CN100444061C - Method for restraining buffet utilizing wave filter - Google Patents

Abstract

The present invention provides a method for restraining buffeting utilizing a wave filter, which belongs to the technical field of automatic control. The present invention utilizes a filter to filter high-frequency buffeting, and thereby, the buffeting is weakened; meanwhile, meanwhile, the filter only acts on arriving a slipform surface in order to avoid the slower dynamic response caused by the hysteresis effect of the filter. The present invention has the advantages and positive effects that the filter is used for filtering the high frequency buffeting to weaken the buffeting; meanwhile, the filter provided by the present invention only acts on arriving the slipform surface in order to avoid the slower dynamic response caused by the hysteresis effect of the filter without influencing the arrival time; the present invention has an extremely great advantage according to the subsequent simulating results.

Description

A kind of wave filter that utilizes suppresses the method for buffeting

Technical field

The present invention relates to automation field, be specifically related to a kind of wave filter that utilizes and suppress the method for buffeting.

Background technology

In automation control area, the unique features of the unchangeability that Sliding mode variable structure control has the perturbation of system self parameter and external interference.This control method can strengthen the stability robustness of control system to uncertain factor, and gives high performance index, breaks through the fixedly framework of control structure.But after the motion state of system arrives slip plane, can near slip plane, produce high frequency and buffet.This buffeting is the problem that can not be ignored in the Sliding mode variable structure control, and it has caused great harm to control system, is seriously restricting using more widely of sliding mode control theory.

The method that weakening commonly used is buffeted has boundary layer method and adjusts the convergence law.The former is that to sacrifice tracking accuracy be cost, and the latter will adjust the convergence rule according to the degree of state convergence sliding-mode surface, often causes the time that arrives sliding-mode surface elongated, and makes the controller to become complicated.These two kinds of methods all are to overcome high frequency with low-pass filter to buffet, and because low-pass filter has delayed action, therefore can cause control lag.

Document " Wang Rongqin, variable bandwidth filter is becoming the application of structure control, Power Electronic Technique, 1999 (6) for Japanese plum army, Zhang Yaosheng " proposes the method that a kind of low-pass filter of frequency conversion rate carries out filtering.The simulated effect of making according to this method is shown in Fig. 6,7.As can be seen, adopt this method to carry out filtering after, export still level and smooth inadequately.

Summary of the invention

(1) technical matters that will solve

The objective of the invention is for overcome transient response and slow down, guarantee into rapidity, effectively thereby the buffeting of team's high frequency is carried out filtering and has been weakened the method for buffeting.

(2) technical scheme

For achieving the above object, employing following steps of the present invention:

A kind of wave filter that utilizes suppresses the method for buffeting, and utilizes wave filter that high frequency is buffeted and carries out filtering, thereby weaken buffeting, as sliding-mode surface s _iValue when very little, when promptly system state is near sliding-mode surface, call in wave filter, controlled quentity controlled variable is carried out filtering, the control law that wherein adds the i dimension component behind the wave filter is:

Wherein, u _EqiBe equivalent control u _EqI dimension component, u _Eq=-(kb) ^-1(x ₂+ kf (x ₁, x ₂)), x ₁, x ₂∈ R ⁿ, b=diag (b ₁... b _n), k=diag (k ₁... k _n), k _i＞0, s _RiFor wave filter is called in the valve value,

For becoming structure control power.

The above-mentioned wave filter that utilizes suppresses the method for buffeting, and a kind of preferred scheme is that described wave filter is a low-pass first order filter, and formula is $G\left(s\right)=\frac{1}{T_{f}s+1},$ $T_f=\frac{1}{W_c},$ T wherein _fIt is the cycle; W _cIt is corner frequency.

The above-mentioned wave filter that utilizes suppresses the method for buffeting, and wherein said valve value is the little positive number of setting as the case may be.

The above-mentioned wave filter that utilizes suppresses the method for buffeting, and a kind of preferred scheme is that described wave filter is a second-order low-pass filter.

