A two-stage speed control method for belt conveyor

Abstract

The present invention provides a two-stage speed control method for a belt conveyor, which relates to the field of belt conveyor control and specifically includes the following steps: establishing a dynamic model with equality constraints; treating the speed of the control target as a constraint and designing robust control for the equality constraint portion in conjunction with the dynamic model; transforming the dynamic model so that it conforms to the state form of the inequality constraints; performing inequality constraint control design on the transformed dynamic model; and performing simulation verification on the belt conveyor system. The technical solution of the present invention overcomes the problem in the prior art of being unable to accurately limit the speed error of a belt conveyor system to within a desired range.

Description

Technical Field

[0001] The invention relates to the field of belt conveyor control, and in particular to a two-stage speed control method for a belt conveyor. Background Art

[0002] During the startup of long-distance belt conveyors, it is crucial to avoid belt breakage and material accumulation. Analyzing the overall operating mechanism of a long-distance belt conveyor, the startup process can be understood as an acceleration process. As speed changes, the corresponding acceleration also changes, causing varying degrees of elastic deformation in the conveyor belt and generating a certain amount of dynamic tension. Therefore, speed control is particularly important. To prevent such events, the displacement difference between adjacent subsystems must be kept within a defined range. This is achieved by limiting the speed error of each subsystem.

[0003] Therefore, a two-stage speed control method for a belt conveyor is needed that can accurately limit the system speed error to a desired range. Summary of the Invention

[0004] The main purpose of the present invention is to provide a two-stage speed control method for a belt conveyor, so as to solve the problem in the prior art that the speed error of the belt conveyor system cannot be accurately limited to a desired range.

[0005] To achieve the above object, the present invention provides a two-stage speed control method for a belt conveyor, which specifically includes the following steps:

[0006] S1, establish a dynamic model of equality constraints.

[0007] S2, the speed of the control target is regarded as a constraint, and the dynamic model is combined to perform robust control design of the equality constraint part.

[0008] S3, transforming the dynamic model so that the dynamic model conforms to the state form of the inequality constraint.

[0009] S4, performing inequality constraint control design on the dynamic model converted in step S3.

[0010] S5, simulate and verify the belt conveyor system.

[0011] Furthermore, step S1 specifically includes the following steps:

[0012] S1.1, consider a dynamic model of a belt conveyor system :

[0013] (1);

[0014] in, 、 、 、 They represent the mass matrix, stiffness matrix, damping matrix and friction matrix of the belt conveyor system respectively. , , are the displacement, velocity and acceleration of the belt conveyor system respectively;

[0015] S1.2, assuming that the desired constraints are of the first-order form:

[0016] (2);

[0017] in, is the coefficient matrix, For the The speed of each subsystem; write formula (2) into matrix form:

[0018] (3);

[0019] in, ; and For dimension.

[0020] S1.3, perform a differentiation on the constraint equation (2):

[0021] (4);

[0022] in,

[0023] (5);

[0024] (6);

[0025] Rewrite Equation (4) as a second-order constraint:

[0026] (7);

[0027] in, ;

[0028] The matrix form of formula (7) is:

[0029] (8);

[0030] in, .

[0031] Furthermore, step S1 further includes the following steps:

[0032] S1.4, introduce the control force and obtain the converted dynamic model:

[0033] (9);

[0034] in,

[0035] ;

[0036] ; ;

[0037] in, is the quality of each subsystem, , is the stiffness of each subsystem, is the damping of each subsystem, is the belt conveyor system error matrix, is the error of each subsystem, is the speed error matrix of the belt conveyor system, is the speed error of each subsystem, is the acceleration error matrix of the belt conveyor system, is the acceleration error of each subsystem, , , , each subsystem has the same expected displacement , expected speed and expected acceleration , 、 and are the displacement, velocity and acceleration of each subsystem respectively, is the expected acceleration matrix of the belt conveyor system, , is the friction force of each subsystem, is the control force matrix of the belt conveyor system, is the control force of each subsystem, is the inverse tangent function.

[0038] S1.5, introduce the uncertainty of the belt conveyor system, and divide the actual belt conveyor system into a deterministic part and an uncertain part, and obtain:

[0039] (10);

[0040] (11);

[0041] (12);

[0042] (13);

[0043] in, is the nominal part of the belt conveyor system, is the uncertainty part of the belt conveyor system, is an uncertain time-varying parameter, let , ,get .

