CN110244564A - A kind of sliding mode variable structure control method applied to gas drive soft robot - Google Patents
A kind of sliding mode variable structure control method applied to gas drive soft robot Download PDFInfo
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- CN110244564A CN110244564A CN201910537949.8A CN201910537949A CN110244564A CN 110244564 A CN110244564 A CN 110244564A CN 201910537949 A CN201910537949 A CN 201910537949A CN 110244564 A CN110244564 A CN 110244564A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The present invention provides a kind of sliding mode variable structure control method applied to gas drive soft robot, includes the following steps: S1: decoupling to the outputting and inputting for nonlinear and time-varying system model of gas drive soft robot；S2: sliding mode variable structure control method applied to gas drive soft robot of the design based on exponentially approaching rule.A kind of sliding mode variable structure control method applied to gas drive soft robot is provided, model decoupling has been carried out by the nonlinear and time-varying system model to gas drive soft robot；Then, the sliding-mode control based on exponentially approaching rule is devised.Performance is better than Position Form PID algorithm and improves increment type PID algorithm when showing the sliding mode control algorithm of design applied to gas drive soft robot to model and sliding mode control algorithm analysis of experiments by building emulation test system.
Description
Technical field
The present invention relates to robotic technology field more particularly to a kind of sliding moding structures applied to gas drive soft robot
Control method.
Background technique
Soft robot is a kind of with theory unlimited freedom degree, different from traditional rigidity with fixed freedom degree
A kind of novel robot of mechanical arm.Because of its high flexibility, safety and to the speciality such as the adaptability of environment, soft robot
It is concerned by people more and more.In recent years, whether in engineer application field or field of scientific study, software machine
People presents its very high potential broad prospect of application.
In recent years, the research in soft robot field has obtained many achievements, but most of researchs still concentrate on novel knot
In the design of the bio-robot of structure and the realization of bionic function, and it is comparatively then not so much for the research of control.
Mainly there are two major classes for the control method of soft robot at present: being controlled using self adaptive control, robust control as the modern times of representative
System theory and the intelligent control method based on the theories of learning, wherein especially burning the hotest with intensified learning.But this kind of learning algorithm
Also there is its disadvantage, one is needing a large amount of trial and errors to find suitable reward value, if algorithm policy is not set, more consume
It is time-consuming, and this cost on hardware is excessively high, it is difficult to it realizes, and still needs to consider if being trained under virtual simulation environment
Evolvement problem still needs to adjust during moving to soft robot material object；The second is algorithm is complex, to its performance of control
It is more demanding, it is difficult to be transplanted on the platforms such as single-chip microcontroller, be not easy to be generalized in industrial application.
The above research method all achieves certain progress in the control of gas drive soft robot, however, the above research master
It need to strengthen the methods of study, wait to study for the sliding mode variable structure control method of gas drive soft robot.
The disclosure of background above technology contents is only used for auxiliary and understands design and technical solution of the invention, not necessarily
The prior art for belonging to present patent application, no tangible proof show above content present patent application the applying date
In disclosed situation, above-mentioned background technique should not be taken to the novelty and creativeness of evaluation the application.
Summary of the invention
The present invention in order to solve the problems, such as the sliding mode variable structure control method for lacking gas drive soft robot in the prior art,
One kind is provided.
To solve the above-mentioned problems, the technical solution adopted by the present invention is as described below:
A kind of sliding mode variable structure control method applied to gas drive soft robot, includes the following steps: S1: soft to gas drive
The the outputting and inputting for nonlinear and time-varying system model of body robot is decoupled；S2: application of the design based on exponentially approaching rule
In the sliding mode variable structure control method of gas drive soft robot.
Preferably, the nonlinear and time-varying system model of the gas drive soft robot are as follows:
Wherein,Y is respectively acceleration, speed and the displacement of the gas drive soft robot；
M is the quality of soft robot, and g is acceleration of gravity；
B (P) is the damped coefficient of the gas drive soft robot, b (P)=b0+b1*P；
K (P) is the coefficient of elasticity of the gas drive soft robot, k (P)=k0+k1*P；
F (P) is the Diastolic Force of the gas drive soft robot, f (P)=f0+f1*P；
Wherein, P is air pressure, b0, b1The respectively intercept and slope of damped coefficient linearity curve, k0, k1Respectively elasticity system
The intercept and slope of number linearity curve, f0, f1The respectively intercept and slope of Diastolic Force linearity curve.
