CN102508503B - Compensation method based on generalized inner module for eccentric torque of three-shaft inertially stabilized platform - Google Patents

Abstract

A compensation method based on a generalized internal module for eccentric torque of a three-shaft inertially stabilized platform includes establishing a state-space equation of a control system of the three-shaft inertially stabilized platform, measuring angular rate information of the platform in real time by the aid of a rate gyroscope, measuring current information in real time by the aid of a current sensor, implanting a joint unstable module of reference input and the eccentric torque into the system, and achieving the purpose of unsteady-state error tracking control by the aid of generalized inner module control algorithm. An internal module controller comprises a servo compensator and a stabilized compensator. By the aid of the compensation method, disturbance attenuation capacity is improved, unsteady-state error tracking is realized, and a high robust performance is realized.

Description

A kind of three axle inertially stabilized platform eccentric moment compensation methodes based on generalized inner

Technical field

The present invention relates to a kind of three axle inertially stabilized platform eccentric moment compensation methodes based on generalized inner, belong to high resolving power aviation earth observation systems field, can be used for the demanding three axle inertially stabilized platform floatings of lasting accuracy and follow the tracks of control, be particularly suitable for small-sized high resolving power airborne remote sensing three axle inertially stabilized platforms.

Background technology

Inertially stabilized platform is to realize the necessaries of high resolving power earth observation, and it can effectively isolate disturbance and the imperfect attitude motion of flying platform, makes the optical axis sensing of observation load and course remain that inertial space is stable.At present, external mainstream product is PAV30 and the PAV80 of Switzerland Leica company, and domestic correlative study is at the early-stage, without matured product.

The ideally impact of interference-free moment, stable platform remains that inertial space is stable, but due to actual mismachining tolerance, the unequal factor of counterweight, the barycenter of platform and framework axle center decentraction, there is certain eccentric throw, so under the effect of acceleration of gravity and motion artifacts acceleration, the athletic meeting of platform is subject to the impact of eccentric moment, thereby affect the performance index such as its lasting accuracy; Quality, eccentric throw and motion artifacts acceleration are larger, and eccentric moment is larger, and lasting accuracy is poorer, so must take measures to suppress the effect of eccentric moment.compensation method for the inertially stabilized platform eccentric moment, applied at present one piece of patent " a kind of unbalanced moment of aerial remote sensing inertially stabilized platform is estimated and compensation method " (application number 200910241242.9), the method is measured the sky to acceleration and motion artifacts acceleration by the mems accelerometer that is arranged on platform, adopt low pass filtering method to carry out filtering to current information, eccentric moment is estimated, and adopt feed forward method to compensate, can suppress the effect of eccentric moment to a certain extent, but there is the deficiency of following three aspects:: first, for three axle inertially stabilized platforms, adopt the method three mems accelerometers to be installed respectively at each framework, the platform by volume quality is corresponding increasing all, be unfavorable for its small-sized structural design, the second, zero stability partially and the repeatability of mems accelerometer are all relatively poor, and measured value contains larger noise, introduce unknown disturbance factor when feedforward compensation, three, for the platform real-time control system, the more difficult realization of Butterworth low-pass filter, low-pass filtering can affect the Disturbance Rejection ability simultaneously.So in sum, the method is more difficult realization physically, this has directly limited the application power in real work.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome prior art and realize the defective of estimation and the compensation of eccentric moment by increasing measuring sensor, provide a kind of and can compensate the method for eccentric moment by CONTROLLER DESIGN on the basis of original system assembly, do not increase volume mass, and simple, reliable.

Technical solution of the present invention is: a kind of three axle inertially stabilized platform eccentric moment compensation methodes based on generalized inner, and performing step is as follows:

(1) adopt the rate gyro that is arranged on three axle inertially stabilized platform gimbal axis to measure the angular speed information ω of three axle inertially stabilized platforms _out, described angular speed information has comprised the angular speed information that Electric Machine Control moment and eccentric moment act on down three axle inertially stabilized platforms simultaneously;

(2) with the angular speed information ω that obtains in step (1) _outWith angular speed setting value ω _setDiffer from, obtain angular speed error e=ω _set-ω _out

(3) the angular speed error e that obtains in step (2) is brought in servo compensator goes, obtain servo compensator controlled quentity controlled variable u _e, the state space equation of servo compensator is

Controlled quentity controlled variable u _e=K _ex _e, A wherein _eBe servo compensator system matrix, B _eBe servo compensator control inputs matrix, K _eBe servo compensator state feedback matrix, x _eBe servo compensator state variable, u _eBe the servo compensator controlled quentity controlled variable;

