CN116551695A - Hydraulic swing joint position servo system and NDOB-SMC control method thereof - Google Patents
Hydraulic swing joint position servo system and NDOB-SMC control method thereof Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J17/00—Joints
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
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Abstract
The invention relates to a hydraulic swing joint position servo system and an NDOB-SMC control method thereof, wherein the hydraulic swing joint position servo system is designed firstly, a servo valve and a cylinder body of a hydraulic cylinder are integrated and directly connected in the system, and an oil pipe is abandoned for connection, so that the structure is more compact, and part of interference factors are reduced; secondly, designing a sliding mode control strategy based on a nonlinear interference observer, combining the nonlinear interference observer with sliding mode control, fully playing respective advantages, and improving the tracking precision and response speed of the hydraulic swing joint; and finally, combining a rich element model library of the AMEsim platform and strong numerical operation capability of the Matlab platform, and realizing the joint simulation of the two platforms by creating an S-function interface to verify the effectiveness and superiority of the proposed control method.
Description
Technical field:
the invention relates to the technical field of hydraulic swing joint control, in particular to a hydraulic swing joint position servo system and an NDOB-SMC control method thereof.
The background technology is as follows:
at present, most robot joints are driven by motors, but the output power is low, and particularly in special tasks such as rescue, exploration, military and the like, the load capacity of the robot joints is difficult to meet the requirements. Through researches and discoveries of scholars, the hydraulic robot driven by the electrohydraulic servo system has the advantages of high unit power-volume ratio, stable operation and high response speed, is gradually applied to the fields of modern industry, military and the like, and the control problem of the hydraulic robot is also gradually focused by people.
The electrohydraulic servo system is affected by the nonlinearity of the flow of the servo valve, the uncertainty of system parameters and models and other interference factors, and the difficulty in developing a high-performance controller of the electrohydraulic servo system is increased. The conventional PID control is widely applied due to the characteristics of simple algorithm, independent control parameters and the like, but has poor positioning control capability in the nonlinear field such as an electrohydraulic servo system. Therefore, many scholars propose many control strategies for the problems of nonlinearity of the system, uncertainty of parameters and influence of external interference on tracking accuracy of the system. For example, adaptive control, robust control, fuzzy control, active tamper control, observer-based control, sliding mode control, etc. Compared with the sliding mode control, the sliding mode control is insensitive to system parameter change and disturbance, has good adaptability and robustness, and is widely applied to the fields of military, aviation, traffic and other nonlinear control. However, since the sliding mode exists in the sliding mode, the "buffeting" phenomenon is caused when the input is controlled, so how to weaken buffeting without affecting the performance of the sliding mode controller is the subject of research by a plurality of students at present. For example, rubagotti et al design a slip-form surface in the form of an integral that allows for increased system robustness. The sliding mode controller designed by Xue et al can enable the position error to be converged to zero in a certain time, but the sliding mode controller is not required to be interfered by the outside, and the buffeting phenomenon still exists in the output parameters of the controller. Gao et al propose a terminal sliding mode control that converges faster and investigate adaptive sliding mode control laws. Yang et al propose a sliding mode controller based on self-adaptive high-order neural network, and through a method of combining a plurality of control strategies, buffeting of the sliding mode controller is reduced well, and better control accuracy is achieved. Thus, with increased system complexity and control requirements, many students have attempted to combine various control methods to achieve optimal performance of the overall control system. Some of these approaches, which have introduced disturbance observers, compensate for controller inputs, nonlinear disturbance observers are linear in comparison.
The design difficulty of the interference observer is greater, but the non-linear interference observer can better eliminate uncertainty and unknown interference existing in a non-linear system, and the interference is estimated in real time. For example, the interference observer used by Zhu et al successfully suppresses external interference and improves the accuracy of the system. Bu et al designed a novel nonlinear disturbance observer based on an improved sliding mode differentiator, which can effectively inhibit nonlinear disturbance, improve the robustness of the system, verify the effectiveness of the observer through simulation, simulate the designed observer, and improve the accuracy after the problem that the elasticity state cannot be measured is solved.
In the simulation experiment process, most scholars perform simulation experiments based on a single software platform at first. The method can effectively shorten development period, cost and risk and ensure better reliability. However, as the complexity of the system is higher and higher, the requirements are continuously improved, and the electro-hydraulic servo system has the characteristics of inherent nonlinear behavior, modeling uncertainty and the like, so that the establishment of an accurate mathematical model becomes very difficult, and the simulation experiment is carried out by adopting a single software platform, so that the requirement of the simulation at the present stage can not be met. Therefore, in recent years, some students adopt a combined simulation method to conduct researches and experiments on electrohydraulic servo systems and other related aspects, and the application fields of the combined simulation method mainly relate to automotive suspensions, machine tools, lifting actuators and the like. For the study of joint simulation, liu et al studied the modeling method of virtual prototypes and simplified the dynamics system to replace them, but the model was not built precisely. Zhang et al call the AMEsim platform by using the S-function interface, so that the joint simulation of the AMEsim and the Matlab platform is performed, the control strategy development capability of the electrohydraulic lifting system is enhanced, and the control precision of the proposed observer-sliding mode control strategy is well verified. In order to solve the problem of valve core blocking, chen et al simultaneously adopts three platforms of Matlab, AMEsim and Fluent to carry out joint simulation, and obtains key flow data of each oil port in the slide valve through experiments.