(3) beneficial effect

The present invention proposes a kind of new inhibition buffeting method, utilize wave filter that high frequency is buffeted and carry out filtering, thereby weaken buffeting; Simultaneously, the dynamic response that causes for fear of the delayed action of wave filter is slower, and the wave filter that the present invention proposes just just strobes arriving on the sliding-mode surface, thereby not to impacting time of arrival.Show that from the result of follow-up emulation this method has extremely great advantage.

Description of drawings

Fig. 1 is a module diagram of the present invention;

Fig. 2 does not add when eliminating the buffeting measure, the sliding-mode surface curve of simulation result;

Fig. 3 does not add when eliminating the buffeting measure, the control moment curve of output of simulation result;

Fig. 4 is when adopting the present invention to suppress to buffet, the sliding-mode surface curve of simulation result

Fig. 5 is when adopting the present invention to suppress to buffet, the control moment curve of output of simulation result;

Fig. 6 is after the low-pass filter of a kind of frequency conversion rate in the employing prior art carries out filtering, the sliding-mode surface curve of simulation result;

Fig. 7 is after the low-pass filter of a kind of frequency conversion rate in the employing prior art carries out filtering, the control moment curve of output of simulation result;

Fig. 8 adopts this paper method and adopts boundary layer method, the site error curve of simulation result.

Embodiment

Below in conjunction with accompanying drawing, further describe the side that the present invention utilizes wave filter suppress to buffet and send out, but be not used for limiting protection scope of the present invention.

Core concept of the present invention is to utilize wave filter that high frequency is buffeted to carry out filtering.And in order to guarantee fast into rate and the response of becoming, wave filter only works when state moves on sliding-mode surface.Like this, low-pass filter just not influence state arrives the process of sliding-mode surface, and into the rapidity of having guaranteed to become is carried out filtering to the buffeting of high frequency again, has weakened buffeting.

To following Nonlinear Second Order System:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f(x_1,x_2)+\mathrm{bu}+\mathrm{\ω}\end{array}\right.,$ Wherein: x ₁, x ₂∈ R ⁿ, b=diag (b ₁..., b _n), u ∈ R ⁿ,

Therefore choosing sliding-mode surface is: S=x ₁+ kx ₂, k=diag (k wherein ₁..., k _n), k _i＞0

Order $\stackrel{\·}{S}=0,$ Can be in the hope of equivalent control: u _Eq=-(kb) ^-1(x ₂+ kf)

Then become structure control rule and be u=u _Eq-λ sgn (S), wherein λ＞

As seen, the state of system finally goes to zero, and such system is stable.But, because control law formula u=u _Eq-λ sgn (S) is discontinuous control, has switching function sgn (), must have chattering phenomenon and take place, and the measure that must take certain elimination to buffet just can guarantee application in practice.

Therefore, the low-pass first order filter in the present embodiment is designed to:

$G\left(s\right)=\frac{1}{T_{f}s+1},$ $T_f=\frac{1}{W_c},$ T in the formula _f---the cycle; W _c---corner frequency

Being chosen as of decision mechanism:, do not insert wave filter, thereby avoided the delayed action of wave filter, the quick convergence sliding-mode surface of the system that guaranteed when state during away from sliding-mode surface; When the value of sliding-mode surface si is very little, when promptly system state is near sliding-mode surface, call in wave filter, controlled quentity controlled variable is carried out filtering, weaken the purpose of buffeting thereby reach.

The control law that then adds the i dimension component behind the wave filter is:

S in the formula _RiFor wave filter is called in the valve value, be the little positive number of setting as the case may be;

For becoming structure control power, through control output after the firstorder filter filtering.

