CN103853048A - Design method for man-machine closed loop combined frequency robust controller of air vehicle multi-loop model cluster - Google Patents

Abstract

The invention provides a design method for a man-machine closed loop combined frequency robust controller of an air vehicle multi-loop model cluster. The method includes the steps that under the condition of different given heights and mach numbers, a model cluster formed by amplitude-frequency and phase-frequency characteristics in a full envelope is directly determined to obtain through a frequency sweeping test; an open-loop cut-off frequency interval is directly determined according to the amplitude-frequency characteristics in a flight envelope; a phase margin interval corresponding to the cut-off frequency interval is directly determined according to the amplitude-frequency characteristics in the flight envelope; a multi-level series connection lag- lead compensation link controller is added, the number of compensation links and parameter values are determined through a model identification method in phase margin index and system identification in the air vehicle full envelope; under the condition of a given decibel value of the phase margin index in the air vehicle full envelope, the effect of the controller is verified; starting from the concepts of phase margin and magnitude margin, the low-altitude flight robust controller which conforms to the full flight envelope and is free of pilot induced vibration, small in overshoot and stable is designed.

Description

Aircraft multiloop model bunch man-machine loop's combination frequency robust Controller Design method

Technical field

The present invention relates to a kind of controller of aircraft method for designing, particularly aircraft multiloop model bunch man-machine loop's combination frequency robust Controller Design method, belongs to the category such as observation and control technology and flight mechanics.

Background technology

The control of aircraft landing process plays an important role to flight safety; Because flying speed in aircraft landing process changes greatly, even also can face strong nonlinearity problem according to longitudinal model; On the other hand, there is the phenomenons such as saturated, dead band in the control vane of aircraft; Consider from flight safety, when hedgehopping (as take off/land), controller must ensure that system has certain stability margin, non-overshoot and stationarity, like this, just make hedgehopping controller design very complicated, can not directly apply mechanically existing control theory and carry out the design of aircraft control.

In the design of modern practical flight controller, a small part adopts state-space method to design, and great majority still adopt the classical frequency domain method taking PID as representative and carry out controller design against Nyquist Array Method as the modern frequency method of representative.Modern control theory is taking state-space method as feature, taking analytical Calculation as Main Means, to realize performance index as optimum modern control theory, then have and developed method for optimally controlling, model reference control method, self-adaptation control method, dynamic inversion control method, feedback linearization method, directly nonlinear optimization control, variable-gain control method, neural network control method, fuzzy control method, a series of controller design methods such as robust control method and several different methods combination control, the scientific paper of delivering is ten hundreds of, for example Ghasemi A in 2011 has designed reentry vehicle (the Ghasemi A of Adaptive Fuzzy Sliding Mode Control, Moradi M, Menhaj M B.Adaptive Fuzzy Sliding Mode Control Design for a Low-Lift Reentry Vehicle[J] .Journal of Aerospace Engineering, 2011, 25 (2): 210-216), Babaei A R in 2013 is that non-minimum phase and Nonlinear Flight device have designed fuzzy sliding mode tracking control robot pilot (Babaei A R, Mortazavi M, Moradi M H.Fuzzy sliding mode autopilot design for nonminimum phase and nonlinear UAV[J] .Journal of Intelligent and Fuzzy Systems, 2013, 24 (3): 499-509), a lot of research only rests on the Utopian simulation study stage, and there are three problems in this design: (1), owing to cannot carrying out the extreme low-altitude handling and stability experiment of aircraft, is difficult to obtain the mathematical model of accurate controlled device, (2) stability margin specifying for army's mark etc. is evaluated the important performance indexes of flight control system, and state-space method far can be expressed with obvious form unlike classical frequency method, (3) too complicated, the constraint of not considering working control device and state of flight of controller architecture, the controller of design physically can not be realized.