According to analysis and research of the existing literature, the existing scholars respectively make a great deal of research contributions in the aspects of sliding mode control, nonlinear disturbance observers, joint simulation and the like, but the method is particularly applied to a hydraulic swing joint position servo system, and particularly aims at the nonlinearity of an electrohydraulic position servo system and the uncertainty of a model thereof, and the technical problems of high-performance control and joint simulation verification of a control strategy are achieved.
The foregoing is not necessarily a prior art, and falls within the technical scope of the inventors.
The invention comprises the following steps:
the invention aims to solve the problems in the prior art and provides a hydraulic swing joint position servo system and an NDOB-SMC control method thereof, wherein the hydraulic swing joint position servo system is designed firstly, a servo valve and a cylinder body of a hydraulic cylinder are integrated and directly connected, and an oil pipe is abandoned to be connected, so that the structure is more compact, and part of interference factors are reduced; secondly, designing a sliding mode control strategy based on a nonlinear interference observer, combining the nonlinear interference observer with sliding mode control, fully playing respective advantages, and improving the tracking precision and response speed of the hydraulic swing joint; and finally, combining a rich element model library of the AMEsim platform and strong numerical operation capability of the Matlab platform, and realizing the joint simulation of the two platforms by creating an S-function interface to verify the effectiveness and superiority of the proposed control method.
The invention realizes the aim by adopting the following technical scheme:
the utility model provides a hydraulic swing joint position servo system, includes hydraulic swing joint, hydraulic swing joint includes the upper connecting plate, be equipped with the oscillating hydraulic cylinder on the upper connecting plate, the piston rod design of oscillating hydraulic cylinder becomes circular-arc, be equipped with down the connecting plate on the piston rod, the connecting plate is rotatory swing down along with the piston rod, the rotatory swing center department of connecting plate is equipped with angle sensor down, be equipped with the servo valve on the cylinder body of oscillating hydraulic cylinder, the servo valve is connected with the hydraulic pressure station, angle sensor is connected with the computer, the computer is connected with the servo valve.
The cylinder body is equipped with the hollow shaft corresponding to the rotation swing center department of lower connecting plate, the hollow shaft both ends are equipped with the bearing respectively, every be equipped with on the bearing one lower connecting plate, be equipped with the bearing shelves dish on the lower connecting plate lateral wall, two lower connecting plate symmetry is installed on the piston rod.
The cylinder body adopts the components of a whole that can function independently design, including interior cylinder and the outer cylinder of symmetry design, interior cylinder and outer cylinder pass through threaded connection, be equipped with the servo valve on the outer cylinder lateral wall, angle sensor sets up in the hollow shaft, angle sensor's pivot is installed on one of them lower connecting plate, and pivot and lower connecting plate's rotatory swing center collineation.
The NDOB-SMC control method of the hydraulic swing joint position servo system comprises the hydraulic swing joint position servo system, which comprises the following specific steps:
s1, establishing a mathematical model of a hydraulic swing joint position servo system, which specifically comprises the following steps:
establishing a load moment balance equation of the hydraulic swing joint position servo system, wherein the expression is as follows:
P L ＝p 1 -p 2 ；
k q ＝C d w(1/ρ) 1/2
wherein A is effective as pistonArea, P L For flow gain, p 1 For upper chamber pressure, p 2 For lower chamber pressure, C d Is the flow coefficient, w is the area gradient of the servo valve, ρ is the hydraulic oil density, R is the piston rod rotation radius, T L For external load torque, B p For equivalent viscous damping coefficient, J L In order for the moment of inertia to be of interest,all unmodeled interference terms in the system;
defining a state variable:
the equation of state of the hydraulic swing joint position servo system is expressed as:
wherein, alpha= [ alpha ] 1 ，α 2 ，α 3 ，α 4 ] T ,α 1 ＝B p R 2 /J L ，d 1 (t)＝[f(t，x 1 ，x 2 )+T L ]/J L ，d 1 (t) Complex interference, d, which is an uncertainty factor of a system mismatch model 2 (t)＝(4ARβ e /V t J L )Q(t)，d 2 (t) Complex interference, α, which is an uncertainty factor of a system matching model 2 ＝4ARβ e k t /V t J L ，α 3 ＝4A 2 R 2 β e /V t J L ，α 4 ＝4β e C i /V t ，λ 1 ＝[p s -x 3 sign (u) J L /AR] 1/2 ，β e Is the elastic modulus of oil liquid, V t Is the total volume of two cavities, Q (t) is a time-varying modeling error, u is the total control law of the system, and k t For total flow gain, C i For internal leakage flow coefficient，C e For external leakage flow coefficient, p s For the supply pressure;
s2, designing a supercoiled disturbance observer, which specifically comprises the following steps:
the supercoiled disturbance observer of the mismatch model is constructed with the following expression:
in the formula
Wherein parameter a 1 、a 2 All are positive numbers, d 1 The interference estimate of (t) is:
the supercoiled disturbance observer of the matching model is constructed with the following expression:
in the formula ,
wherein parameter a 3 、a 4 All are positive numbers, d 2 The interference estimate of (t) is:
s3, designing a sliding mode controller to obtain a system overall control law, wherein the method specifically comprises the following steps:
servo system for setting hydraulic swing joint positionThe angular expected signal of the system is x d The actual angular displacement output signal of the hydraulic swing joint position servo system is x 1 The error vector of the hydraulic swing joint position servo system is as follows:
order theThe control object may be rewritten as:
combining this with the equation of state of the hydraulic swing joint position servo system:
the conversion from this formula can be:
get [ c ] 1 ,c 2 ,1] T All are greater than zero, the switching function of the sliding mode surface is selected as follows:
s(x)＝c 1 e 1 +c 2 e 2 +e 3
conduct the derivation on the two sides and willThe equation is substituted to obtain:
wherein :
from the formulaAnd->Available compensation control law->The method comprises the following steps:
the design method of the sliding mode controller for selecting the exponential approach law comprises the following steps:
the total control law u of the system is obtained as follows:
in the formula ,k1 、k 2 Discontinuous gains of the sliding mode controller are larger than zero;
accurately controlling the hydraulic swing joint according to the total control law u of the system;
s4, carrying out a joint simulation experiment, which specifically comprises the following steps:
firstly, building a hydraulic swing joint position servo system model and setting parameters on an AMEsim platform, establishing a Simucosim interface, operating the hydraulic swing joint position servo system model to generate an S function and outputting information comprising angles, angular speeds and pressures so as to be connected with Matlab/Simulink; secondly, a sliding mode control model is established and operated on the Matlab/Simulink platform, an output control signal u is generated for the AMEsim platform, and real-time control of the AMEsim platform is achieved; and finally, the AMEsim platform feeds information back to the Matlab platform, so that joint simulation is realized.
