CN103823378A - Design method for longitudinal flight model cluster flutter-restraining composite PID robust controller - Google Patents

Abstract

The invention provides a design method for a longitudinal flight model cluster flutter-restraining composite PID robust controller. According to the design method, a model cluster composed of amplitude-frequency characteristics and phase-frequency characteristics in a whole envelope is determined directly through frequency sweep flight tests with different heights and different Mach numbers given; an open-loop cut-off frequency section is directly determined according to the amplitude-frequency characteristics within a flight envelope; a phase margin section corresponding to the open-loop cut-off frequency section is directly determined according to the phase-frequency characteristics in the flight envelope; a multi-stage PID controller is additionally arranged, and therefore the number of stages and parameter values of a multi-stage PID robust controller are determined through a model identification method in a phase margin index and system identification process in the whole envelope of an air vehicle; the effect of the controller is verified with the decibel of a magnitude margin index L* in the whole envelope of the air vehicle given; a low-altitude flight robust controller which is capable of restraining flutter and small in overshoot and accords with a whole flight envelope can be designed from the conceptions of phase margin and magnitude margin.

Description

Longitudinal Flight model cluster Flutter Suppression Composite PID robust Controller Design method

Technical field

The present invention relates to a kind of controller of aircraft method for designing, particularly Longitudinal Flight model cluster Flutter Suppression Composite PID 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 guarantee 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 take PID as representative and carry out controller design against Nyquist Array Method as the modern frequency method of representative.Modern control theory is take state-space method as feature, take 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 stipulating 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; (tall and big far away, sieve becomes, Shen Hui, Hu Dewen, Flexible Satellite Attitude Decoupling Controller Design Using Multiple Variable Frequency Domain Method, aerospace journal, 2007, Vol.28 (2), pp442-447 multivariate frequency method have been carried out improving research both at home and abroad; 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; Particularly, in the time of aircraft generation flutter, designed control system is likely difficult to the stability of the system that guarantees.

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

Summary of the invention

The technological deficiency that can not design the stability margin index meeting in full flight envelope at aircraft in the situation that full flight envelope inner model changes greatly and can suppress little, the steady low-latitude flying controller of overshoot of flutter in order to overcome existing method, the invention provides a kind of Longitudinal Flight model cluster Flutter Suppression Composite PID 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 multistage PID robust controller sum of series parameter value by adding the identification Method in multistage PID 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; From the concept of phase margin and magnitude margin design meet full flight envelope can suppress that flutter, 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 Longitudinal Flight model cluster Flutter Suppression Composite PID robust Controller Design method, is characterized in comprising the following steps:

1, under 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 elevating rudder in the full envelope curve of aircraft and the model cluster of flying height, and the flutter frequency that can cross over flight envelope acquisition aircraft, obtains open-loop transfer function clustering model between corresponding aircraft elevating rudder and flying height

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

With flutter frequency ω _aSE(h, M);

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, △ (s) is the indeterminate in model;

2, judge in the uncertain part of known models | [△ (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 | G (j ω) |=1 $\left|{[\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+\mathrm{\Δ}\left(s\right)]}_{s=\mathrm{j\ω}}\right|=1$ In, be approximately

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 γ in envelope curve _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, the transport function of the multistage PID controller of candidate is:

$G_c\left(s\right)=\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}$

In formula, k _cfor constant gain to be determined, N is integer, represents the progression of multistage PID controller to be determined, k _p(i), k _i(i), k _d(i) i=1,2 ..., N is constant to be determined, k _aSEfor Flutter Suppression gain;

Add after multistage PID controller,

From | G (j ω) G _c(j ω) |=1 $\left|{\{\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}\·\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\}}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0$ 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 multistage PID controller _f(ω _fc) should meet:

Meet:

Meanwhile, at flutter frequency ω _aSE(h, M) locates also should meet:

Meet:

Under These parameters and maximum likelihood criterion or the common constraint of other criterion, can determine according to the maximum likelihood method in system model Structure Identification or discrimination method progression N, the constant k of multistage PID controller _p(i), k _i(i), k _d(i) i=1,2 ..., N and Flutter Suppression gain k _aSE;

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

From 20log ₁₀| G (j ω) G _c(j ω) |=-L ^*?

${20\log }_{10}\left|{\{\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}\·\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\}}_{s=\mathrm{j\ω}}\right|=-L^{*}$ 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 increase the progression of multistage PID controller.

The invention has the beneficial effects as follows: from the concept of phase margin and magnitude margin, by adding multistage PID 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 multistage PID robust controller, design meet full flight envelope can suppress that flutter, overshoot are little, low-latitude flying robust controller stably.