That is, the nonlinear and time-varying system model of the gas drive soft robot are as follows:
Bounded function B (t) are as follows:
Wherein, BminAnd BmaxLower bound and the upper bound for the bounded function；
The then geometrical mean of the bounded function B (t)Are as follows:
AndFollowing condition should be met:
Preferably, the state variable of the nonlinear and time-varying system model of the gas drive soft robot is chosen are as follows:
x1=y,
Wherein,
Wherein, f is the dynamic part of the nonlinear and time-varying system model of the gas drive soft robot, specifically:
F=F (x1,x2)
Wherein,For the dynamic part f of the nonlinear and time-varying system model of the gas drive soft robot observation or
Estimated value, F are then the bounded function of the nonlinear and time-varying system model of the gas drive soft robot.
Preferably, slip plane are as follows:
Wherein, xdIt is inputted for expectation,For the error between expectation input and reality output, λ is fixed constant.
Preferably, the control input of the nonlinear and time-varying system model of the gas drive soft robot needs to pass through when s=0
It solvesIt obtains, i.e., list-directed input list reaches formula are as follows:
Wherein,It is inputted for equivalence control.
Preferably, the control law u of the nonlinear and time-varying system model of the gas drive soft robot:
Wherein, ε indicates that the state of the nonlinear and time-varying system model of the gas drive soft robot levels off to slip plane
Rate；
Then the system inputs expression formula are as follows:
Preferably, the sliding condition of the nonlinear and time-varying system model of the gas drive soft robot are as follows:
Wherein, η is the constant greater than zero；
Arrangement obtains:
That is,
Preferably, it enables:
Wherein ,-τ s is exponential approach item, and solution is s=s (0) e-τs。
It preferably, further include constructing emulation test system to the sliding mode variable structure control method of the gas drive soft robot
It is verified.
The present invention also provides a kind of computer readable storage medium, the computer-readable recording medium storage has computer
Program, when the computer program is executed by processor realize as above any the method the step of.
The invention has the benefit that a kind of sliding mode variable structure control method applied to gas drive soft robot is provided,
Model decoupling has been carried out by the nonlinear and time-varying system model to gas drive soft robot；Then, it devises to become based on index
The sliding-mode control closely restrained.Design is shown to model and sliding mode control algorithm analysis of experiments by building emulation test system
Sliding mode control algorithm be applied to gas drive soft robot when performance be better than Position Form PID algorithm and improve increment type PID calculate
Method.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of closure works system in the embodiment of the present invention.
Fig. 2 is the boundary of bounded function B (t) and geometric average in the embodiment of the present inventionSchematic diagram.
Fig. 3 is sliding mode schematic diagram in the embodiment of the present invention.
Fig. 4 is emulation platform control system schematic diagram in the embodiment of the present invention.
Fig. 5 is the displacement tracking contrast schematic diagram of different control algolithms in the embodiment of the present invention.
Fig. 6 (a)-Fig. 6 (b) is the speed tracing contrast schematic diagram of different control algolithms in the embodiment of the present invention.
Specific embodiment
In order to which technical problem to be solved of the embodiment of the present invention, technical solution and beneficial effect is more clearly understood,
The present invention is further described in detail below with reference to the accompanying drawings and embodiments.It should be appreciated that specific implementation described herein
Example is only used to explain the present invention, is not intended to limit the present invention.
It should be noted that it can be directly another when element is referred to as " being fixed on " or " being set to " another element
On one element or indirectly on another element.When an element is known as " being connected to " another element, it can
To be directly to another element or be indirectly connected on another element.In addition, connection can be for fixing
Effect is also possible to act on for circuit communication.
It is to be appreciated that term " length ", " width ", "upper", "lower", "front", "rear", "left", "right", "vertical",
The orientation or positional relationship of the instructions such as "horizontal", "top", "bottom" "inner", "outside" is that orientation based on the figure or position are closed
System is merely for convenience of the description embodiment of the present invention and simplifies description, rather than the device or element of indication or suggestion meaning must
There must be specific orientation, be constructed and operated in a specific orientation, therefore be not considered as limiting the invention.