In the step S1, 1: the angle expected signal of the hydraulic swing joint position servo system is x d ，x d ∈C 3 Under the normal working condition of the hydraulic swing joint position servo system, the swing type hydraulic cylinder meets the following conditions: p is 0 < p r ＜p 1 ＜p s ，0＜p r ＜p 2 ＜p s ，p 1 For upper chamber pressure, p 2 For lower chamber pressure, p s To supply pressure, p r Is the return oil pressure; and |P L Ratio of I to P s Is small enough to ensure alpha 2 λ 1 ≠0；
Setting 2: composite interference d i (t) is bounded, and d i (t) is conductive.
In the step S1, the lemma 1 is: setting 1.ltoreq.i.ltoreq.n, considering the controlled system:
wherein ,x～i Is a state variable d i (t) is complex interference, d i First order derivative of (t)Presence;
adopts a supercoiled control law:
u si (t)＝u 1i (t)+u 2i (t)；
setting: a, a i 、a i+1 Is positive and satisfies:
this can be achieved by:
so the hydraulic swing joint position servo system is stable, andconverging to zero in a limited time.
In the step S2, an estimated error between the supercoiled disturbance observer and the hydraulic swing joint position servo system is set as follows:
will beAnd (3) with
And (3) subtracting to obtain:
combining the above withThe combination is as follows:
as can be seen from the index 1, andWill converge to zero in a finite time, thus yielding d 1 The interference estimate of (t) is:
in the same way, willAnd (3) with
Subtraction gives:
as can be seen from the index 1, andWill converge to zero in a finite time, thus yielding d 2 The interference estimate of (t) is:
in the step S3, a Lyapunov function of the hydraulic swing joint position servo system is taken as follows:
simultaneously deriving two sides and leading toand
Substitution can be obtained:
from the formulaIt can be seen that when (gamma-k) 2 ) < 0 and k 1 > 0, then->The constant holds, and only when s=0,the closed loop system is stable.
The invention adopts the structure, and has the following beneficial effects:
on the basis of researches of other scholars, the hydraulic swing joint position servo system is creatively designed, and the system is improved in that a servo valve is directly connected with a cylinder body, so that the use of an oil liquid conveying pipeline between the servo valve and a traditional hydraulic cylinder is abandoned, the space utilization rate is greatly improved, the problem of nonlinearity of the volume change of the conveying pipeline caused by oil pressure and oil temperature is weakened, and part of interference factors are reduced. On the basis of the above, a sliding mode control strategy based on a nonlinear disturbance observer is designed, a mathematical model of the hydraulic swing joint position servo system is established, and on the basis, the method of the disturbance observer is adopted for compensating uncertain factors and disturbance of the system so as to weaken the influence of the uncertain factors and the disturbance on the hydraulic swing joint position servo system, and the whole controller adopts sliding mode control so as to improve the tracking precision and response speed of the hydraulic swing joint. And finally, constructing a model of the hydraulic swing joint position servo system by using an AMEsim platform, erecting a sliding mode controller based on a nonlinear interference observer on the Matlab/Simulink platform, and finally calling the AMEsim platform through an S-function interface to develop joint simulation, thereby verifying the effectiveness and superiority of the proposed control method.
