor speed of the bridge crane should drop to 0, and the load should land smoothly on the platform. The constraint conditions at this time are

[0208]

[0209] The model of the bridge crane at the equilibrium position during this process is

[0210]

[0211] The actual trajectory planning of the load should be considered from the perspective of acceleration. After analyzing the acceleration, the trajectory of the load can be obtained by integration.

[0212]

[0213] During the change of acceleration, a transition link needs to be introduced to overcome the sudden impact, and a sine curve is added to the trajectory

[0214]

[0215] A is a coefficient to be determined. Integrating the above formula with respect to time can obtain the speed trajectory of the load

[0216]

[0217] In the formula, a1 and a2 are coefficients to be determined. Integrating the time again gives the displacement trajectory of the load:

[0218]

[0219] Eliminating the undetermined coefficients in the formula by the constraint conditions, the displacement, velocity, and acceleration trajectories of the load can be obtained.

[0220]

[0221] After writing the code for the S-shaped trajectory in MATLAB, the speed of the motor is made to track the planned trajectory through the constant voltage-frequency ratio control method. The constant voltage-frequency ratio control method is an open-loop control method and also the basic control method for variable-frequency speed regulation of AC induction motors. The basic principle is to keep the ratio of the motor voltage to the frequency constant to maintain the relative constancy of the magnetic flux and torque when changing the operating frequency of the motor. Under the condition of a constant load, the slip ratio of the motor remains basically unchanged, enabling the motor to have good speed regulation performance.

[0222] As Figure 10 shown, the acceleration and deceleration time setting module is mainly used to achieve soft start to limit the frequency and avoid the impact of current and torque caused by too fast speed increase; the low-frequency voltage compensation module is mainly used to keep the ratio of voltage to frequency constant; the SPWM modulation drive module is mainly used to generate a sine pulse width modulation wave to send a control signal to the inverter and thus achieve the control of the motor.

[0223] In the design of this algorithm, in order to make the speed track the planned trajectory, speed closed-loop PI control is adopted, so that the speed of the motor can be closed-loop adjusted under the constant voltage-frequency ratio open-loop control. The simplified structural block diagram of the speed loop PI control is Figure 11 .

[0224] The open-loop transfer function is

[0225]

[0226] Where is a constant, then the closed-loop characteristic equation is

[0227] D(s) = T s S 2 +(1 + mK ρ )S + mK I = 0 (62)

[0228] All the roots of the closed-loop characteristic equation have negative real parts. According to the Routh criterion, the system is stable. After parameter adjustment, the PI parameters of the system can be selected as K p = 26, K I = 2.4.

[0229] 2.3 Simulation and Analysis

[0230] The overall control flow block diagram is Figure 12 shown. In the S-type trajectory planning module in the controller, the ramp signal is superimposed and then modulated through the Function module according to the constraint conditions and mathematical model in the controller to generate the desired trajectory. A speed loop PI control module is added to the output position of the planned trajectory so that the motor speed can track the planned trajectory signal. Figure 13 This is the built S-type curve trajectory planning module. The speed signal output from the motor is received by the From module in the figure.

[0231] Based on the S-type algorithm, the trajectory of the load during the hoisting process is planned, and the S-type trajectory of the hoisting can be obtained as Figure 14 shown.

[0232] The PWM pulse width modulation module adjusts the voltage signal by receiving the modulation signal. Its internal structure is Figure 15 shown.

[0233] The overall built simulation model is Figure 16 shown.

[0234] The parameters of the motor can be set for simulation, Figure 16 and this is the speed image of the motor tracking the planned trajectory obtained.

[0235] Through Figure 17 it can be seen that the output speed of the motor can effectively track the planned trajectory signal. When the trajectory approaches the deceleration target position until it completely reaches the end point, the motor starts to track and decelerate. It can be seen from the image that the motor can perform effective flexible deceleration during the deceleration time. Compared with Figure 18 it can be clearly seen that the speed of the motor has been well adjusted and the control target is basically achieved.

[0236] 3. Experimental Verification

[0237] 3.1 Experimental Scheme

[0238] Based on the built platform system and the designed control algorithm, the experimental scheme steps can be determined as

[0239] (1) Ensure that all the connecting wires of the platform system are normal. Use the basic control program in the upper computer to control the trolley, the bridge and the hook, and confirm that all parts of the bridge crane are in good condition without abnormalities.

[0240] (2) Connect the force sensor of the hardware-in-the-loop experimental device to the DC power supply, set the serial port in its communication software, and wait for the communication software interface to show normal connection.