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

Embodiment

1, under 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, amplitude-frequency and phase-frequency characteristic in the full envelope curve that can directly obtain allowing to fly, elevating rudder in the full envelope curve of formation aircraft and the model cluster of flying height, and the flutter frequency that can cross over flight envelope acquisition aircraft, obtains open-loop transfer function clustering model between corresponding aircraft elevating rudder and flying height

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

With flutter frequency ω _aSE(h, M);

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, △ (s) is the indeterminate in model;

2, judge in the uncertain part of known models | [△ (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 | G (j ω) |=1 $\left|{[\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+\mathrm{\Δ}\left(s\right)]}_{s=\mathrm{j\ω}}\right|=1$ In, be approximately

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 γ in envelope curve _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, the transport function of the multistage PID controller of candidate is:

$G_c\left(s\right)=\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}$

In formula, k _cfor constant gain to be determined, N is integer, represents the progression of multistage PID controller to be determined, k _p(i), k _i(i), k _d(i) i=1,2 ..., N is constant to be determined, k _aSEfor Flutter Suppression gain;

Add after multistage PID controller,

From | G (j ω) G _c(j ω) |=1 $\left|{\{\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}\·\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\}}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0$ 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 multistage PID controller _f(ω _fc) should meet:

Meet:

Meanwhile, at flutter frequency ω _aSE(h, M) locates also should meet:

Meet:

Under These parameters and maximum likelihood criterion or the common constraint of other criterion, can determine according to the maximum likelihood method in system model Structure Identification or discrimination method progression N, the constant k of multistage PID controller _p(i), k _i(i), k _d(i) i=1,2 ..., N and Flutter Suppression gain k _aSE;

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

From 20log ₁₀| G (j ω) G _c(j ω) |=-L ^*?

${20\log }_{10}\left|{\{\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}\·\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\}}_{s=\mathrm{j\ω}}\right|=-L^{*}$ 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 increase the progression of multistage PID controller.

Claims (1)

1. a Longitudinal Flight model cluster Flutter Suppression Composite PID robust Controller Design method, is characterized in comprising the following steps:

1) under 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 elevating rudder in the full envelope curve of aircraft and the model cluster of flying height, and the flutter frequency that can cross over flight envelope acquisition aircraft, obtains open-loop transfer function clustering model between corresponding aircraft elevating rudder and flying height

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

With flutter frequency ω _aSE(h, M);

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, △ (s) is the indeterminate in model;

2) judge in the uncertain part of known models | [△ (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 | G (j ω) |=1 $\left|{[\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}+\mathrm{\Δ}\left(s\right)]}_{s=\mathrm{j\ω}}\right|=1$ In, be approximately

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 γ in envelope curve _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 the multistage PID controller of candidate is:

$G_c\left(s\right)=\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}$

In formula, k _cfor constant gain to be determined, N is integer, represents the progression of multistage PID controller to be determined, k _p(i), k _i(i), k _d(i) i=1,2 ..., N is constant to be determined, k _aSEfor Flutter Suppression gain;

Add after multistage PID controller,

From | G (j ω) G _c(j ω) |=1 $\left|{\{\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}\·\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\}}_{s=\mathrm{j\ω}}\right|=1+{\mathrm{\Δ}}_0$ 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 _fc _min≤ 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 multistage PID controller _f(ω _fc) should meet:

Meet:

Meanwhile, at flutter frequency ω _aSE(h, M) locates also should meet:

Meet:

Under These parameters and maximum likelihood criterion or the common constraint of other criterion, can determine according to the maximum likelihood method in system model Structure Identification or discrimination method progression N, the constant k of multistage PID controller _p(i), k _i(i), k _d(i) i=1,2 ..., N and Flutter Suppression gain k _aSE;

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

From 20log ₁₀| G (j ω) G _c(j ω) |=-L ^*?

${20\log }_{10}\left|{\{\frac{\underset{i=1}{\overset{N}{\mathrm{\Π}}}[k_P\left(i\right)+k_I\left(i\right)/s+k_D\left(i\right)\·s]}{\frac{k_{\mathrm{ASE}}}{{\mathrm{\ω}}_{\mathrm{ASE}}}s+1}\·\frac{e^{-\mathrm{\σ}(h,M)s}K(h,M)A(h,M,s)}{B(h,M,s)}\}}_{s=\mathrm{j\ω}}\right|=-L^{*}$ 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 increase the progression of multistage PID controller.