Description of the drawings:
FIG. 1 is a schematic view of the structure of a hydraulic swing joint of the present invention;
FIG. 2 is a schematic view of a hydraulic swing joint according to another aspect of the present invention;
FIG. 3 is an exploded view of the hydraulic swing joint of the present invention;
FIG. 4 is an exploded view of another view of the hydraulic swing joint of the present invention;
FIG. 5 is a schematic view of the hydraulic swing joint of the present invention mounted on a wearable device;
FIG. 6 is a schematic diagram of the operation of the hydraulic swing joint position servo system of the present invention;
FIG. 7 is a schematic diagram of co-simulation between AMEsim16 and Matlab 2016a according to the present invention;
FIG. 8 is a schematic diagram of a hydraulic system model in AMEsim according to the present invention;
FIG. 9 is a schematic diagram of an NDOB-SMC controller in Matlab of the present invention;
FIG. 10 is a graph of simulation results of the constant load validation of the NDOB-SMC of the present invention;
FIG. 11 is a graph of a variable load sub-model and its mass change in accordance with the present invention;
FIG. 12 is a graph of the results of a joint simulation using variable load in accordance with the present invention;
FIG. 13 is a graph of angular error versus amplitude sinusoidal signal of the present invention;
FIG. 14 is a graph comparing angle tracking curves under a sinusoidal signal of amplitude of the present invention;
FIG. 15 is a graph comparing angle tracking curves under triangular wave signals according to the present invention;
FIG. 16 is a graph comparing angle tracking curves under a horn signal of the present invention;
FIG. 17 is a graph showing the comparison of angle errors under a triangular wave input signal according to the present invention;
FIG. 18 is a graph of angular error versus amplitude input signal for the present invention;
in the figure, 1, an upper connecting plate, 2, a swinging hydraulic cylinder, 201, a cylinder body, 202, a piston rod, 203, an inner cylinder, 204, an outer cylinder, 3, a lower connecting plate, 4, an angle sensor, 401, a rotating shaft, 5, a servo valve, 6, a hydraulic station, 601, an oil tank, 602, a hydraulic pump, 603, a motor, 604, a safety valve, 605, an oil absorption filter, 7, a computer, 8, a hollow shaft, 9, a bearing, 10, a bearing baffle, 11 and wearing equipment.
The specific embodiment is as follows:
in order to more clearly illustrate the general inventive concept, a detailed description is given below by way of example with reference to the accompanying drawings.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments.
Furthermore, the terms "upper," "lower," "rotational oscillation," "inner," "outer," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the location of an indicated technical feature.
In the present invention, for convenience of description and better understanding of the present application, the present application sets (n) after the formula, where n is a positive integer, and (n) represents only the sequential reference numerals of the formula.
In the present invention, unless explicitly stated and limited otherwise, the terms "provided," "configured," "connected," and the like are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrated; may be a mechanical connection; can be directly connected or indirectly connected through an intermediate medium. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
As shown in fig. 1-6, a hydraulic swing joint position servo system comprises a hydraulic swing joint, wherein the hydraulic swing joint comprises an upper connecting plate 1, a swing type hydraulic cylinder 2 is arranged on the upper connecting plate 1, a piston rod 202 of the swing type hydraulic cylinder 2 is designed to be arc-shaped, a lower connecting plate 3 is arranged on the piston rod 202, the lower connecting plate 3 follows the piston rod 202 to do rotary swing, an angle sensor 4 is arranged at the rotary swing center of the lower connecting plate 3, a servo valve 5 is arranged on a cylinder body 201 of the swing type hydraulic cylinder 2, the servo valve 5 is connected with a hydraulic station 6 through an oil way, the angle sensor 4 is connected with a computer 7 in a communication manner, and the computer 7 is connected with the servo valve 5 in a communication manner. In a hydraulically driven robot, two driving modes, a linear telescopic piston cylinder type and a swing cylinder type, are most common. The linear telescopic piston cylinder type hydraulic driving robot is used for indirectly realizing the movement of the robot joint, but the performance of the robot is restricted by the excessive size and the extra nonlinearity problem caused by the structure. According to the hydraulic swing joint with the integrated cylinder body and servo valve, the servo valve 5 is arranged on the swing type hydraulic cylinder 2, so that the use of an oil conveying pipeline between the servo valve 5 and a traditional hydraulic cylinder is abandoned, the space utilization rate is greatly improved, the problem of nonlinearity of volume change of the conveying pipeline caused by oil pressure and oil temperature is weakened, and part of interference factors are reduced. In the working process of the hydraulic swing joint position servo system, firstly, oil in the system flows under the action of a hydraulic pump 602 (a part of a hydraulic station 6, the hydraulic pump 602 is driven by a motor 603, an oil tank 601, a safety valve 604, an oil suction filter 605 and the like are further arranged in the whole oil way), the flow and the direction of the oil are controlled by a servo valve 5, and then the oil is supplied to a swing hydraulic cylinder 2, so that a piston rod 202 in the swing hydraulic cylinder 2 starts to operate and drives the joint to rotate and swing. When the joint swings, the angle sensor 4 observes the rotation angle of the swinging joint and outputs an angle signal to the computer 7, the computer 7 calculates the rotation angle, and a control signal is output to adjust the opening direction and the opening degree of the servo valve 5, so that the angle position control of the hydraulic swinging joint is realized. The hydraulic swing joint position servo system needs to be installed on the wearing equipment 11 in practical application, and interaction with a human body is achieved through the wearing equipment.
The cylinder 201 is provided with a hollow shaft 8 corresponding to the rotation swing center of the lower connecting plate 3, two ends of the hollow shaft 8 are respectively provided with a bearing 9, each bearing 9 is provided with one lower connecting plate 3, the outer side wall of the lower connecting plate 3 is provided with a bearing baffle disc 10, and the two lower connecting plates 3 are symmetrically arranged on the piston rod 202. Through design hollow shaft 8 and bearing 9 can support lower connecting plate 3 rotation, and lower connecting plate 3's structural strength and rotatory swing stability are better.