[0241] (3) Horizontally calibrate the six-axis angle sensor of the hardware-in-the-loop experimental device to ensure it is in the horizontal zero position and then enter the normal working state.

[0242] (4) Use the wireless transmission function in the upper computer to write the compiled PLC algorithm program.

[0243] (5) Lift the load to the target height.

[0244] (6) Press the start button and wait for the asynchronous motor to drive the load to fall onto the hardware-in-the-loop experimental device.

[0245] (7) Start recording the data collected by the sensor after the load is stationary on the hardware-in-the-loop experimental device.

[0246] (8) Lift the load and then let it fall to the ground, and return the bridge crane to its original position to ensure it is in good condition and safe.

[0247] (9) Organize and compare the collected data and images to verify the effectiveness of the actual use of the algorithm.

[0248] Conduct the following several groups of experiments based on the established experimental steps:

[0249] (1) Lift a 100KG load to a height of 4m and let it fall from a stationary state.

[0250] (2) Lift a 500KG load to a height of 4m and let it fall from a stationary state.

[0251] (3) Lift a 100KG load to a height of 2m and let it fall from a stationary state.

[0252] (4) Lift a 500KG load to a height of 2m and let it fall from a stationary state.

[0253] (5) Control experiment: Without using the two designed control methods, only relying on the basic motion control program, let a 500KG load fall from a height of 4m.

[0254] For the other four groups of experiments except the control experiment, both of the two designed algorithms need to be used respectively.

[0255] 3.2 Experimental results and analysis

[0256] As Figure 19As shown, it can be seen from the control group experiment that the force received by the experimental device increases rapidly in a short period of time. This indicates that without control, the impact force of the load on the vehicle will be very large, causing a hard impact. When the load completely falls on the platform, it can only stabilize by relying on the buffering of the spring, which will also have a certain negative impact on the service life of the spring damper. From the images fed back by the angle sensor, at the initial moment, the angles of the X, Y, and Z axes are 0°, 0°, and 90°. However, after the load contacts the platform, the angle jitter is very obvious. If a precision instrument is hoisted, it will inevitably affect its interior.

[0257] Verification experiment results of the flexible falling control method of the S-curve speed regulation algorithm

[0258] As Figures 20 - 23 shown:

[0259] Comparing experiment (1), experiment (2), and the control group experiment, it can be seen that when 100 Kg and 500 kg loads fall from a height of 4 m respectively, the pressure received by the semi-physical experimental device is buffered, and there is no situation where the pressure increases sharply in the control group, indicating that the control algorithm achieved the control effect required by the target during the experiment. From the data of the angle sensor, it can be seen that the platform is very stable after the load contacts the platform, basically stabilizing near the initial angle.

[0260] Comparing experiment (1) with experiment (3), and experiment (2) with experiment (4), it can be seen that good control effects can be achieved when loads of the same weight fall from different heights.

[0261] Comparing experiment (1) with experiment (2), and experiment (3) with experiment (4), it can be known that for loads of different weights falling from the same height, the designed control method can make them fall flexibly and stably. Although the slope of the force curve of the 500 Kg load is larger than that of the 100 kg load, and the vibration of the platform is also slightly larger, the overall control effect meets the target requirements.

[0262] The above-described embodiments are only preferred specific implementation manners of the present invention, and the protection scope of the present invention is not limited thereto. Any simple changes or equivalent replacements of technical solutions that can be obviously obtained by those skilled in the art within the technical scope disclosed by the present invention all belong to the protection scope of the present invention.

Claims

1. A flexible falling control method for bridge cranes based on an S-curve speed regulation algorithm, characterized in that, The control method includes the following steps: Step 1: Analyze the constraint conditions that the bridge crane is subject to during the load lifting process, and establish a model of the bridge crane at the equilibrium position during the load lifting process; Step 2: Based on the model of the bridge crane during the load lifting process, design the acceleration trajectory, velocity trajectory, and displacement trajectory of the load falling, that is, complete the S-shaped trajectory planning of the load falling; Step 3: After encoding the S-shaped trajectory into MATLAB, use the speed closed-loop PI control to achieve closed-loop adjustment of the speed of the three-phase AC asynchronous motor under the constant voltage-frequency ratio open-loop control, track the planned S-shaped trajectory, and realize the flexible falling of the load.