During concrete the application, choose the two-joint robot system and carry out simulation study, the result of emulation outputs to general mathematical software matlab, and kinetic model and parameter that it is main are as follows:

$M\left(\mathrm{\θ}\right)\stackrel{\·\·}{\mathrm{\θ}}+C(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\stackrel{\·}{\mathrm{\θ}}+G\left(\mathrm{\θ}\right)+D\left(\stackrel{\·}{\mathrm{\θ}}\right)+\mathrm{\ω}=\mathrm{\τ}$

The form that is converted to state space is:

$M\left(\mathrm{\θ}\right)\stackrel{\·\·}{e}+W(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})+\mathrm{\ω}=\mathrm{\τ}-M\left(\mathrm{\θ}\right){\stackrel{\·\·}{\mathrm{\θ}}}_d$

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_1=e_2\\ {\stackrel{\·}{e}}_2=M{\left(\mathrm{\θ}\right)}^{-1}(\mathrm{\τ}-W(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})-\mathrm{\ω})-{\stackrel{\·\·}{\mathrm{\θ}}}_d\end{array}\right.$

Wherein: $W(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})=C(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\stackrel{\·}{\mathrm{\θ}}+G\left(\mathrm{\θ}\right)+D\left(\stackrel{\·}{\mathrm{\θ}}\right),$ E=θ-θ _d, θ _dBe desired output,

$M\left(\mathrm{\θ}\right)=\left[\begin{array}{cc}v+\mathrm{\β}+2\mathrm{\γ}\cos \left({\mathrm{\θ}}_2\right)& \mathrm{\β}+\mathrm{\γ}\cos \left({\mathrm{\θ}}_2\right)\\ \mathrm{\β}+\mathrm{\γ}\cos \left({\mathrm{\θ}}_2\right)& \mathrm{\β}\end{array}\right].$

$C(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})=\left[\begin{array}{cc}-\mathrm{\γ}{\stackrel{\·}{\mathrm{\θ}}}_2\sin \left({\mathrm{\θ}}_2\right)& -\mathrm{\γ}({\stackrel{\·}{\mathrm{\θ}}}_1+{\stackrel{\·}{\mathrm{\θ}}}_2)\sin \left({\mathrm{\θ}}_2\right)\\ \mathrm{\γ}{\stackrel{\·}{\mathrm{\θ}}}_1\sin \left({\mathrm{\θ}}_2\right)& 0\end{array}\right]$

$G\left(\mathrm{\θ}\right)=\left[\begin{array}{c}{\mathrm{\κ}}_1\cos \left({\mathrm{\θ}}_1\right)+{\mathrm{\κ}}_2\cos ({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)\\ {\mathrm{\κ}}_2\cos ({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)\end{array}\right],$ $D\left(\stackrel{\·}{\mathrm{\θ}}\right)=\left[\begin{array}{c}5{\stackrel{\·}{\mathrm{\θ}}}_1\\ 5{\stackrel{\·}{\mathrm{\θ}}}_2\end{array}\right].$

The structural parameters of the two-joint robot in the present embodiment are respectively: ν=15.8, β=5.8, γ=5, κ ₁=150, κ ₂=100, κ ₃=50.Error disturbance, expectation angular displacement and the initial state of choosing are respectively:

$\mathrm{\ω}=\left[\begin{array}{c}2+3\left|\right|e\left|\right|+6\left|\right|\stackrel{\·}{e}\left|\right|\\ 2\cos \left(t\right)\end{array}\right]$

$\left\{\begin{array}{c}{\mathrm{\θ}}_{1d}=\cos \left(\mathrm{\πt}\right)\\ {\mathrm{\θ}}_{2d}=\sin \left(\mathrm{\πt}\right)\end{array}\right.$

$\left[\begin{array}{c}{\mathrm{\θ}}_1\\ {\mathrm{\θ}}_2\\ {\stackrel{\·}{\mathrm{\θ}}}_1\\ {\stackrel{\·}{\mathrm{\θ}}}_2\end{array}\right]=\left[\begin{array}{c}2\\ 0.5\\ 0\\ 3\end{array}\right]$

By low-pass first order filter then become structure control rule into:

τ=τ _Eq-λ sgn (S), wherein ${\mathrm{\τ}}_{\mathrm{eq}}={\left({\mathrm{kM}}^{-1}\right)}^{-1}({\mathrm{kM}}^{-1}W+k{\stackrel{\·\·}{\mathrm{\θ}}}_d-e_2)$

Some major parameters of controlled quentity controlled variable τ are: K=diag (1,1), λ=35, W _c=70, s _Ri=0.1.