The cylinder 201 adopts the components of a whole that can function independently design, including the interior cylinder 203 of symmetrical design and outer cylinder 204, interior cylinder 203 and outer cylinder 204 pass through threaded connection (adopt threaded structure such as bolt, nut to connect, have schematically shown the installation hole site in the figure), be equipped with wind spring 11 between outer cylinder 204 and the lower connecting plate 3 that is located the outside, be equipped with wind spring 11 between interior cylinder 203 and the lower connecting plate 3 that is located the inboard, be equipped with servo valve 5 on the outer cylinder 204 lateral wall, angle sensor 4 sets up in hollow shaft 8, the pivot 401 of angle sensor 4 is installed on one of them lower connecting plate 3, just pivot 401 and the rotatory swing center collineation of lower connecting plate 3. The cylinder 201 adopts a split design, so that the piston rod 202 is convenient to mount, dismount and mount, and a required oil way is convenient to directly process on the outer cylinder 204, and the direct connection with the servo valve 5 (without oil pipe connection) is realized.
As shown in fig. 7-9, a method for controlling the NDOB-SMC of a hydraulic swing joint position servo system, comprising a hydraulic swing joint position servo system as described above, comprises the following specific steps:
s1, establishing a mathematical model of a hydraulic swing joint position servo system, which specifically comprises the following steps:
first, the flow equation of the servo valve 5 can be expressed as:
Q L ＝(Q 1 +Q 2 )/2 (2)
P L ＝p 1 -p 2 (3)
k q ＝C d w(1/ρ) 1/2 (4)
in the formula ,QL For load flow, Q 1 For the flow rate of the high-liquid-level cavity, Q 2 Is the flow rate of the low liquid level cavity, X v For spool displacement of spool valve, P s To supply pressure, P L For flow gain, C d The flow coefficient is w is the area gradient of the servo valve, and ρ is the hydraulic oil density;
wherein sign (X v ) Can be described as:
the present application uses a high response servo valve, so that the control of the servo valve 5 is proportional to the spool displacement, i.e. X v ＝k vu, wherein kv For the amplification gain of the servo amplifier, u is the overall control law of the system, so equation (1) can be converted into:
k t ＝k v k q (7)
wherein ,kt Is the total flow gain relative to u.
The flow continuity equation of the swing type hydraulic cylinder is as follows:
equations (8) and (9) above can be converted into pressure dynamics equations for the two chambers of the oscillating cylinder:
wherein Q (t) is a time-varying modeling error (caused by internal leakage, parameter bias, unmodeled pressure dynamics, etc.), C i For internal leakage flow coefficient, C e For external leakage flow coefficient, V 1 V is the effective volume of the upper cavity 2 For effective volume of lower cavity, V t Is the total volume of two cavities beta e Is the elastic modulus of oil.
The hydraulic swing joint is built and controlled based on an arc-shaped hydraulic cylinder mathematical model, and compared with a load force balance equation of a traditional straight rod piston hydraulic cylinder, the arc-shaped swing hydraulic cylinder adopts a load bending moment balance equation. Since the motion characteristics of the hydraulic cylinder power element are affected by the load, including viscous damping force, inertial force, elastic force, cylinder wall friction force and random load force, the load moment balance equation of the hydraulic swing joint position servo system can be expressed as:
P L ＝p 1 -p 2 (12)
k q ＝C d w(1/ρ) 1/2 (13)
wherein A is the effective area of the piston, p 1 For upper chamber pressure, p 2 R is the rotation of the piston rod for the lower cavity pressureRadius, T L For external load torque, B p For equivalent viscous damping coefficient, J L In order for the moment of inertia to be of interest,all unmodeled interference terms in the system;
defining a state variable:
the equation of state of the hydraulic swing joint position servo system is expressed as:
wherein, alpha= [ alpha ] 1 ，α 2 ，α 3 ，α 4 ] T ,α 1 ＝B p R 2 /J L ，d 1 (t)＝[f(t，x 1 ，x 2 )+T L ]/J L ，d 1 (t) Complex interference, d, which is an uncertainty factor of a system mismatch model 2 (t)＝(4ARβ e /V t J L )Q(t)，d 2 (t) Complex interference, α, which is an uncertainty factor of a system matching model 2 ＝4ARβ e k t /V t J L ，α 3 ＝4A 2 R 2 β e /V t J L ，α 4 ＝4β e C i /V t ，λ 1 ＝[p s -x 3 sign (u) J L /AR] 12 。
Suppose 1: the angle expected signal of the hydraulic swing joint position servo system is x d ，x d ∈C 3 Under the normal working condition of the hydraulic swing joint position servo system, the swing type hydraulic cylinder meets the following conditions: p is 0 < p r ＜p 1 ＜p s ，0＜p r ＜p 2 ＜p s, wherein pr Is the return oil pressure; and |P L Ratio of Ip s Is small enough to ensure alpha 2 λ 1 ≠0；
Suppose 2: composite interference d i (t) bounded, i.e. there is an unknown positive real number ψ i > 0, such that |d i (t)|≤ψ i At the same time d i (t) is conductive, i.e. exists
Lemma 1: setting 1.ltoreq.i.ltoreq.n, considering the controlled system:
wherein ,is a state variable d i (t) is complex interference, d i First order derivative of (t)>Presence;
adopts a supercoiled control law:
u si (t)＝u 1i (t)+u 2i (t) (17)
setting: a, a i 、a i+1 Is positive and satisfies:
this can be achieved by:
so the hydraulic swing joint position servo system is stable, andconverging to zero in a limited time.