The scholar Rosenbrock of Britain systematically, study in a creative way in the design that how frequency domain method is generalized to multi-variable system and gone, utilize matrix diagonal dominance concept, Multivariable is converted into the design problem of the single-variable system of the classical approach that can know with people, in succession there is Mayne sequence return difference method later, MacFarlane System with Characteristic Locus Method, the methods such as Owens dyadic expansion, common feature is many input more than one outputs, the design of serious associated multi-variable system between loop, turn to the design problem of a series of single-variable systems, and then can select a certain classical approach (frequency response method of Nyquist and Bode, the root-locus technique of Evans etc.) design of completion system, above-mentioned these methods retain and have inherited the advantage of classic graphic-arts technique, do not require accurate especially mathematical model, easily meet the restriction in engineering.Particularly, in the time that employing has the conversational computer-aided design system of people's one machine of graphic display terminal to realize, can give full play to deviser's experience and wisdom, design and both meet quality requirements, be again controller physically attainable, simple in structure; Both at home and abroad to multivariate frequency method carried out improving research (tall and big far away, Luo Cheng, Shen Hui, Hu Dewen, Flexible Satellite Attitude Decoupling Controller Design Using Multiple Variable Frequency Domain Method, aerospace journal, 2007, Vol.28 (2), pp442-447; Xiong Ke, Xia Zhixun, Guo Zhenyun, the hypersonic cruise vehicle multivariable frequency domain approach of banked turn Decoupling design, plays arrow and guidance journal, 2011, Vol.31 (3), pp25-28) still, when this method for designing can taking into account system uncertain problem, conservative property is excessive, under aircraft control vane limited case, can not obtain rational design result.

In the development of high performance airplane, evaluate the quality of an airplane flight quality, not only depend on aircraft itself and driver-operated dynamics, also depend between driver and aircraft and highly as one man coordinate, and the rationality that between driver and Advanced Aircraft flight control system, function is distributed.Until after 1980, the American army mark of evaluating flying qualifies of aircraft still exists major defect, does not consider that driver is in the effect of handling in loop, thus thus the evaluation of gained and Aviatrix take a flight test after the result of gained still have certain gap.In recent years, developing the closed loop criterion (Neil 2 Smith's criterions) that a kind of driver of having participates in system, but how to realize so far still without efficient algorithm.Neil-Smith criterion proposed in 1970, and it is a closed loop following in elevation criterion.The method that it considers a problem is: in the time that driver drives an airplane and aircraft form a closed-loop system, driver handles like a cork and just can reach specific airmark, flight quality is good.In order to obtain the evaluation opinion to aircraft consistent with driver, in theoretical analysis, driver must be included.Conventionally, the mathematical model of driving behavior is nonlinear, may be discrete, but in the time that research has the manipulating objects of stability, useful approximate model is still linear.Shown by a large amount of flight practices and simulation study, the task that driver's behavior will be completed by his psychological characteristic, physiological property, surrounding environment, control system, manipulating objects decides, although driver has feature separately, but completing in single aerial mission, most of drivers' action can be described by completely specified mathematical model, it is the mean state of the lot of experiments of driving behavior, very approaching with actual conditions, the therefore present man-machine loop's characteristic pilot model that mostly adopts following form:

$Y_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}$

Estimate man-machine loop's characteristic with system open-loop transfer function or frequency characteristic.

Wherein: K _pfor the static gain of driver's link, inherent delay characteristic, the T that τ is driver _dfor driver's lead compensation time constant, T _ifor driver's lag compensation time constant; After this model adds, that in flight controller, will consider that the slower driver of reaction brings brings out oscillation problem, in thru-flight envelope curve, the slower driver of reaction is allowed to controller design does not also have systematic method, just has part Study to single state of flight.

In sum, current control method can't change at dummy vehicle, design non-driver bring out that vibration, overshoot are little, low-latitude flying controller stably according to the stability margin index in full flight envelope.