In addition, term " first ", " second " are used for descriptive purposes only and cannot be understood as indicating or suggesting relative importance
Or implicitly indicate the quantity of indicated technical characteristic.Define " first " as a result, the feature of " second " can be expressed or
Implicitly include one or more this feature.In the description of the embodiment of the present invention, the meaning of " plurality " is two or two
More than, unless otherwise specifically defined.
Embodiment 1
As shown in Figure 1, the present invention provides the sliding mode variable structure control method for being applied to gas drive soft robot, including as follows
Step:
S1: the outputting and inputting for nonlinear and time-varying system model of gas drive soft robot is decoupled；
S2: sliding mode variable structure control method applied to gas drive soft robot of the design based on exponentially approaching rule.
It is a in one embodiment, when the Voight model for the gas drive soft robot that the present invention designs is a kind of non-linear
Change system is shown in formula (1):
In formula,Y is respectively the acceleration (m/s of gas drive soft robot2), speed (m/s) and displacement (m)；
B (P) is the damped coefficient (N/ (m/s)) of gas drive soft robot, related with air pressure；
K (P) is the coefficient of elasticity (N/m) of gas drive soft robot, related with air pressure；
F (P) is the Diastolic Force (N) of gas drive soft robot, related with air pressure；
Since above-mentioned three element and air pressure have following relationship:
B (P)=b0+b1*P；K (P)=k0+k1*P；F (P)=f0+f1*P (2)
Wherein, P is air pressure, b0, b1The respectively intercept and slope of damped coefficient linearity curve, k0, k1Respectively elasticity system
The intercept and slope of number linearity curve, f0, f1The respectively intercept and slope of Diastolic Force linearity curve.
So arranging formula (1) for following form:
From formula (3) it is not difficult to find that the gas drive soft robot system model is difficult to directly carry out controller, main cause
It is to exist to couple between input and output, if being directly used in emulation solves the problem of will appear " algebraic loop ".Therefore to input
It is decoupled with output, thus allows for the design of controller.
For input-output modeling problem, design bounded function B (t):
B in formulaminAnd BmaxLower bound and the upper bound for function are obtained by experimental data.Simultaneously according to Principle of Statistics
The geometrical mean of Selection of Function BAre as follows:
AndFollowing condition should be met:
As shown in Fig. 2, B (t) is as similar in coefficient of elasticity k and Diastolic Force f, the relationship with input air pressure P be also with
60kPa is boundary, just like two kinds of situations shown in figure.
In this way, having carried out a degree of simplification to gas drive soft robot system model in this way, reduce
The nonlinear degree of system gas drive soft robot system model, so that present gas drive soft robot system model is also enough
For carrying out the design of controller.
Preferably, it is specifically included in step S2:
The design of control algolithm is carried out to the system.Take the state variable of gas drive soft robot system model are as follows:
x1=y,
Formula (1) is arranged as following form simultaneously:
In formula, f is the dynamic part of system, specifically:
F=F (x1,x2) (6)
In above formula,For the observation or estimated value of the dynamic part f of gas drive soft robot system model, F is then one
Determining bounded function, specific boundary and expression formula need to be by testing or emulating acquisition.
Slip plane is designed according to following expression:
In formula (7), xdIt is inputted for expectation,For the error between expectation input and reality output, λ is fixed constant.Such as figure
Shown in 3, s (x1, t) and it is actually a hyperplane, the case where s=0, is mapped to (x1,x2) phase plane on show as straight line.
And target is exactly to allow the state (x of gas drive soft robot system model1,x2) remain on this straight line, i.e. gas drive software
Robot system model is in sliding mode, at this time s=0, as shown below.
As shown in figure 3, system reaches on slip plane in finite time, and along the linear motion, can say at this time
Gas drive soft robot system model is in sliding mode, that is, can reach the state of no error following for expectation input.