S2, designing a supercoiled disturbance observer, which specifically comprises the following steps:
constructing a supercoiled disturbance observer of a mismatch model according to the formula (15) and on the premise of hypothesis 1 and hypothesis 2, wherein the expression is as follows:
in the formula
Wherein parameter a 1 、a 2 All are positive numbers, d 1 The interference estimate of (t) is:
according to formula (15) and under the premise of hypothesis 1 and hypothesis 2, constructing a supercoiled disturbance observer of a matching model, wherein the expression is as follows:
in the formula ,
wherein parameter a 3 、a 4 All are positive numbers, d 2 The interference estimate of (t) is:
the calculation and verification are carried out:
the estimation error between the supercoiled disturbance observer and the system is set as follows:
in the formula (15)Subtracting from formula (22):
combining formula (23) with formula (29) gives:
as can be seen from the index 1, andWill converge to zero in a finite time, thus yielding d 1 The interference estimate of (t) is given by equation (24).
In the same way, the compound of formula (15)Subtracting from formula (25):
as can be seen from the index 1, andWill converge to zero in a finite time, thus yielding d 2 The interference estimate of (t) is equation (27).
S3, designing a sliding mode controller to obtain a system overall control law, wherein the method specifically comprises the following steps:
setting the angle expected signal of the hydraulic swing joint position servo system as x d The actual angular displacement output signal of the hydraulic swing joint position servo system is x 1 The error vector of the hydraulic swing joint position servo system is as follows:
order theThe control object may be rewritten as:
combining this with the equation of state of the hydraulic swing joint position servo system:
the conversion from this formula can be:
get [ c ] 1 ,c 2 ,1] T All are greater than zero, the switching function of the sliding mode surface is selected as follows:
s(x)＝c 1 e 1 +c 2 e 2 +e 3 (36)
conduct the derivation on the two sides and willThe equation is substituted to obtain:
wherein :
from the formulaAnd->Available compensation control law->The method comprises the following steps:
the design method of the sliding mode controller for selecting the exponential approach law comprises the following steps:
the total control law u of the system is obtained as follows:
in formula (41), k 1 、k 2 Discontinuous gains of the sliding mode controller are larger than zero;
and accurately controlling the hydraulic swing joint according to the total control law u of the system.
Stability analysis:
the Lyapunov function of the system is taken as follows:
simultaneously deriving both sides of the formula (42), and substituting the formula (37) and the formula (40) into the available formula (43):
from the formulaIt can be seen that when (gamma-k) 2 ) < 0 and k 1 > 0, then->The constant holds, and only when s=0,the closed loop system is stable.
S4, carrying out a joint simulation experiment, which specifically comprises the following steps:
the nonlinearity and the modeling uncertainty of the electrohydraulic servo control system make it difficult to directly establish an accurate mathematical model, however, the AMEsim and Matlab joint simulation platform not only fuses the fluid simulation capability of AMEsim on the mechanical and hydraulic systems, but also fully utilizes the powerful numerical calculation capability of Matlab, therefore, the S-function interface is adopted to call the two platforms, the advantages of the two platforms are drawn, and perfect complementation can be realized. And a joint simulation model is built in Matlab 2016a and AMEsim16, so that the effectiveness of the proposed controller is verified.
Firstly, building a hydraulic swing joint position servo system model and setting parameters on an AMEsim platform, establishing a Simucosim interface, operating the hydraulic swing joint position servo system model to generate an S function, and outputting information including angles, angular speeds, pressure and the like so as to be connected with Matlab/Simulink; secondly, a sliding mode control model is established and operated on the Matlab/Simulink platform, an output control signal u is generated for the AMEsim platform, and real-time control of the AMEsim platform is achieved; and finally, the AMEsim platform feeds information back to the Matlab platform, so that joint simulation is realized.
The main parameters of the AMEsim hydraulic system are as follows:
to verify the effectiveness and superiority of the nonlinear disturbance observer-based sliding mode control method presented herein in a hydraulic swing joint position servo system. Simulation comparison experiments are carried out on three control schemes of NDOB-SMC, traditional PID and traditional SMC. The section mainly designs the following two simulation scenes (1), and when the condition that an input signal is a sinusoidal signal is considered, the NDOB-SMC controls the effectiveness analysis under two working conditions of constant load and variable load. (2) On the premise of changing load, sine signals, triangular wave signals and amplitude value signals are input to three control methods, and superiority analysis is carried out.
(1) Validity analysis
When the load force is constant, the swing time of the hydraulic swing joint is t=24 s, sinusoidal motion of-20 degrees to 20 degrees is carried out, sinusoidal signals with amplitude of 20 degrees, frequency of pi/4 and phase of-pi/2 are given, and the constant load is 15kg. The NDOB-SMC control parameters are k respectively 1 ＝3.9e3，k 2 ＝5，c 1 ＝4e4，c 2 =400. The interference observer parameters are as follows a 1 ＝5，a 2 ＝3，a 3 ＝5，a 4 =3, the gains of the interference observer are 0.8e-5, 0.6e-6, respectively. The simulation results are shown in fig. 10.
In order to better verify the effectiveness of the proposed control, a variable load is used instead of a constant load, but there is no submodel in AMEsim that meets the need, so a submodel with variable load is designed by using the AMEsim set function in the AMEsim platform, so that it varies sinusoidally within the range of 5kg to 25kg, and its submodel design diagram and load variation curve are shown in FIG. 11. As shown in fig. 12, the result of the joint simulation using variable load is shown.
The effectiveness of the NDOB-SMC can ensure that the tracking precision is stabilized in a fixed range under the constant load or variable load running state through the combined simulation test.