Summary of the invention

Can not in the situation that full flight envelope inner model changes greatly, design at aircraft and meet the technological deficiency that the non-driver of the stability margin index in full flight envelope brings out vibration, little, the steady low-latitude flying controller of overshoot in order to overcome existing method, the invention provides a kind of aircraft multiloop model bunch man-machine loop's combination frequency robust Controller Design method, the method directly determines by frequency sweep flight test the model cluster that the amplitude-frequency that obtains in full envelope curve and phase-frequency characteristic form under given differing heights, Mach number condition; Directly determine open loop cutoff frequency interval according to the amplitude versus frequency characte in flight envelope; Directly determine and the interval corresponding phase margin of cutoff frequency interval according to the phase-frequency characteristic in flight envelope; Determine compensation tache number and parameter value by adding the identification Method in plural serial stage hysteresis-lead compensation link controller phase margin index and System Discrimination in the full envelope curve of aircraft; Magnitude margin index L* decibels in the full flight envelope of aircraft is to carrying out controller's effect checking under stable condition; Design from the concept of phase margin and magnitude margin the non-driver that meets full flight envelope and bring out that vibration, overshoot are little, low-latitude flying robust controller stably.

The technical solution adopted for the present invention to solve the technical problems: a kind of aircraft multiloop model bunch man-machine loop's combination frequency robust Controller Design method, is characterized in comprising the following steps:

Under step 1, given differing heights, Mach number by frequency sweep flight test directly by allowing amplitude-frequency and phase-frequency characteristic in the full envelope curve of flight to form primary control surface in the full envelope curve of aircraft and the model cluster of flying height, and can cross over flight envelope and obtain the flutter frequency of aircraft, obtain open-loop transfer function model cluster matrix between corresponding aircraft primary control surface and flying height and be:

Wherein, G is m × m square formation, and m>1 is positive integer, the independent variable that s is Laplace transformation, h is aircraft altitude, and M is Mach number, and Δ is uncertain vector, and P is m × m single mode square formation, D is m × m polynomial expression diagonal matrix, and Q is m × m single mode square formation

for polynomial expression, n>1 is positive integer;

Choose

satisfy condition:

and

Wherein, G _efor m × m square formation, P _efor m × m single mode square formation, D _efor m × m polynomial expression diagonal matrix, d _i,Efor D _ei _erow, I _ecolumn element,

for the I of D _erow, I _ecolumn element, I _e=1,2 ..., m, Q _efor m × m single mode square formation,

for polynomial expression, arg is phase angle mathematic sign;

The controller of aircraft multiloop system is made as:

$G_{\mathrm{CA}}\left(s\right)=Q_E^{-1}\left(s\right)G_{a0}\left(s\right)P_E^{-1}\left(s\right)$

Wherein, G _cA(s) be m × m square formation, G _a0(s)=diag[G _{c, 1}(s), G _{c, 2}(s) ..., G _c,m(s)] be m × m diagonal matrix;

for G _a0(s) I _erow, I _ecolumn element, I _e=1,2 ..., m;

Step 2, controller

i _e=1,2 ..., the design process of m is as follows:

(1) order

the form of embodying is:

$G_{0,I_E}\left(s\right)=\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_{I_E}\left(s\right)$

Wherein

A(h,M,s)=s ^m+a _m-1(h,M)s ^m-1+a _m-2(h,M)s ^m-2+…+a ₁(h,M)s+a ₀(h,M)、

B (h, M, s)=s ⁿ+ b _n-1(h, M) s ^n-1+ b _n-2(h, M) s ^n-2+ ... + b ₁(h, M) s+b ₀(h, M) is polynomial expression, and s is the variable after laplace transform conventional in transport function, h, and M is respectively flying height and Mach number, and σ (h, M) is the time delay of pitch channel, and K (h, M) is with h, the gain that M changes, a _l(h, M), l=0,1,2 ..., m-1 be in polynomial expression A (h, M, s) with h, M change coefficient bunch, b _i(h, M), i=0,1,2 ..., n-1 be in polynomial expression B (h, M, s) with h, M change coefficient bunch,

for the indeterminate in model;

Pilot model while considering man-machine loop's characteristic:

$Y_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}$

Estimate man-machine loop's characteristic with system open-loop transfer function or frequency characteristic;

Wherein: K _pfor the static gain of driver's link, inherent delay characteristic, the T that τ is driver _dfor driver's lead compensation time constant, T _ifor driver's lag compensation time constant;

Like this, the open loop models of man-machine system just becomes:

$G_{I_E}\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_p\left(s\right)$

Wherein: ${\mathrm{\Δ}}_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}{\mathrm{\Δ}}_{I_E}\left(s\right);$

(2) judge in the uncertain part of known models | [△ _p(s)] _{s=j ω}|≤△ ₀time, directly determine that according to the amplitude versus frequency characte in flight envelope the interval definite method of open loop cutoff frequency is:

From

? $\left|{[K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_p\left(s\right)]}_{s=\mathrm{j\ω}}\right|=1$ In, be approximately $\left|{\left[K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\right]}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0,$ Obtain open loop cutoff frequency ω _cthe maximal value ω separating _cmaxwith minimum value ω _cmin, open loop cutoff frequency ω _cinterval is ω _cmin≤ ω _c≤ ω _cmax;

In formula, △ ₀for arithmetic number, j ω is the variable in frequency characteristic, and j is that imaginary part represents, ω is angular frequency;

(3) judge in the uncertain part of known models

time, according to the phase-frequency characteristic in flight envelope, calculate maximum phase nargin in envelope curve:

γ _max(ω _c)=max{180 °-σ (h, M) ω _c+ arg[A (h, M, j ω _c)]-arg[B (h, M, ω _c)], ω _cmin≤ ω _c≤ ω _cmaxwith minimum phase nargin in envelope curve:

Directly determine with the interval corresponding phase margin of cutoff frequency interval and be:

γ _min(ω _c)≤γ(ω _c)≤γ _max(ω _c),ω _cmin≤ω _c≤ω _cmax；

Wherein, △ ₁for arithmetic number;

(4) transport function of candidate's plural serial stage hysteresis-lead compensation link is:

$G_{c,I_E}\left(s\right)=k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}$

In formula, k _cfor constant gain to be determined, N is integer, represents the progression of hysteresis-lead compensation link to be determined, T _d1(i), T _l1(i), T _d2(i), T _l2(i), i=1,2 ..., N is time constant to be determined, a (i) >1, and i=1,2 ..., N is parameter to be determined;

Add after plural serial stage hysteresis-lead compensation link,

From $\left|G_{I_E}\left(\mathrm{j\ω}\right)G_{c,I_E}\left(\mathrm{j\ω}\right)\right|=1$ ?

$\left|{[k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}{K}_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}]}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0$ In, obtain open loop cutoff frequency ω _fcthe maximal value ω separating _fcmaxwith minimum value ω _fcmin, open loop cutoff frequency ω _fcinterval is ω _fcmin≤ ω _fc≤ ω _fcmax,

Phase margin index γ in the full envelope curve of aircraft ^*under stable condition, add the phase margin γ of system after plural serial stage hysteresis-lead compensation link _f(ω _fc) should meet:

Meet:

Under These parameters and maximum likelihood criterion or the common constraint of other criterion, can be according to progression N, the constant gain k of the maximum likelihood method in system model Structure Identification or the definite hysteresis-lead compensation link of discrimination method _c, time constant T _d1(i), T _l1(i), T _d2(i), T _l2(i), i=1,2 ..., N, parameter a (i) >1 to be determined, i=1,2 ..., N;

(5) the magnitude margin index L in the full envelope curve of aircraft ^*decibels is under stable condition,

From ${20\log }_{10}\left|G_{I_E}\left(\mathrm{j\ω}\right)G_{c,I_E}\left(\mathrm{j\ω}\right)\right|=-L^{*}$ ?