[0044] S1.6, Assumptions:

[0045] (14);

[0046] in, is the identity matrix, is the constraint matrix, and there is an unknown constant , so that all All meet the following requirements:

[0047] (15);

[0048] in, represents the smallest eigenvalue of the matrix, is an uncertain parameter boundaries.

[0049] Furthermore, step S2 specifically includes the following steps:

[0050] S2.1, the control of the nominal part Designed to:

[0051] (16);

[0052] in, , “+” represents the Moore-Penrose generalized inverse.

[0053] Compensation control for nominal parts Designed to:

[0054] (17);

[0055] in, is a positive constant, the error between the expected trajectory and the actual trajectory Expressed as:

[0056] (18).

[0057] S2.2, Assumption: There exists an unknown constant vector And a known function , for all have:

[0058] (19);

[0059] For each right Perform linear decomposition: there exists a function satisfy:

[0060] (20).

[0061] Control of uncertainty Designed to:

[0062] (twenty one);

[0063] is a positive tunable control parameter, and:

[0064] (twenty two);

[0065] The total control input for:

[0066] (twenty three).

[0067] Furthermore, step S2 further includes the following steps:

[0068] S2.3, to prove the stability, we choose the Lyapunov function as:

[0069] (twenty four);

[0070] in, is a symmetric matrix;

[0071] Derivative of formula (24) yields:

[0072] (25).

[0073] S2.4, to simplify formula (25), substitute formula (18) to obtain:

[0074] (26).

[0075] According to formulas (16), (17), (18), and let , continue to simplify and get:

[0076] (27);

[0077] Solved:

[0078] (28).

[0079] Furthermore, step S3 specifically includes the following steps:

[0080] S3.1, let ,and , formula (1) is rewritten as:

[0081] ;

[0082] (29);

[0083] in, ,make ,get:

[0084] (30);

[0085] Then, yes Make restrictions so that:

[0086] (31);

[0087] in, 、 Respectively The upper and lower bounds of .

[0088] S3.2, transform the state variables of the belt conveyor system using the diffeomorphism theory;

[0089] (32);

[0090] in, are the transformed coordinates, is the conversion equation, , , , is the speed boundary set.

[0091] S3.3, yes Taking the derivative we get:

[0092] (33).

[0093] Furthermore, step S4 specifically includes the following steps:

[0094] S4.1, the control of inequality constraints Applied in belt conveyor systems:

[0095] (34);

[0096] in, It's about function.

[0097] Apply inequality constraints Designed to:

[0098] (35);

[0099] in, , and is a positive constant, we can get the inequality constraint by adding After for:

[0100] (36).

[0101] S4.2, find a Lyapunov function and a strictly monotonically increasing increasing function ,in, satisfy:

[0102] (37);

[0103] (38).

[0104] At this point, the derivative of the Lyapunov function is:

[0105] (39).

[0106] For the first term in formula (39), based on formula (35), we get:

[0107] (40).

[0108] For the second term in formula (39):

[0109] (41).

[0110] For the third term in formula (39):

[0111] (42).

[0112] Combining formulas (41) and (42), we get:

[0113] (43);

[0114] in, is a constant;

[0115] at this time,

[0116] (44).

[0117] The present invention has the following beneficial effects:

[0118] This paper designs a two-layer speed control method to limit the speed error of each belt conveyor subsystem. Under the first-layer control method (equality constraints), the speed of each belt conveyor subsystem can be initially controlled, ensuring that the belt conveyor system satisfies both uniformly bounded and uniformly ultimately bounded requirements. However, the speed of the subsystem still fluctuates significantly, falling outside the ideal speed range. Therefore, a second-layer control method (inequality constraints) is designed. By applying inequality constraints, the system speed is effectively and precisely controlled to within the desired range, resolving the issue of excessive speed fluctuations. Furthermore, the belt conveyor system, after adding inequality constraints, satisfies both uniformly bounded and uniformly ultimately bounded requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0119] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0120] Figure 1 A flow chart showing a two-stage speed control method for a belt conveyor according to the present invention is shown.

[0121] Figure 2 A schematic structural diagram of a belt conveyor system model of the present invention is shown.

[0122] Figure 3 A schematic diagram of verifying the control effect of the present invention is shown.

[0123] Figure 4 Shown Figure 3 A magnified detail of point A.

[0124] Figure 5 Shown Figure 3 A magnified view of the detail at point B.

[0125] Figure 6 The error accumulation comparison diagram of the three subsystems during the simulation process is shown. DETAILED DESCRIPTION

[0126] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0127] like Figure 1 A two-stage speed control method for a belt conveyor is shown, comprising the following steps:

[0128] S1, establish a dynamic model of equality constraints.