(4) adopt the current sensor measurement that is connected in electric motor loop to go out to be arranged on the current information i of the torque motor on three axle inertially stabilized platform frameworks _out, the angular speed information ω that obtains in integrating step (1) simultaneously _outBe brought in calm compensator and go, obtain calm compensator controlled quentity controlled variable u ₂=Kx, x=[ω _outi _out] ', wherein K is calm compensator state feedback matrix, u ₂Be calm compensator controlled quentity controlled variable;

(5) with the servo compensator controlled quentity controlled variable u that obtains in step (3) _eWith the calm compensator controlled quentity controlled variable u that obtains in step (5) ₂Differ from, obtain generalized inner control algolithm controlled quentity controlled variable u=u _e-u ₂

(6) the generalized inner control algolithm controlled quentity controlled variable u that obtains in step (5) is brought at reference input r and eccentric moment T _dGo in former speed open cycle system (as the former speed open cycle system in accompanying drawing 1) under effect, realize the compensation of eccentric moment, realize that finally the floating of system is followed the tracks of.

Former speed open cycle system i.e. three axle inertially stabilized platform speed open cycle systems, it be input as generalized inner controlled quentity controlled variable u, be output as angular speed ω _out, the state space equation of establishing former speed open cycle system is $\left\{\begin{array}{c}\stackrel{\·}{x}=\mathrm{Ax}+\mathrm{Bu}+B_d{T}_d\\ y=\mathrm{Cx}+\mathrm{Du}+D_d{T}_d\end{array}\right.;$ Wherein, x is the state variable of former speed open cycle system, x=[ω _outi _out] '; A is the system matrix of former speed open cycle system; B is the control inputs matrix of former speed open cycle system; B _dThe eccentric moment input matrix of former speed open cycle system; T _dBe eccentric moment; Y is the output variable of former speed open cycle system, y=ω _outC is the output matrix of former speed open cycle system; D is the transmission matrix of former speed open cycle system; D _dEccentric moment output matrix for former speed open cycle system; U is control inputs;

Servo compensator system matrix A in described step (3) _e, servo compensator control inputs matrix B _e, servo compensator state feedback matrix K _eSpecifically to obtain step as follows with the state feedback matrix K of calm compensator:

(31) at first determine reference input ω _setWith eccentric moment T _dThe common time-dependent model of model obtains reference input ω _setWith eccentric moment T _dThe least common multiple formula of two time-dependent models: φ (s)=s ^l+ α _l-1s ^l-1+ ... + α ₁s ¹+ α ₀, reference input ω _setWith eccentric moment T _dModel is known, factor alpha ₀～α _l-1Be known quantity; L is the high-order term of φ (s), and s is frequency domain symbol, α ₀～α _l-1Each time item coefficient for φ (s).

(32) by the factor alpha of φ (s) ₀～α _l-1Determine blocking factor matrix Γ _l*1And β _l*1, ${\mathrm{\Γ}}_{l*l}=\left[\begin{array}{cccc}0& & & \\ 0& & I_{l-1}& \\ .& & & \\ .& & & \\ .& & & \\ {\mathrm{\α}}_0& {\mathrm{\α}}_1& ...& {\mathrm{\α}}_{l-1}\end{array}\right],$ ${\mathrm{\β}}_{l*1}=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 1\end{array}\right];$ Wherein, l is the high-order term of φ (s), α ₀～α _l-1Be each time item coefficient of φ (s), I _l-1Be l-1 rank unit matrix;

(33) the blocking factor matrix Γ that is obtained by step (32) _l*1And β _l*1, obtain the coefficient matrices A of servo compensator state space equation _eWith the control inputs matrix B _e, wherein,

So just obtain the state space equation of servo compensator

Servo compensator state feedback matrix K _eState feedback matrix K with calm compensator;

(34) the servo compensator state space equation that step (33) is obtained and former speed open cycle system state space equation make up, and obtain the state space equation of final cascade system: $\left[\begin{array}{c}\stackrel{\·}{x}\\ {\stackrel{\·}{x}}_e\end{array}\right]=\left[\begin{array}{cc}A& 0\\ -B_{e}C& A_e\end{array}\right]\left[\begin{array}{c}x\\ x_e\end{array}\right]+\left[\begin{array}{c}B\\ -B_{e}D\end{array}\right]u+\left[\begin{array}{c}{B}_d\\ -B_e{D}_d\end{array}\right]T_d+\left[\begin{array}{c}0\\ B_e\end{array}\right]r,$ The definition front of each coefficient provides;

(35) the cascade system state space equation that obtains in step (34) is adopted classical POLE PLACEMENT USING u=K _Tx _TMethod is carried out POLE PLACEMENT USING, obtains state feedback matrix K _T, wherein, $x_T={\left[\begin{array}{c}x\\ x_e\end{array}\right]}^{\′};$

(36) with the state feedback matrix K that obtains in step (35) _TDecompose, make K _T=[K K _e], obtain the state feedback matrix K of servo compensator _eState feedback matrix K with calm compensator.