After wave filter inhibition buffeting, Fig. 2-8 has provided main simulation result relatively.Wherein, only provided the simulation result in one of them joint, for the ease of comparing, the sliding-mode surface curve does not all provide.

Wherein, Fig. 2 and Fig. 3 do not add when eliminating the buffeting measure, joint 1 sliding-mode surface curve and control moment curve of output, and wherein the horizontal ordinate of Fig. 2 is the time, and ordinate is a distance, and the horizontal ordinate of Fig. 3 is the time, moment during ordinate.Tangible chattering phenomenon is arranged as can be seen; Fig. 6 and Fig. 7 are that the low-pass filter according to the employing frequency conversion rate of prior art carries out the simulation result that the method for filtering obtains, as can be seen, adopt this method to carry out filtering after, export still level and smooth inadequately; Fig. 4 and Fig. 5 are after adopting the method for inhibition buffeting proposed by the invention, the curve of output of joint 1 sliding-mode surface and control moment.As can be seen, the method that adopts the present invention to propose can effectively weaken buffeting, level and smooth output.Comparison diagram 6 and Fig. 7 adopt method that the present invention proposes than prior art as can be seen, can better weaken buffeting, and it is shorter to arrive time of sliding-mode surface.

Fig. 8 is comparison (wherein, place of switches switching function the sgn () use of adopting this paper method and adopting boundary layer method to do $\mathrm{sat}\left(S\right)=\left\{\begin{array}{cc}\frac{S}{\left|\right|S\left|\right|},& \left|\right|S\left|\right|\&GreaterEqual;\mathrm{\&rho;}\\ \frac{S}{\mathrm{\&rho;}},& \left|\right|S\left|\right|<\mathrm{\&rho;}\end{array}\right.,$ P=0.01 wherein)), curve 1 is the site error of the designed method of this paper, and curve 2 is boundary layer method site errors.By more as can be seen, though boundary layer method can be good at eliminating buffeting,, there is bigger final state error, it is to coincide with the theory of sacrificing tracking accuracy that this and boundary layer method eliminate buffeting.

From above analogous diagram as can be seen, comparing does not have to adopt the measure that eliminates buffeting, the method that adopts the present invention to propose can suppress to buffet greatly, and can reduce the final state error, level and smooth input control moment, this can be so that the control response quickening in the actual robot system applies, and aspect Stability Control, be better than prior art, therefore be extremely important.

More than be preferred forms of the present invention, according to content disclosed by the invention, some identical, replacement schemes that those of ordinary skill in the art can expect apparently all should fall into the scope of protection of the invention.

Claims (4)

1, a kind of wave filter that utilizes suppresses the method for buffeting, and it is characterized in that utilizing wave filter that high frequency is buffeted and carries out filtering, thereby weaken buffeting, as sliding-mode surface s _iValue when very little, when promptly system state is near sliding-mode surface, call in wave filter, controlled quentity controlled variable is carried out filtering, the control law that wherein adds the i dimension component behind the wave filter is:

Wherein, u _EqiBe equivalent control u _EqI dimension component, u _Eq=-(kb) ^-1(x ₂+ kf (x ₁, x ₂)), x ₁, x ₂∈ R ⁿ, b=diag (b ₁... b _n), k=diag (k ₁... k _n), k _i＞0, s _RiFor wave filter is called in the valve value, For becoming structure control power.

2, the wave filter that utilizes as claimed in claim 1 suppresses the method for buffeting, and it is characterized in that described wave filter is a low-pass first order filter, and formula is $G\left(s\right)=\frac{1}{T_{f}s+1},$ $T_f=\frac{1}{W_c},$ T wherein _fIt is the cycle; W _cIt is corner frequency.

3, the wave filter that utilizes as claimed in claim 1 suppresses the method for buffeting, and it is characterized in that described valve value is the little positive number of setting as the case may be.

4, the wave filter that utilizes as claimed in claim 1 suppresses the method for buffeting, and it is characterized in that described wave filter is a second-order low-pass filter.

Images