[0129] S2, the speed of the control target is regarded as a constraint, and the dynamic model is combined to perform robust control design of the equality constraint part.

[0130] S3, transforming the dynamic model so that the dynamic model conforms to the state form of the inequality constraint.

[0131] S4, performing inequality constraint control design on the dynamic model converted in step S3.

[0132] S5, simulate and verify the belt conveyor system.

[0133] Specifically, step S1 includes the following steps:

[0134] S1.1, consider a dynamic model of a belt conveyor system :

[0135] (1);

[0136] in, 、 、 、 They represent the mass matrix, stiffness matrix, damping matrix and friction matrix of the belt conveyor system respectively. , , are the displacement, velocity and acceleration of the belt conveyor system, respectively.

[0137] S1.2, assuming that the desired constraints are of the first-order form:

[0138] (2);

[0139] in, is the coefficient matrix, For the The speed of each subsystem; these constraints may not be integrable, so it is non-holonomic. Write formula (2) in matrix form:

[0140] (3);

[0141] in, ; and For dimension.

[0142] S1.3, assuming that formula (2) is smooth enough, it can be transformed into a second-order constraint by differentiation. Differentiate the constraint equation formula (2) once:

[0143] (4);

[0144] in,

[0145] (5);

[0146] (6);

[0147] Rewrite Equation (4) as a second-order constraint:

[0148] (7);

[0149] in, ;

[0150] The matrix form of formula (7) is:

[0151] (8);

[0152] in, .

[0153] Specifically, step S1 further includes the following steps:

[0154] S1.4, introduce the control force and obtain the converted dynamic model:

[0155] (9);

[0156] in,

[0157] ;

[0158] ; ;

[0159] in, is the quality of each subsystem, , is the stiffness of each subsystem, is the damping of each subsystem, is the belt conveyor system error matrix, is the error of each subsystem, is the speed error matrix of the belt conveyor system, is the speed error of each subsystem, is the acceleration error matrix of the belt conveyor system, is the acceleration error of each subsystem, , , , each subsystem has the same expected displacement , expected speed and expected acceleration , 、 and are the displacement, velocity and acceleration of each subsystem respectively, is the expected acceleration matrix of the belt conveyor system, , is the friction force of each subsystem, is the control force matrix of the belt conveyor system, is the control force of each subsystem, is the inverse tangent function.

[0160] S1.5, introduce the uncertainty of the belt conveyor system, and divide the actual belt conveyor system into a deterministic part and an uncertain part, and obtain:

[0161] (10);

[0162] (11);

[0163] (12);

[0164] (13);

[0165] in, is the nominal part of the belt conveyor system, is the uncertainty part of the belt conveyor system, is an uncertain time-varying parameter, let , ,get .

[0166] S1.6, Assumptions:

[0167] (14);

[0168] in, is the identity matrix, is the constraint matrix, and there is an unknown constant , so that all All meet the following requirements:

[0169] (15);

[0170] in, represents the smallest eigenvalue of the matrix, is an uncertain parameter The uncertain parameters are bounded because infinite uncertainty would lead to infinite driving forces, which is impossible in mechanics.

[0171] Specifically, step S2 includes the following steps:

[0172] S2.1, the control of the nominal part Designed to:

[0173] (16);

[0174] in, , “+” represents the Moore-Penrose generalized inverse;

[0175] Compensation control for nominal parts Designed to:

[0176] (17);

[0177] in, is a positive constant, the error between the expected trajectory and the actual trajectory Expressed as:

[0178] (18).

[0179] S2.2, Assumption: There exists an unknown constant vector And a known function , for all have:

[0180] (19);

[0181] For each right Perform linear decomposition: there exists a function satisfy:

[0182] (20);

[0183] Control of uncertainty Designed to:

[0184] (twenty one);

[0185] is a positive tunable control parameter, and:

[0186] (twenty two);

[0187] The total control input for:

[0188] (twenty three).

[0189] Furthermore, step S2 further includes the following steps:

[0190] S2.3, to prove the stability, we choose the Lyapunov function as:

[0191] (twenty four);

[0192] in, is a symmetric matrix;

[0193] Derivative of formula (24) yields:

[0194] (25).

[0195] S2.4, to simplify formula (25), substitute formula (18) to obtain:

[0196] (26).

[0197] According to formulas (16), (17), (18), and let , continue to simplify and get:

[0198] (27);

[0199] Solved:

[0200] (28);

[0201] when When is large enough, the belt conveyor system satisfies the conditions of uniformly bounded and uniformly eventually bounded.