Principle of work of the present invention: three axle inertially stabilized platforms remain that inertial space is stable, and under quiescent conditions, there is normal value eccentric moment T in platform _dCThe impact of=mgl, platform control system are by the effect of close-loop feedback, and the control moment motor is exported and T _dCThe torque keeping platform inertia spatial stability of equal and opposite in direction, opposite direction; Under current intelligence, there is the motion artifacts acceleration in platform framework, and the eccentric moment formula is:

T _d＝m(g+a)l ①

In formula, m is the framework quality, and g is acceleration of gravity, and a is the motion artifacts acceleration, and l is eccentric throw.

In the practical flight process, the most typical disturbance form of aircraft is sinusoidal perturbation, and the disturbed motion acceleration a with aircraft is considered as the sinusoidal quantity that frequency is 1HZ here, and its frequency structure characteristic is:

${\mathrm{\&phi;}}_{T_d}\left(s\right)={\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000104328880000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+4{\mathrm{\&pi;}}^2$ ②

The frequency structure characteristic of step reference input is:

φ _r(s)＝s ③

The common time-dependent model that 2., 3. can be got reference input and eccentric moment by formula is:

φ(s)＝s(s ²+4π ²) ④

4. can set up servo compensator state space equation in the generalized inner control algolithm by formula:

${\stackrel{\&CenterDot;}{x}}_e=A_e{x}_e+B_{e}e$ ⑤

Obtain the controlled quentity controlled variable form of servo compensator and calm compensator by the pole-assignment of classics:

$\left\{\begin{array}{c}{u}_e=K_e{\mathrm{<figure-callout\; id="2"\; label="x\; e\; u"\; filenames="HDA0000104328880000032.png"\; state="\{\{state\}\}">x</figure-callout>}}_e& \\ u_{}{}_2=\mathrm{Kx}\end{array}\right.$ ⑥

In formula, x is the state variable of former speed open cycle system, x=[ω _outi _out] ', ω _outBe the mesa corners rate information, measured by rate gyro; ω _outFor platform current of electric information, by current sensor measurement.

Finally, generalized inner control algolithm controlled quentity controlled variable is u=u _e-u ₂, this controlled quentity controlled variable is applied in former speed open cycle system goes, the driving moment motor action, implementation platform is to the asymptotic tracking of reference input and the compensation of eccentric moment.

The present invention's advantage compared with prior art is:

(1) the present invention by platform self assembly rate gyro and current sensor, measures respectively mesa corners rate information and current of electric information, realizes the generalized inner control algolithm, and its process does not increase the platform by volume quality, is conducive to small-sized structural design.

(2) generalized inner of the present invention is controlled and is based upon on the state space equation basis, is comprised of common integrator, proportional component, and algorithm is simple, easily realizes and reliable, and stronger actual application ability is arranged.

(3) the present invention has taken into account reference input and eccentric moment acts on the impact that brings simultaneously, and the disturbances such as modeling error, Parameter Perturbation are had stronger insensitivity, has improved the robust performance of system.

Description of drawings

Fig. 1 is generalized inner control algolithm implementation step schematic diagram of the present invention;

Fig. 2 is servo compensator of the present invention and calm design of Compensator process flow diagram;

Fig. 3 is the eccentric moment compensation method structural drawing based on generalized inner of the present invention;

Fig. 4 is not for adopting the angular speed output of three axle inertially stabilized platforms of the present invention under the eccentric moment effect;

Fig. 5 has adopted the angular speed output of three axle inertially stabilized platforms of the present invention under the eccentric moment effect.