The control input of system needs to lead to when gas drive soft robot system model is in sliding mode, that is, when s=0
Cross solutionIt obtains:
In formula (9)Referred to as equivalence control inputs, it can be understood as when moving for gas drive soft robot system model
State is it is known that there is no when various uncertainties, so that system is keptContinuous control law ideally, can not be straight
It scoops out in actual conditions.But in actually control, to meetIt needs to increase noncontiguous item so that gas drive software machine
Device people's system model state can pass repeatedly through slip plane and gradually approach.It therefore, can be very according to formula (9) and above-mentioned analysis
It is easy to provide control law u:
The control law of sliding mode controller is so just acquired.But still there is a unknown ε in this up-to-date style, which indicates system
The state of system levels off to the rate of slip plane, and the small then velocity of approach of ε is slow, and then velocity of approach is fast greatly by ε.The control that formula (10) is acquired
System input expression formula, which substitutes into formula (8), to be obtained:
Design for sliding mode controller, it is necessary to meet condition:
In above formula, η is a constant for being greater than zero, is determined by experiment for different control objects needs.In fact, formula
(12) what is expressed is a kind of square " distance " to hyperplane, in the entire dynamic process of gas drive soft robot system model
By s2To characterize.It in the ideal case, would not be further out slip plane once after system trajectory arrival slip plane.Cause
This, also referred to as formula (12) is sliding condition.
For formula (12), we are easy to acquire:
Formula (13) and formula (11) result, which are substituted into formula (12), to be obtained:
It can be obtained after above formula is arranged:
Review formula (6) can do following change to f in formula (15):
Formula (16), which are substituted into formula (15) inequality, to be arranged:
With reference to formula (4), formula (17) inequality can be arranged as following form:
Target is to design the Sliding Mode Controller based on exponentially approaching rule, it is therefore desirable to it improves again, it is specific to improve
It is as follows:
Formula (4.19) is the General Expression form of constant speed Reaching Law, and improvement is exactly to increase an exponential approach item:
In formula ,-τ s is exponential approach item, and solution is s=s (0) e-τs。
In this way, having determined that the range of the last one unknown number ε, also just completes the sliding formwork based on exponentially approaching rule and become knot
The algorithm of structure controller designs.Simply arrange the above derivation process:
1) for system:
2) sliding mode controller is designed, so that control law are as follows:
3) for parameter ε, should meet:
4) and there is exponentially approaching rule:
It is namely based on the algorithm design process of the Sliding mode variable structure control of exponentially approaching rule, meaning of parameters in each step above
It can be found in specific derive.Theoretically, which is realized, analyzes controlled device characteristic, wherein not for sliding mode controller
Fixed parameter carries out that ginseng is adjusted to can reach ideal control effect.
Embodiment 2
In order to verify the control algolithm that the experiment effect contrived experiment verifying present invention of the invention designs.
Emulation platform control system schematic diagram as shown in Figure 4, it is contemplated that the working range and peace of gas drive soft robot
Full property and the representativeness of experiment select 5Hz, and amplitude is used as desired displacement signal in the sinusoidal signal of 10mm to 50mm, respectively
It chooses sliding mode controller, Position Form PID controller and improves incremental timestamp device to control to gas drive soft robot
System.
Displacement tracking situation as shown in Figure 5 is it is not difficult to find that the effect of PID control and sliding formwork control has bigger difference.It is aobvious
So, only sliding formwork control can accomplish no error following, can reach no error following in 0.1 second after input signal.And PID control
Then there are obvious errors, and there is certain oscillation in the incipient stage, it is opposite that improvement increment type PID probably needs four periods that can reach error
The stable stage, and not only there is oscillation in the incipient stage to Position Form PID, and can not still converge to desired displacement after undergoing several periods
Signal has always large error.
Likewise, such as the velocity tracking scenario as shown in Fig. 6 (a) and Fig. 6 (b), Position Form PID and improvement increment type PID
Also there is different degrees of oscillation, and tracking effect also has obvious mistake at wave crest and trough in rate curve after several periods
Difference is not especially desirable.The velocity tracking scenario of only sliding mode controller is more satisfactory, with the speed of desired signal basic one
It causes.
A kind of sliding mode variable structure control method applied to gas drive soft robot of preferred design of the present invention, and to the party
Method has carried out algorithm design and experimental verification.Firstly, having carried out model decoupling for gas drive soft robot；Then, it devises
Sliding-mode control based on exponentially approaching rule；Finally, being tried by building emulation test system model and sliding mode control algorithm
Test analysis.Test result shows that performance is better than position model when the sliding mode control algorithm of design is applied to gas drive soft robot
Pid algorithm and improvement increment type PID algorithm.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those skilled in the art to which the present invention belongs, it is not taking off
Under the premise of from present inventive concept, several equivalent substitute or obvious modifications can also be made, and performance or use is identical, all answered
When being considered as belonging to protection scope of the present invention.