[0202] Specifically, step S3 includes the following steps:

[0203] S3.1, let ,and , formula (1) is rewritten as:

[0204] ;

[0205] (29);

[0206] in, ,make ,get:

[0207] (30);

[0208] Then, yes Make restrictions so that:

[0209] (31);

[0210] in, 、 Respectively The upper and lower bounds of .

[0211] S3.2, transform the state variables of the belt conveyor system using the diffeomorphism theory;

[0212] (32);

[0213] in, are the transformed coordinates, is the conversion equation, , , , is the speed boundary set.

[0214] S3.3, yes Taking the derivative we get:

[0215] (33).

[0216] Based on formula (33), it has been proved that the system without inequality constraints conforms to the uniform boundedness and uniformly eventually boundedness. is bounded. Its value range is (0,1). Therefore, for all ( ), there exists a ,have ,in, for The upper bound of .

[0217] Specifically, step S4 includes the following steps:

[0218] S4.1, the control of inequality constraints Applied in belt conveyor systems:

[0219] (34);

[0220] in, It's about function.

[0221] Apply inequality constraints Designed to:

[0222] (35);

[0223] in, , and is a positive constant, we can get the inequality constraint by adding After for:

[0224] (36).

[0225] S4.2, find a Lyapunov function and a strictly monotonically increasing increasing function ,in, satisfy:

[0226] (37);

[0227] (38);

[0228] At this point, the derivative of the Lyapunov function is:

[0229] (39).

[0230] For the first term in formula (39), based on formula (35), we get:

[0231] (40).

[0232] For the second term in formula (39):

[0233] (41).

[0234] For the third term in formula (39):

[0235] (42).

[0236] Combining formulas (41) and (42), we get:

[0237] (43);

[0238] in, is a constant;

[0239] at this time,

[0240] (44).

[0241] when When large enough, the Lyapunov function is negative definite, so the system after adding the inequality control force satisfies the uniformly bounded and uniformly ultimately bounded conditions.

[0242] Step S5 is specifically as follows:

[0243] Figure 2 The belt conveyor system shown is the control target of the present invention. This system considers two drive wheels and one tensioning pulley and is divided into three subsystems (Subsystem 1, Subsystem 2, and Subsystem 3). The system also includes two drive wheels and one tensioning pulley. To achieve stricter speed control of the belt conveyor system and reduce its accident rate, a dynamic model with equality constraints is first established. The speed of the control target is treated as a constraint. Robust control design for the equality constraint portion is performed in conjunction with a dynamic model. The dynamic model is then transformed to conform to the state form of inequality constraints. Inequality constraint control design is performed in conjunction with the transformed model, and the system is simulated and verified. The technical solution of the present invention overcomes the problems of the prior art, such as the inability to effectively and accurately control the system speed within the expected range and the excessively large speed fluctuation boundary of the system.

[0244] The present invention first performs equality constraint control on the nominal part and the uncertain part in the dynamic model. The total control force of the equality constraint is u. Then the dynamic model is transformed and the system state is transformed by using differential homeomorphism. The control force of the inequality constraint is proposed according to the transformed system. ,Finally, the system obtains the control output torque through a two-layer control method, achieving excellent control effect.

[0245] like Figure 3 As shown in Figure 2, the control effect of a two-stage speed control method for a belt conveyor is compared with that of sliding film control (SMC). Figure 4 、 Figure 5 As shown, the speed error of the two-level speed control method reaches the desired speed throughout the acceleration and stabilization phases and is within the given limits (±0.1). While the speed under SMC control can reach the desired speed, the speed fluctuation is too large and does not achieve the given accuracy. Furthermore, regardless of the given desired speed, the two-level control method of the present invention can achieve consistent and ultimately bounded results for both the desired speed and the desired error.

[0246] like Figure 6As shown in FIG, it is the error accumulation diagram of the three subsystems during the simulation process. Compared with SMC control, the two-layer control method of the present invention has more precise speed control, smaller error, smaller cumulative error, and is more in line with our expectations.