Embodiment

Concrete implementation step is as shown in Figure 1:

(1) system powers on, initialization, rate gyro signal acquisition circuit and motor current signal Acquisition Circuit life's work;

(2) adopt the rate gyro that is arranged on three axle inertially stabilized platform gimbal axis to measure the angular speed information ω of three axle inertially stabilized platforms _out, described angular speed information has comprised the angular speed information that Electric Machine Control moment and eccentric moment act on down three axle inertially stabilized platforms simultaneously;

(3) with the angular speed information ω that obtains in step (2) _outWith angular speed setting value ω _setDiffer from, obtain angular speed error e=ω _set-ω _out

(4) the angular speed error e that obtains in step (3) is brought in servo compensator goes, controlled amount u _e, the state space equation of servo compensator is Controlled quentity controlled variable u _e=K _ex _e

Wherein, A _eBe servo compensator system matrix, B _eBe servo compensator control inputs matrix, K _eBe servo compensator state feedback matrix, x _eBe servo compensator state variable, u _eBe the servo compensator controlled quentity controlled variable;

(5) adopt the current sensor measurement that is connected in electric motor loop to go out to be arranged on the current information i of the torque motor on three axle inertially stabilized platform frameworks _out, the angular speed information ω that obtains in integrating step (2) simultaneously _outBe brought in calm compensator and go, controlled amount u ₂=Kx, x=[ω _outi _out] ';

Wherein, K is calm compensator state feedback matrix, u ₂Be calm compensator controlled quentity controlled variable;

(6) with the controlled quentity controlled variable u that obtains in step (4) _eAnd the controlled quentity controlled variable u that obtains in step (5) ₂Differ from, obtain generalized inner control algolithm controlled quentity controlled variable u=u _e-u ₂

(7) the generalized inner control algolithm controlled quentity controlled variable u that obtains in step (6) is brought at reference input r and eccentric moment T _dGo in former speed open cycle system (as the former speed open cycle system in accompanying drawing 1) under effect, realize the compensation of eccentric moment, realize that finally the floating of system is followed the tracks of.

Former speed open cycle system i.e. three axle inertially stabilized platform speed open cycle systems, it be input as generalized inner controlled quentity controlled variable u, be output as angular speed ω _out, the state space equation of establishing former speed open cycle system is: $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{Ax}+\mathrm{Bu}+B_d{T}_d\\ y=\mathrm{Cx}+\mathrm{Du}+D_d{T}_d\end{array}\right.;$ Wherein, x is the state variable of former speed open cycle system, x=[ω _outi _out] '; A is the system matrix of former speed open cycle system; B is the control inputs matrix of former speed open cycle system; B _dThe eccentric moment input matrix of former speed open cycle system; T _dBe eccentric moment; Y is the output variable of former speed open cycle system, y=ω _outC is the output matrix of former speed open cycle system; D is the transmission matrix of former speed open cycle system; D _dEccentric moment output matrix for former speed open cycle system; U is control inputs;

Be illustrated in figure 2 as the state space equation system matrix A of servo compensator of the present invention _e, the control inputs matrix B _e, state feedback matrix K _eAs follows with the state feedback matrix K specific implementation step of calm compensator:

(1) at first determine reference input ω _setWith eccentric moment T _dThe common time-dependent model of model obtains reference input ω _setWith eccentric moment T _dThe least common multiple formula φ (s) of two time-dependent models=s ^l+ α _l-1s ^l-1+ ... + α ₁s ¹+ α ₀, reference input ω _setWith eccentric moment T _dModel is known, factor alpha ₀～α _l-1Be known quantity; Wherein, l is the high-order term of φ (s), and s is frequency domain symbol, α ₀～α _l-1Each time item coefficient for φ (s);

(2) by the factor alpha of φ (s) ₀～α _l-1Determine blocking factor matrix Γ _l*1And β _l*1, ${\mathrm{\&Gamma;}}_{l*l}=\left[\begin{array}{cccc}0& & & \\ 0& & I_{l-1}& \\ .& & & \\ .& & & \\ .& & & \\ {\mathrm{\&alpha;}}_0& {\mathrm{\&alpha;}}_1& ...& {\mathrm{\&alpha;}}_{l-1}\end{array}\right],$ ${\mathrm{\&beta;}}_{l*1}=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 1\end{array}\right];$ Wherein, l is the high-order term of φ (s), α ₀～α _l-1Be each time item coefficient of φ (s), I _l-1Be l-1 rank unit matrix;

(3) the blocking factor matrix Γ that is obtained by step (2) _l*1And β _l*1, obtain the coefficient matrices A of servo compensator state space equation _eWith the control inputs matrix B _e, wherein,

So just obtain the state space equation of servo compensator

Servo compensator state feedback matrix K _eState feedback matrix K with calm compensator;