2. The flexible falling control method for a bridge crane based on the S-curve speed regulation algorithm according to claim 1, characterized in that In Step 1, the constraint conditions include: (1) Starting moment constraint: Among them, \(x(0)\) is the position at the starting moment of the suspended load, is the velocity at the starting moment of the suspended load, is the acceleration at the starting moment of the suspended load, \(\theta(0)\) is the swing angle at the starting moment of the suspended load, is the swing angular velocity at the starting moment of the suspended load, is the swing angular acceleration at the starting moment of the suspended load; (2) Constraints during the falling process: |θ(t)| ≤ θ max , 0 < t ≤ t d Among them, is the falling speed of the suspended load at time t, is the falling acceleration of the suspended load at time t, θ(t) is the swinging angle of the suspended load at time t, ν max is the upper limit of the speed during the falling process of the suspended load, a max is the upper limit of the acceleration during the falling process of the suspended load, θ max is the upper limit of the swinging angle during the falling process of the suspended load, t d is the total time of the entire falling process of the suspended load; (3) Constraint at the end of work When the work is over, the speed of the three-phase AC asynchronous motor of the bridge crane should drop to 0, and the load should land steadily on the platform. The constraint conditions at this time are: where \(x(t)\) is the position of the suspended load at time \(t\), is the falling velocity of the suspended load at time \(t\), is the falling acceleration of the suspended load at time \(t\), and \(\theta(t)\) is the swing angle of the suspended load at time \(t\), is the swing angular velocity of the suspended load at time \(t\), is the swing angular acceleration of the suspended load at time \(t\), and \(t\) d is the total time of the entire falling process of the suspended load.

3. A flexible falling control method for a bridge crane based on an S-curve speed regulation algorithm according to claim 2, characterized in that, The model of the bridge crane at the equilibrium position during the load lifting process established in Step 1 is: Where, m is the load mass; M is the trolley mass; l is the length of the suspension rope.

4. The flexible falling control method for a bridge crane based on the S-curve speed regulation algorithm according to claim 3, characterized in that, The specific steps of Step 2 are as follows: Step 201: The motion trajectory of the load is actually analyzed from the perspective of acceleration first. After analyzing the acceleration, the acceleration trajectory of the load is obtained through integration: Step 202: During the acceleration change process, introduce a transition link to overcome the sudden impact, and add a sine curve to the acceleration trajectory: where A is the coefficient to be determined and t d is the total time for the entire falling process of the suspended load; Step 203: Integrate the formula in Step 202 over time to obtain the velocity trajectory of the load: Where, a1 and a2 are coefficients to be determined; Step 204: Integrate the velocity trajectory of the load over time to obtain the displacement trajectory of the load: Where, b1 and b2 are coefficients to be determined; Step 205: Use the constraint conditions to eliminate the undetermined coefficients in the above formula, and the effective displacement trajectory, velocity trajectory, and acceleration trajectory of the load can be obtained: where x d is the target position of the suspended load falling.

5. A flexible falling control method for a bridge crane based on an S-curve speed regulation algorithm according to claim 4, characterized in that, The specific implementation method of Step 4 is: Input the S-shaped trajectory tracking control signal into the low-frequency voltage compensation module through the speed closed-loop PI control module. At the same time, the frequency increase speed limit module outputs a frequency limit signal to the low-frequency voltage compensation module to keep the voltage-frequency ratio unchanged; The SPWM modulation drive module modulates the voltage and frequency to generate a sine pulse width modulation wave to send a speed control signal to the inverter. The output speed is collected by the sensor and fed back to the speed closed-loop PI control module to achieve closed-loop adjustment of the speed of the three-phase AC asynchronous motor.

6. A flexible falling control system for a bridge crane based on an S-curve speed regulation algorithm, characterized in that, Including: S-shaped curve trajectory planning module, which executes Steps 1 - 2 described in claim 4 to generate the S-shaped trajectory of the load falling; Speed loop PI control module, which receives the S-shaped trajectory, combines the control signal to achieve closed-loop adjustment of the speed of the three-phase AC asynchronous motor under the constant voltage-frequency ratio open-loop control, and outputs a speed adjustment signal; Frequency increase speed limit module, which is used to limit the frequency to avoid the impact of current and torque caused by too fast speed increase; Low-frequency voltage compensation module, which receives the input frequency limit signal and speed adjustment signal to keep the voltage-frequency ratio of the three-phase AC asynchronous motor unchanged; The SPWM modulation drive module generates a sinusoidal pulse width modulation wave to send a control signal to the inverter, and the control signal is returned to the speed loop PI control module.

7. A flexible falling control device for a bridge crane based on an S-curve speed regulation algorithm, the device comprising a memory storing a computer program and a processor for executing the computer program, characterized in that, When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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