Claims (10)
1. a kind of sliding mode variable structure control method applied to gas drive soft robot, which comprises the steps of:
S1: the outputting and inputting for nonlinear and time-varying system model of gas drive soft robot is decoupled；
S2: sliding mode variable structure control method applied to gas drive soft robot of the design based on exponentially approaching rule.
2. being applied to the sliding mode variable structure control method of gas drive soft robot as described in claim 1, which is characterized in that institute
State the nonlinear and time-varying system model of gas drive soft robot are as follows:
Wherein,Y is respectively acceleration, speed and the displacement of the gas drive soft robot；
M is the quality of soft robot, and g is acceleration of gravity；
B (P) is the damped coefficient of the gas drive soft robot, b (P)=b0+b1*P；
K (P) is the coefficient of elasticity of the gas drive soft robot, k (P)=k0+k1*P；
F (P) is the Diastolic Force of the gas drive soft robot, f (P)=f0+f1*P；
Wherein, P is air pressure, b0, b1The respectively intercept and slope of damped coefficient linearity curve, k0, k1Respectively coefficient of elasticity line
The intercept and slope of linearity curve, f0, f1The respectively intercept and slope of Diastolic Force linearity curve.
That is, the nonlinear and time-varying system model of the gas drive soft robot are as follows:
Bounded function B (t) are as follows:
Wherein, BminAnd BmaxLower bound and the upper bound for the bounded function；
The then geometrical mean of the bounded function B (t)Are as follows:
AndFollowing condition should be met:
3. being applied to the sliding mode variable structure control method of gas drive soft robot as claimed in claim 2, which is characterized in that choosing
Take the state variable of the nonlinear and time-varying system model of the gas drive soft robot are as follows:
x1=y,
Wherein,
Wherein, f is the dynamic part of the nonlinear and time-varying system model of the gas drive soft robot, specifically:
F=F (x1,x2)
Wherein,For the observation or estimation of the dynamic part f of the nonlinear and time-varying system model of the gas drive soft robot
Value, F is then the bounded function of the nonlinear and time-varying system model of the gas drive soft robot.
4. being applied to the sliding mode variable structure control method of gas drive soft robot as claimed in claim 3, which is characterized in that sliding
Dynamic plane are as follows:
Wherein, xdIt is inputted for expectation,For the error between expectation input and reality output, λ is fixed constant.
5. being applied to the sliding mode variable structure control method of gas drive soft robot as claimed in claim 4, which is characterized in that s
The control input of the nonlinear and time-varying system model of the gas drive soft robot needs to pass through solution when=0It obtains, i.e.,
List-directed input list reaches formula are as follows:
Wherein,It is inputted for equivalence control.
6. being applied to the sliding mode variable structure control method of gas drive soft robot as claimed in claim 5, which is characterized in that institute
State the control law u of the nonlinear and time-varying system model of gas drive soft robot:
Wherein, ε indicates that the state of the nonlinear and time-varying system model of the gas drive soft robot levels off to the speed of slip plane
Rate；
Then the system inputs expression formula are as follows:
7. being applied to the sliding mode variable structure control method of gas drive soft robot as claimed in claim 6, which is characterized in that institute
State the sliding condition of the nonlinear and time-varying system model of gas drive soft robot are as follows:
Wherein, η is the constant greater than zero；
Arrangement obtains:
That is,
8. the use as claimed in claim 7 in the sliding mode variable structure control method of gas drive soft robot, which is characterized in that
It enables:
Wherein ,-τ s is exponential approach item, and solution is s=s (0) e-τs。
9. the sliding mode variable structure control method a method as claimed in any one of claims 1-8 applied to gas drive soft robot, feature
It is, further includes that building emulation test system verifies the sliding mode variable structure control method of the gas drive soft robot.
10. a kind of computer readable storage medium, the computer-readable recording medium storage has computer program, and feature exists
In being realized when the computer program is executed by processor such as the step of claim 1-9 any the method.
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