(4) the servo compensator state space equation that step (3) is obtained and former speed open cycle system state space equation make up, and obtain the state space equation of final cascade system: $\left[\begin{array}{c}\stackrel{\&CenterDot;}{x}\\ {\stackrel{\&CenterDot;}{x}}_e\end{array}\right]=\left[\begin{array}{cc}A& 0\\ -B_{e}C& A_e\end{array}\right]\left[\begin{array}{c}x\\ x_e\end{array}\right]+\left[\begin{array}{c}B\\ -B_{e}D\end{array}\right]u+\left[\begin{array}{c}{B}_d\\ -B_e{D}_d\end{array}\right]T_d+\left[\begin{array}{c}0\\ B_e\end{array}\right]r,$ The definition front of each coefficient provides;

(5) the cascade system state space equation that obtains in step (4) is adopted classical POLE PLACEMENT USING u=K _Tx _TMethod is carried out POLE PLACEMENT USING, obtains state feedback matrix K _T, wherein, $x_T={\left[\begin{array}{c}x\\ x_e\end{array}\right]}^{\&prime;};$

(6) with the state feedback matrix K that obtains in step (5) _TDecompose, make K _T=[K K _e], obtain the state feedback matrix K of servo compensator _eState feedback matrix K with calm compensator.

Be illustrated in figure 3 as the eccentric moment compensation method structural drawing based on generalized inner of the present invention.With reference to input ω _setThe rate information ω that measures with the rate gyro Real-time Measuring _outMake the poor margin of error e=ω that obtains _set-ω _outMargin of error e is applied to servo compensator $\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_e=A_e{x}_e+B_{e}e\\ u_e=K_e{x}_e\end{array}\right.$ In controlled amount u _eWith servo compensator controlled quentity controlled variable u _e=K _ex _eWith calm compensator controlled quentity controlled variable u ₂=Kx makes the poor overhead control amount u=u that obtains _e-u ₂Controlled quentity controlled variable u is applied in former speed open cycle system goes, can realize reference input ω _setAsymptotic tracking and eccentric moment T _dCompensation, the state space equation of its Central Plains speed open cycle system is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{Ax}+\mathrm{Bu}+B_d{T}_d\\ y=\mathrm{Cx}+\mathrm{Du}+D_d{T}_d\end{array}\right..$

For verifying validity of the present invention, carried out emulation experiment.Simulation parameter is: framework quality 100Kg, airplane motion disturbing acceleration a is that 1g, frequency are 1Hz, the platform framework eccentric throw is 1cm, and under the effect of the airplane motion disturbing acceleration of acceleration of gravity and alternation, the expression formula of eccentric moment is (10+10sin (2 π t)) Nm.The system state matrix: $A=\left[\begin{array}{cc}0& 1.25\\ -130& -588\end{array}\right],$ $B=\left[\begin{array}{c}0\\ 130\end{array}\right],$ C＝[0 1]，D＝0， $A_e=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& -4{\mathrm{\&pi;}}^2& 0\end{array}\right],$ $B_e=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],$ System state feedback matrix K _e=[3882.7 670.6 56], K=[3.129-3.826].

Be illustrated in figure 4 as and do not adopt under these conditions the angular speed output of three axle inertially stabilized platforms of the present invention under the eccentric moment effect, can find out that angular speed output presents with frequency and the larger sinusoidal fluctuation of amplitude under the Eccentric Sinusoidal moment loading, obviously can make system can't keep stable, platform is with ineffective.

Be illustrated in figure 5 as and adopt under these conditions the angular speed output of three axle inertially stabilized platforms of the present invention under the eccentric moment effect, can find out under the generalized inner algorithm is controlled, angular speed is exported very, and rapid convergence arrives steady-state value, and finally maintain near null value, eccentric moment is played good inhibiting effect, guaranteed the rate stabilization of platform, realized that the floating of system is followed the tracks of.

The non-elaborated part of the present invention belongs to techniques well known.