[0247] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A two-stage speed control method for a belt conveyor, characterized in that: The specific steps include: S1, establish a dynamic model with equality constraints; S2, considers the speed of the control target as a constraint and combines the dynamic model to perform robust control design of the equality constraint part; S3, transforming the dynamic model so that the dynamic model conforms to the state form of the inequality constraint; S4, performing inequality constraint control design on the dynamic model converted in step S3; S5, simulation verification of the belt conveyor system; Step S1 specifically includes the following steps: S1.1, consider a dynamic model of a belt conveyor system : （1）； in, 、 、 、 They represent the mass matrix, stiffness matrix, damping matrix and friction matrix of the belt conveyor system respectively. , , are the displacement, velocity and acceleration of the belt conveyor system respectively; S1.2, assuming that the desired constraints are of the first-order form: （2）； in, is the coefficient matrix, For the The speed of each subsystem; write formula (2) into matrix form: （3）； in, ; and is the dimension; S1.3, perform a differentiation on the constraint equation (2): （4）； in, （5）； （6）； Rewrite Equation (4) as a second-order constraint: （7）； in, ; The matrix form of formula (7) is: （8）； in, .

2. A two-stage speed control method for a belt conveyor according to claim 1, characterized in that: Step S1 also includes the following steps: S1.4, introduce the control force and obtain the converted dynamic model: （9）； in, ； ； ； in, is the quality of each subsystem, , is the stiffness of each subsystem, is the damping of each subsystem, is the belt conveyor system error matrix, is the error of each subsystem, is the speed error matrix of the belt conveyor system, is the speed error of each subsystem, is the acceleration error matrix of the belt conveyor system, is the acceleration error of each subsystem, , , , each subsystem has the same expected displacement , expected speed and expected acceleration , 、 and are the displacement, velocity and acceleration of each subsystem respectively, is the expected acceleration matrix of the belt conveyor system, , is the friction force of each subsystem, is the control force matrix of the belt conveyor system, is the control force of each subsystem, is the inverse tangent function; S1.5, introduce the uncertainty of the belt conveyor system, and divide the actual belt conveyor system into a deterministic part and an uncertain part, and obtain: （10）； （11）； （12）； （13）； in, is the nominal part of the belt conveyor system, is the uncertainty part of the belt conveyor system, is an uncertain time-varying parameter, let , ,get ; S1.6, Assumptions: （14）； in, is the identity matrix, is the constraint matrix, and there is an unknown constant , so that all All meet the following requirements: （15）； in, represents the smallest eigenvalue of the matrix, is an uncertain parameter boundaries.

3. The two-stage speed control method for a belt conveyor according to claim 1, characterized in that: Step S2 specifically includes the following steps: S2.1, the control of the nominal part Designed to: （16）； in, , "+" represents the Moore-Penrose generalized inverse; Compensation control for nominal parts Designed to: （17）； in, is a positive constant, the error between the expected trajectory and the actual trajectory Expressed as: （18）； S2.2, Assumption: There exists an unknown constant vector And a known function , for all have: （19）； For each right Perform linear decomposition: there exists a function satisfy: （20）； Control of uncertainty Designed to: （21）； is a positive tunable control parameter, and: （22）； The total control input for: （23）。 4. A two-stage speed control method for a belt conveyor according to claim 3, characterized in that: Step S2 also includes the following steps: S2.3, to prove the stability, we choose the Lyapunov function as: （24）； in, is a symmetric matrix; Derivative of formula (24) yields: （25）； S2.4, to simplify formula (25), substitute formula (18) to obtain: （26）； According to formulas (16), (17), (18), and let , continue to simplify and get: （27）； Solved: （28）； when When is large enough, the belt conveyor system satisfies the conditions of uniformly bounded and uniformly eventually bounded.

5. The two-stage speed control method for a belt conveyor according to claim 1, characterized in that: Step S3 specifically includes the following steps: S3.1, let ,and , formula (1) is rewritten as: ； （29）； in, ,make ,get: （30）； Then, yes Make restrictions so that: （31）； in, 、 Respectively The upper and lower bounds of S3.2, transform the state variables of the belt conveyor system using the diffeomorphism theory; （32）； in, are the transformed coordinates, is the conversion equation, , , , is the set speed boundary; S3.3, yes Taking the derivative we get: （33）。 6. A two-stage speed control method for a belt conveyor according to claim 1, characterized in that: Step S4 specifically includes the following steps: S4.1, the control of inequality constraints Applied in belt conveyor systems: （34）； in, It's about function; Apply inequality constraints Designed to: （35）； in, , and is a positive constant, we can get the inequality constraint by adding After for: （36）； S4.2, find a Lyapunov function and a strictly monotonically increasing increasing function ,in, satisfy: （37）； （38）； At this point, the derivative of the Lyapunov function is: （39）； For the first term in formula (39), based on formula (35), we get: （40）； For the second term in formula (39): （41）； For the third term in formula (39): （42）； Combining formulas (41) and (42), we get: （43）； in, is a constant; at this time, （44）。

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