${20\log }_{10}\left|{[k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}{K}_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}]}_{s=\mathrm{j\ω}}\right|=-L^{*}$ In, obtain frequencies omega _lcthe maximal value ω separating _lcmaxwith minimum value ω _lcmin, ω _lcinterval is ω _lcmin≤ ω _lc≤ ω _lcmax,

Judgement:

Meet:

If meet, Flight Controller Design completes, if do not meet, then increases compensation tache progression or reduces constant gain k _c.

The invention has the beneficial effects as follows: from the concept of phase margin and magnitude margin, by adding plural serial stage hysteresis-lead compensation link controller, in full flight envelope, according to the parameter that meets the requirement of given phase margin and magnitude margin and identification Method and determine plural serial stage hysteresis-lead compensation link robust controller, design the non-driver that meets full flight envelope and bring out that vibration, overshoot are little, low-latitude flying robust controller stably.

Below in conjunction with embodiment, the present invention is elaborated.

Embodiment

Under step 1, given differing heights, Mach number, use Linear chirp

(f ₀for initial frequency, f ₁for cutoff frequency, r=(f ₁-f ₀)/T, T is the frequency sweep time) or logarithm swept-frequency signal f (t)=A (t) sin{2 π f ₀/ r[exp (rt)-1] } (f ₀for initial frequency, f ₁for cutoff frequency, r=ln (f ₁/ f ₀)/T, T is the frequency sweep time) aircraft is encouraged, by frequency sweep flight test directly by allowing amplitude-frequency and phase-frequency characteristic in the full envelope curve of flight to form primary control surface in the full envelope curve of aircraft and the model cluster of flying height, and can cross over flight envelope and obtain the flutter frequency of aircraft, obtain open-loop transfer function model cluster matrix between corresponding aircraft primary control surface and flying height and be:

Wherein, G is m × m square formation, and m>1 is positive integer, the independent variable that s is Laplace transformation, h is aircraft altitude, and M is Mach number, and Δ is uncertain vector, and P is m × m single mode square formation, D is m × m polynomial expression diagonal matrix, and Q is m × m single mode square formation

for polynomial expression, n>1 is positive integer;

Choose

satisfy condition:

and

Wherein, G _efor m × m square formation, P _efor m × m single mode square formation, D _efor m × m polynomial expression diagonal matrix, d _i,Efor D _ei _erow, I _ecolumn element,

for the I of D _erow, I _ecolumn element, I _e=1,2 ..., m, Q _efor m × m single mode square formation, for polynomial expression, arg is phase angle mathematic sign;

The controller of aircraft multiloop system is made as:

$G_{\mathrm{CA}}\left(s\right)=Q_E^{-1}\left(s\right)G_{a0}\left(s\right)P_E^{-1}\left(s\right)$

Wherein, G _cA(s) be m × m square formation, G _a0(s)=diag[G _{c, 1}(s), G _{c, 2}(s) ..., G _c,m(s)] be m × m diagonal matrix;

for G _a0(s) I _erow, I _ecolumn element, I _e=1,2 ..., m;

Step 2, controller

i _e=1,2 ..., the design process of m is as follows:

(1) order

the form of embodying is:

$G_{0,I_E}\left(s\right)=\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_{I_E}\left(s\right)$

Wherein

A(h,M,s)=s ^m+a _m-1(h,M)s ^m-1+a _m-2(h,M)s ^m-2+…+a ₁(h,M)s+a ₀(h,M)、

B (h, M, s)=s ⁿ+ b _n-1(h, M) s ^n-1+ b _n-2(h, M) s ^n-2+ ... + b ₁(h, M) s+b ₀(h, M) is polynomial expression, and s is the variable after laplace transform conventional in transport function, h, and M is respectively flying height and Mach number, and σ (h, M) is the time delay of pitch channel, and K (h, M) is with h, the gain that M changes, a _l(h, M), l=0,1,2 ..., m-1 be in polynomial expression A (h, M, s) with h, M change coefficient bunch, b _i(h, M), i=0,1,2 ..., n-1 be in polynomial expression B (h, M, s) with h, M change coefficient bunch,

for the indeterminate in model;

Pilot model while considering man-machine loop's characteristic:

$Y_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}$

Estimate man-machine loop's characteristic with system open-loop transfer function or frequency characteristic;

Wherein: K _pfor the static gain of driver's link, inherent delay characteristic, the T that τ is driver _dfor driver's lead compensation time constant, T _ifor driver's lag compensation time constant;

Like this, the open loop models of man-machine system just becomes:

$G_{I_E}\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_p\left(s\right)$

Wherein: ${\mathrm{\Δ}}_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}{\mathrm{\Δ}}_{I_E}\left(s\right);$

(2) judge in the uncertain part of known models | [△ _p(s)] _{s=j ω}|≤△ ₀time, directly determine that according to the amplitude versus frequency characte in flight envelope the interval definite method of open loop cutoff frequency is:

From

? $\left|{[K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_p\left(s\right)]}_{s=\mathrm{j\ω}}\right|=1$ In, be approximately $\left|{\left[K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\right]}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0,$ Obtain open loop cutoff frequency ω _cthe maximal value ω separating _cmaxwith minimum value ω _cmin, open loop cutoff frequency ω _cinterval is ω _cmin≤ ω _c≤ ω _cmax;

In formula, △ ₀for arithmetic number, j ω is the variable in frequency characteristic, and j is that imaginary part represents, ω is angular frequency;

(3) judge in the uncertain part of known models

time, according to the phase-frequency characteristic in flight envelope, calculate maximum phase nargin in envelope curve:

γ _max(ω _c)=max{180 °-σ (h, M) ω _c+ arg[A (h, M, j ω _c)]-arg[B (h, M, ω _c)], ω _cmin≤ ω _c≤ ω _cmaxwith minimum phase nargin in envelope curve:

Directly determine with the interval corresponding phase margin of cutoff frequency interval and be:

γ _min(ω _c)≤γ(ω _c)≤γ _max(ω _c),ω _cmin≤ω _c≤ω _cmax；

Wherein, △ ₁for arithmetic number;

(4) transport function of candidate's plural serial stage hysteresis-lead compensation link is:

$G_{c,I_E}\left(s\right)=k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}$

In formula, k _cfor constant gain to be determined, N is integer, represents the progression of hysteresis-lead compensation link to be determined, T _d1(i), T _l1(i), T _d2(i), T _l2(i), i=1,2 ..., N is time constant to be determined, a (i) >1, and i=1,2 ..., N is parameter to be determined;

Add after plural serial stage hysteresis-lead compensation link,

From $\left|G_{I_E}\left(\mathrm{j\ω}\right)G_{c,I_E}\left(\mathrm{j\ω}\right)\right|=1$ ?

$\left|{[k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}{K}_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}]}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0$ In, obtain open loop cutoff frequency ω _fcthe maximal value ω separating _fcmaxwith minimum value ω _fcmin, open loop cutoff frequency ω _fcinterval is ω _fcmin≤ ω _fc≤ ω _fcmax,

Phase margin index γ in the full envelope curve of aircraft ^*under stable condition, add the phase margin γ of system after plural serial stage hysteresis-lead compensation link _f(ω _fc) should meet:

Meet:

Under These parameters and maximum likelihood criterion or the common constraint of other criterion, can be according to progression N, the constant gain k of the maximum likelihood method in system model Structure Identification or the definite hysteresis-lead compensation link of discrimination method _c, time constant T _d1(i), T _l1(i), T _d2(i), T _l2(i), i=1,2 ..., N, parameter a (i) >1 to be determined, i=1,2 ..., N;

(5) the magnitude margin index L* decibels in the full envelope curve of aircraft is under stable condition,

From ${20\log }_{10}\left|G_{I_E}\left(\mathrm{j\ω}\right)G_{c,I_E}\left(\mathrm{j\ω}\right)\right|=-L^{*}$ ?