Claims (2)

1. three axle inertially stabilized platform eccentric moment compensation methodes based on generalized inner is characterized in that performing step is as follows:

(1) adopt the rate gyro that is arranged on three axle inertially stabilized platform gimbal axis to measure the angular speed information ω of three axle inertially stabilized platforms _out, described angular speed information has comprised the angular speed information that Electric Machine Control moment and eccentric moment act on down three axle inertially stabilized platforms simultaneously;

(2) with the angular speed information ω that obtains in step (1) _outWith angular speed setting value ω _setDiffer from, obtain angular speed error e=ω _set-ω _out

(3) the angular speed error e that obtains in step (2) is updated in servo compensator goes, obtain servo compensator controlled quentity controlled variable u _e, the state space equation of servo compensator is Controlled quentity controlled variable u _e=K _ex _e, A wherein _eBe servo compensator system matrix, B _eBe servo compensator control inputs matrix, K _eBe servo compensator state feedback matrix, x _eBe servo compensator state variable, u _eBe the servo compensator controlled quentity controlled variable;

(4) adopt the current sensor measurement that is connected in electric motor loop to go out to be arranged on the current information i of the torque motor on three axle inertially stabilized platform frameworks _out, the angular speed information ω that obtains in integrating step (1) simultaneously _outBe updated in calm compensator and go, obtain calm compensator controlled quentity controlled variable u ₂=Kx, x=[ω _outi _out] ', wherein K is calm compensator state feedback matrix, u ₂Be calm compensator controlled quentity controlled variable;

(5) with the servo compensator controlled quentity controlled variable u that obtains in step (3) _eWith the calm compensator controlled quentity controlled variable u that obtains in step (4) ₂Differ from, obtain generalized inner control algolithm controlled quentity controlled variable u=u _e-u ₂

(6) the generalized inner control algolithm controlled quentity controlled variable u that obtains in step (5) is updated at reference input r and eccentric moment T _dGo in former speed open cycle system under effect, realize the compensation of eccentric moment, realize that finally the floating of system is followed the tracks of.

2. three axle inertially stabilized platform eccentric moment compensation methodes based on generalized inner according to claim 1, is characterized in that: the servo compensator system matrix A in described step (3) _e, servo compensator control inputs matrix B _e, servo compensator state feedback matrix K _eAnd the state feedback matrix K of the calm compensator of step (4) specifically to obtain step as follows:

(31) at first determine reference input ω _setWith eccentric moment T _dThe common time-dependent model of model obtains reference input ω _setWith eccentric moment T _dThe least common multiple formula of two time-dependent models: φ (s)=s ^l+ α _l-1s ^l-1+ ... + α ₁s ¹+ α ₀, reference input ω _setWith eccentric moment T _dModel is known, factor alpha ₀～α _l-1Be known quantity; L is the high-order term of φ (s), and s is frequency domain symbol, α ₀～α _l-1Each time item coefficient for φ (s);

(32) by factor alpha 0～α of φ (s) _l-1Determine blocking factor matrix Γ _l*1And β _l*1,

Wherein, l is the high-order term of φ (s), α ₀～α _l-1Be each time item coefficient of φ (s), I _l-1Be l-1 rank unit matrix;

(33) the blocking factor matrix Γ that is obtained by step (32) _l*1And β _l*1, obtain the coefficient matrices A of servo compensator state space equation _eWith the control inputs matrix B _e, wherein,

So just obtain the state space equation of servo compensator

Servo compensator state feedback matrix K _eState feedback matrix K with calm compensator:

(34) the servo compensator state space equation that step (33) is obtained and former speed open cycle system state space equation make up, and obtain the state space equation of final cascade system: $\left[\begin{array}{c}\stackrel{.}{x}\\ \stackrel{.}{x_e}\end{array}\right]=\left[\begin{array}{cc}A& 0\\ -B_{e}C& A_e\end{array}\right]\left[\begin{array}{c}x\\ x_e\end{array}\right]+\left[\begin{array}{c}B\\ -B_{e}D\end{array}\right]u+\left[\begin{array}{c}{B}_d\\ -B_e{D}_d\end{array}\right]T_d+\left[\begin{array}{c}0\\ B_e\end{array}\right]r,$ The definition front of each coefficient provides; A is the system matrix of former speed open cycle system; B is the control inputs matrix of former speed open cycle system; B _dEccentric moment input matrix for former speed open cycle system; C is the output matrix of former speed open cycle system; D is the transmission matrix of former speed open cycle system; D _dEccentric moment output matrix for former speed open cycle system;

(35) the cascade system state space equation that obtains in step (34) is adopted classical POLE PLACEMENT USING u=K _Tx _TMethod is carried out POLE PLACEMENT USING, obtains state feedback matrix K _T, wherein, x _T=[x x _e] ';

(36) with the state feedback matrix K that obtains in step (35) _TDecompose, make K _T=[K K _e], obtain the state feedback matrix K of servo compensator _eState feedback matrix K with calm compensator.

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