(2) Superiority analysis
In order to verify the superiority of the proposed control algorithm, this experiment compares the conventional PID control with the conventional SMC control. PID is widely used in the control field because of its structural advantage, its parameters are p=0.04, i=0.1, d=0 as follows. The SMC controller parameters are k as follows 3 ＝3.9e3，k 4 ＝5，c 3 ＝4e4，c 4 =400. Also given a sinusoidal signal, the amplitude is 20, the frequency is pi/4, and the phase is-pi/2. The load is still a variable load, the curve of which is shown in fig. 10. The error curve results of the simulation experiment are shown in fig. 13, and the angle tracking curve is shown in fig. 14.
It can be clearly observed from fig. 13 and 14 that the angle error of the SMC control is within ±0.15° with the same sinusoidal desired signal input, whereas the angle error of the conventional PID control reaches ±0.2°. As can be seen from the data in fig. 11, the sliding mode control with the nonlinear disturbance observer can stably control the angle error to be about ±0.1°, and has more excellent tracking accuracy than the conventional SMC and the conventional PID control.
And simultaneously, in order to fully verify the advantages and the adaptability of the NDOB-SMC control provided herein in the practical application of the hydraulic swing joint position servo system. The experiment adopts triangular wave signals with the angle of +/-20 degrees and sine signals with amplitude values ranging from minus 20 degrees to 90 degrees as expected signals respectively, and the performance of the three controllers is inspected. The triangle wave signal angle tracking result of the simulation experiment is shown in fig. 15, and the amplitude value sine signal angle tracking result is shown in fig. 16. The angular errors for the two signals are shown in figures 17 and 18, respectively.
As shown in fig. 15 and 17, when the desired signal is a triangular wave, the NDOB-SMC control can stabilize the angle error within ±0.05° in spite of a large fluctuation in the vicinity of the turning point of the triangular wave, make the tracking angle converge rapidly, and obtain a better tracking accuracy, compared with the conventional PID control (error ±0.1°) and the conventional SMC control (error ±0.15°).
As shown in fig. 16 and 18, when the amplitude value is taken as a desired signal, the integral angle error of the NDOB-SMC can be stably controlled within +/-0.5 degrees, and the tracking precision is better, while the angle error of the traditional PID control fluctuates within +/-1 degrees, and the angle error of the traditional SMC control fluctuates within +/-0.75 degrees, and the tracking effect is poorer than that of the NDOB-SMC control. The NDOB-SMC control can well adapt to various changes of load quality while receiving various signal inputs. The experimental result shows that the control strategy provided by the method has higher control precision, and simultaneously, the system can obtain better dynamic performance and stable state, and the actual working condition requirement can be met.
The above embodiments are not to be taken as limiting the scope of the invention, and any alternatives or modifications to the embodiments of the invention will be apparent to those skilled in the art and fall within the scope of the invention.
The present invention is not described in detail in the present application, and is well known to those skilled in the art.
Claims (8)
1. The utility model provides a hydraulic swing joint position servo system, its characterized in that, includes hydraulic swing joint, hydraulic swing joint includes the upper junction plate, be equipped with swing type pneumatic cylinder on the upper junction plate, the piston rod of swing type pneumatic cylinder designs into circular-arc, be equipped with down the connecting plate on the piston rod, the lower connecting plate is rotatory swing along with the piston rod, the rotatory swing center department of connecting plate is equipped with angle sensor down, be equipped with the servo valve on the cylinder body of swing type pneumatic cylinder, the servo valve is connected with the hydraulic pressure station, angle sensor is connected with the computer, the computer is connected with the servo valve.
2. The hydraulic swing joint position servo system according to claim 1, wherein a hollow shaft is arranged at the rotary swing center of the cylinder body corresponding to the lower connecting plate, bearings are respectively arranged at two ends of the hollow shaft, one lower connecting plate is arranged on each bearing, bearing baffle discs are arranged on the outer side wall of the lower connecting plate, and the two lower connecting plates are symmetrically arranged on the piston rod.
3. The hydraulic swing joint position servo system according to claim 2, wherein the cylinder body is of a split design and comprises an inner cylinder barrel and an outer cylinder barrel which are symmetrically designed, the inner cylinder barrel and the outer cylinder barrel are connected through threads, a servo valve is arranged on the side wall of the outer cylinder barrel, the angle sensor is arranged in a hollow shaft, a rotating shaft of the angle sensor is arranged on one of the lower connecting plates, and the rotating shaft is collinear with the rotation swing center of the lower connecting plate.