${20\log }_{10}\left|{[k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}{K}_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}]}_{s=\mathrm{j\ω}}\right|=-L^{*}$ In, obtain frequencies omega _lcthe maximal value ω separating _lcmaxwith minimum value ω _lcmin, ω _lcinterval is ω _lcmin≤ ω _lc≤ ω _lcmax,

Judgement:

Meet:

If meet, Flight Controller Design completes, if do not meet, then increases compensation tache progression or reduces constant gain k _c.

Claims (1)

1. aircraft multiloop model bunch man-machine loop's combination frequency robust Controller Design method, is characterized in comprising the following steps:

Under step 1, given differing heights, Mach number by frequency sweep flight test directly by allowing amplitude-frequency and phase-frequency characteristic in the full envelope curve of flight to form primary control surface in the full envelope curve of aircraft and the model cluster of flying height, and can cross over flight envelope and obtain the flutter frequency of aircraft, obtain open-loop transfer function model cluster matrix between corresponding aircraft primary control surface and flying height and be:

Wherein, G is m × m square formation, and m>1 is positive integer, the independent variable that s is Laplace transformation, h is aircraft altitude, and M is Mach number, and Δ is uncertain vector, and P is m × m single mode square formation, D is m × m polynomial expression diagonal matrix, and Q is m × m single mode square formation

for polynomial expression, n>1 is positive integer;

Choose

satisfy condition:

and

Wherein, G _efor m × m square formation, P _efor m × m single mode square formation, D _efor m × m polynomial expression diagonal matrix, d _i,Efor D _ei _erow, I _ecolumn element,

for the I of D _erow, I _ecolumn element, I _e=1,2 ..., m, Q _efor m × m single mode square formation,

for polynomial expression, arg is phase angle mathematic sign;

The controller of aircraft multiloop system is made as:

$G_{\mathrm{CA}}\left(s\right)=Q_E^{-1}\left(s\right)G_{a0}\left(s\right)P_E^{-1}\left(s\right)$

Wherein, G _cA(s) be m × m square formation, G _a0(s)=diag[G _{c, 1}(s), G _{c, 2}(s) ..., G _c,m(s)] be m × m diagonal matrix;

for G _a0(s) I _erow, I _ecolumn element, I _e=1,2 ..., m;

Step 2, controller

i _e=1,2 ..., the design process of m is as follows:

(1) order

the form of embodying is:

$G_{0,I_E}\left(s\right)=\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_{I_E}\left(s\right)$

Wherein

A(h,M,s)=s ^m+a _m-1(h,M)s ^m-1+a _m-2(h,M)s ^m-2+…+a ₁(h,M)s+a ₀(h,M)、

B (h, M, s)=s ⁿ+ b _n-1(h, M) s ^n-1+ b _n-2(h, M) s ^n-2+ ... + b ₁(h, M) s+b ₀(h, M) is polynomial expression, and s is the variable after laplace transform conventional in transport function, h, and M is respectively flying height and Mach number, and σ (h, M) is the time delay of pitch channel, and K (h, M) is with h, the gain that M changes, a _l(h, M), l=0,1,2 ..., m-1 be in polynomial expression A (h, M, s) with h, M change coefficient bunch, b _i(h, M), i=0,1,2 ..., n-1 be in polynomial expression B (h, M, s) with h, M change coefficient bunch,

for the indeterminate in model;

Pilot model while considering man-machine loop's characteristic:

$Y_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}$

Estimate man-machine loop's characteristic with system open-loop transfer function or frequency characteristic;

Wherein: K _pfor the static gain of driver's link, inherent delay characteristic, the T that τ is driver _dfor driver's lead compensation time constant, T _ifor driver's lag compensation time constant;

Like this, the open loop models of man-machine system just becomes:

$G_{I_E}\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_p\left(s\right)$

Wherein: ${\mathrm{\Δ}}_p\left(s\right)=K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}{\mathrm{\Δ}}_{I_E}\left(s\right);$

(2) judge in the uncertain part of known models | [△ _p(s)] s=j ω |≤△ ₀time, directly determine that according to the amplitude versus frequency characte in flight envelope the interval definite method of open loop cutoff frequency is:

From

? $\left|{[K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+{\mathrm{\Δ}}_p\left(s\right)]}_{s=\mathrm{j\ω}}\right|=1$ In, be approximately $\left|{\left[K_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\right]}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0,$ Obtain open loop cutoff frequency ω _cthe maximal value ω separating _cmaxwith minimum value ω _cmin, open loop cutoff frequency ω _cinterval is ω _cmin≤ ω _c≤ ω _cmax;

In formula, △ ₀for arithmetic number, j ω is the variable in frequency characteristic, and j is that imaginary part represents, ω is angular frequency;

(3) judge in the uncertain part of known models

time, according to the phase-frequency characteristic in flight envelope, calculate maximum phase nargin in envelope curve:

γ _max(ω _c)=max{180 °-σ (h, M) ω _c+ arg[A (h, M, j ω _c)]-arg[B (h, M, ω _c)], ω _cmin≤ ω _c≤ ω _cmaxwith minimum phase nargin in envelope curve:

Directly determine with the interval corresponding phase margin of cutoff frequency interval and be:

γ _min(ω _c)≤γ(ω _c)≤γ _max(ω _c),ω _cmin≤ω _c≤ω _cmax；

Wherein, △ ₁for arithmetic number;

(4) transport function of candidate's plural serial stage hysteresis-lead compensation link is:

$G_{c,I_E}\left(s\right)=k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}$

In formula, k _cfor constant gain to be determined, N is integer, represents the progression of hysteresis-lead compensation link to be determined, T _d1(i), T _l1(i), T _d2(i), T _l2(i), i=1,2 ..., N is time constant to be determined, a (i) >1, and i=1,2 ..., N is parameter to be determined;

Add after plural serial stage hysteresis-lead compensation link,

From $\left|G_{I_E}\left(\mathrm{j\ω}\right)G_{{c,I}_E}\left(\mathrm{j\ω}\right)\right|=1$ ?

$\left|{[k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}{K}_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}]}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0$ In, obtain open loop cutoff frequency ω _fcthe maximal value ω separating _fcmaxwith minimum value ω _fcmin, open loop cutoff frequency ω _fcinterval is ω _fcmin≤ ω _fc≤ ω _fcmax,

Phase margin index γ in the full envelope curve of aircraft ^*under stable condition, add the phase margin γ of system after plural serial stage hysteresis-lead compensation link _f(ω _fc) should meet:

Meet:

Under These parameters and maximum likelihood criterion or the common constraint of other criterion, can be according to progression N, the constant gain k of the maximum likelihood method in system model Structure Identification or the definite hysteresis-lead compensation link of discrimination method _c, time constant T _d1(i), T _l1(i), T _d2(i), T _l2(i), i=1,2 ..., N, parameter a (i) >1 to be determined, i=1,2 ..., N;

(5) the magnitude margin index L in the full envelope curve of aircraft ^*decibels is under stable condition,

From ${20\log }_{10}\left|G_{I_E}\left(\mathrm{j\ω}\right)G_{c,I_E}\left(\mathrm{j\ω}\right)\right|=-L^{*}$ ?

${20\log }_{10}\left|{[k_c\underset{i=1}{\overset{N}{\mathrm{\Π}}}\frac{T_{D1}\left(i\right)s+1}{a\left(i\right)T_{L1}\left(i\right)s+1}\·\frac{T_{D2}\left(i\right)s/a\left(i\right)+1}{T_{L2}\left(i\right)s+1}{K}_p\frac{T_{D}s+1}{T_{I}s+1}{e}^{-\mathrm{\τs}}\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}]}_{s=\mathrm{j\ω}}\right|=-L^{*}$ In, obtain frequencies omega _lcthe maximal value ω separating _lcmaxwith minimum value ω _lcmin, ω _lcinterval is ω _lcmin≤ ω _lc≤ ω _lcmax,

Judgement:

Meet:

If meet, Flight Controller Design completes, if do not meet, then increases compensation tache progression or reduces constant gain k _c.