4. A method for controlling an NDOB-SMC of a hydraulic swing joint position servo system, comprising a hydraulic swing joint position servo system according to any of claims 1-3, comprising the steps of:
s1, establishing a mathematical model of a hydraulic swing joint position servo system, which specifically comprises the following steps:
establishing a load moment balance equation of the hydraulic swing joint position servo system, wherein the expression is as follows:
P L ＝p 1 -p 2 ；
k q ＝C d w(1/ρ )1/2 ；
wherein A is the effective area of the piston, P L For flow gain, p 1 For upper cavity pressure，p 2 For lower chamber pressure, C d Is the flow coefficient, w is the area gradient of the servo valve, ρ is the hydraulic oil density, R is the piston rod rotation radius, T L For external load torque, B p For equivalent viscous damping coefficient, J L In order for the moment of inertia to be of interest,all unmodeled interference terms in the system;
defining a state variable:
the equation of state of the hydraulic swing joint position servo system is expressed as:
wherein, alpha= [ alpha ] 1 ，α 2 ，α 3 ，α 4 ] T ,α 1 ＝B p R 2 /J L ，d 1 (t)＝[f(t，x 1 ，x 2 )+T L ]/J L ，d 1 (t) Complex interference, d, which is an uncertainty factor of a system mismatch model 2 (t)＝(4ARβ e /V t J L )Q(t)，d 2 (t) Complex interference, α, which is an uncertainty factor of a system matching model 2 ＝4ARβ e k t /V t J L ，α 3 ＝4A 2 R 2 β e /V t J L ，α 4 ＝4β e C i /V t ，λ 1 ＝[p s -x 3 sign(u)J L /AR] 1/2 ，β e Is the elastic modulus of oil liquid, V t Is the total volume of two cavities, Q (t) is a time-varying modeling error, u is the total control law of the system, and k t For total flow gain, C i For internal leakage flow coefficient, C e For discharging outsideLeakage flow coefficient, p s For the supply pressure;
s2, designing a supercoiled disturbance observer, which specifically comprises the following steps:
the supercoiled disturbance observer of the mismatch model is constructed with the following expression:
in the formula
Wherein parameter a 1 、a 2 All are positive numbers, d 1 The interference estimate of (t) is:
the supercoiled disturbance observer of the matching model is constructed with the following expression:
in the formula ,
wherein parameter a 3 、a 4 All are positive numbers, d 2 The interference estimate of (t) is:
s3, designing a sliding mode controller to obtain a system overall control law, wherein the method specifically comprises the following steps:
setting the angle expected signal of the hydraulic swing joint position servo system as x d The actual angular displacement output signal of the hydraulic swing joint position servo system is x 1 The error vector of the hydraulic swing joint position servo system is as follows:
order theThe control object may be rewritten as:
combining this with the equation of state of the hydraulic swing joint position servo system:
the conversion from this formula can be:
get [ c ] 1 ,c 2 ,1] T All are greater than zero, the switching function of the sliding mode surface is selected as follows:
s(x)＝c 1 e 1 +c 2 e 2 +e 3
conduct the derivation on the two sides and willThe equation is substituted to obtain:
wherein :
from the formulaAnd->Available compensation control law->The method comprises the following steps:
the design method of the sliding mode controller for selecting the exponential approach law comprises the following steps:
the total control law u of the system is obtained as follows:
in the formula ,k1 、k 2 Discontinuous gains of the sliding mode controller are larger than zero;
accurately controlling the hydraulic swing joint according to the total control law u of the system;
s4, carrying out a joint simulation experiment, which specifically comprises the following steps:
firstly, building a hydraulic swing joint position servo system model and setting parameters on an AMEsim platform, establishing a Simucosim interface, operating the hydraulic swing joint position servo system model to generate an S function and outputting information comprising angles, angular speeds and pressures so as to be connected with Matlab/Simulink; secondly, a sliding mode control model is established and operated on the Matlab/Simulink platform, an output control signal u is generated for the AMEsim platform, and real-time control of the AMEsim platform is achieved; and finally, the AMEsim platform feeds information back to the Matlab platform, so that joint simulation is realized.
5. The method for controlling the NDOB-SMC of a hydraulic swing joint position servo system according to claim 4, wherein in said step S1, 1: the angle expected signal of the hydraulic swing joint position servo system is x d ，x d ∈C 3 Under the normal working condition of the hydraulic swing joint position servo system, the swing type hydraulic cylinder meets the following conditions: p is 0 < p r ＜p 1 ＜p s ，0＜p r ＜p 2 ＜p s ，p 1 For upper chamber pressure, p 2 For lower chamber pressure, p s To supply pressure, p r Is the return oil pressure; and |P L Ratio of I to P s Is small enough to ensure alpha 2 λ 1 ≠0；
Setting 2: composite interference d i (t) is bounded, and d i (t) is conductive.
6. The method for controlling the NDOB-SMC of a hydraulic swing joint position servo system of claim 5, wherein in said step S1, primer 1 is: setting 1.ltoreq.i.ltoreq.n, considering the controlled system:
wherein ,is a state variable d i (t) is complex interference, d i First order derivative of (t)>Presence;
adopts a supercoiled control law:
u si (t)＝u 1i (t)+u 2i (t)；
setting: a, a i 、a i+1 Is positive and satisfies:
this can be achieved by:
so the hydraulic swing joint position servo system is stable, andconverging to zero in a limited time.
7. The method according to claim 6, wherein in the step S2, an estimated error between the supercoiled disturbance observer and the hydraulic swing joint position servo is set as follows:
will beAnd (3) with
And (3) subtracting to obtain:
combining the above withThe combination is as follows:
as can be seen from the index 1, andWill converge to zero in a finite time, thus yielding d 1 The interference estimate of (t) is:
in the same way, willAnd (3) with
Subtraction gives:
as can be seen from the index 1, andWill converge to zero in a finite time, thus yielding d 2 The interference estimate of (t) is:
8. the method for controlling the NDOB-SMC of the hydraulic swing joint position servo system of claim 7, wherein in said step S3, the Lyapunov function of the hydraulic swing joint position servo system is taken as follows:
simultaneously deriving two sides and leading toand
Substitution can be obtained:
from the formulaIt can be seen that when (gamma-k) 2 ) < 0 and k 1 > 0, then->The constant holds, and only when s=0,the closed loop system is stable.
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