JP2927127B2 - Feedback compensator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a feedback compensator applied to a control system such as an auxiliary steering angle control device for a vehicle.

[0002]

2. Description of the Related Art Conventionally, as a feedback compensator,
For example, those described on pages 56 to 62 of "System Control Theory for Advanced Control" (published by Asakura Shoten) are known.

Further, as a method of setting a limiter, for example, a method described in Japanese Patent Application Laid-Open No. 3-74259 is known.

[0004]

However, the above-mentioned conventional feedback compensator has the following problems.

Hereinafter, a case where the plant has one input and one output will be described with reference to FIG. 9 for simplicity.

In reality, the control input u of the plant always has saturation. The effect of saturation is denoted by d _1L as follows.

U _P = d _1L + u (1) d _1L = −u + sign (u) u _L | u |> u _{L d1L} = 0 | u | ≦ u _L (2) u _P is an input of the plant, u _L > 0 is the input saturation point of the plant, u is the output of the feedback compensator, and sign (u) is u
Represents the sign of

Using equation (1), plant P with input saturation
Is represented as follows:

Y = P (u _P + d ₁ ) + d ₂ (3) where P is a nominal model of the plant represented by a linear transfer function. Also, assuming that there is a feedback compensator, a transfer function from y to u is represented by C.

Now, some influence (for example, disturbance d ₁ , d
₂ ) Consider a situation in which the state of | u |> u _L is maintained.
According to the equations (1), (2) and (3), u becomes as follows.

[0011] _{u = -CPu L sign (u)} -CPd 1 -Cd 2 ... (4) C For example type 1 servo system includes an integrator 1 / s.

At this time, it is understood from Equation (4) that u diverges because C contains 1 / s.

That is, even if the feedback system is stable when the input is not saturated, the operation of the control input u may overflow due to the input saturation of the plant.

In such a case, if the gain of C is large even if it is not a servo system, the calculation result of u becomes large.

Therefore, if the dynamic range is increased in anticipation of the increase of u when the controller is mounted, a problem occurs in that the resolution of u becomes coarse.

The "system control theory for advanced control" cited in the conventional example shows various construction methods of C, but does not mention the above problems.

In Japanese Patent Application Laid-Open No. 3-74259,
The above problem is solved only in a limited compensator configuration.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems, and has as its object to control a feedback compensator applied to a one-degree-of-freedom control system or a two-degree-of-freedom control system. An object of the present invention is to prevent a control input operation from overflowing due to input saturation of a plant in all cases if the system is linear.

[0019]

In order to achieve the above object, in the feedback compensator according to the present invention, the control input u in the one-degree-of-freedom control system is determined by the deviation e between the target value v and the output y.
= Ce, the unstable elements of the compensator are replaced by the stable transfer function matrix compensation elements M _O , M _D , L, and a limiter is inserted in a loop having the compensation elements M _O , M _D. Was configured.

That is, upon receiving the input disturbance d ₁ or the output disturbance d ₂ , the control input u is a controller of the plant P which is input at the saturation at the upper limit u _U and the lower limit u _L and outputs the output y. In a feedback compensator that receives a deviation e of the output y from the target value v, outputs a control input u, and expresses u = Ce in the transfer function matrix C when the control input u has a linear relationship with the deviation e. A first compensation element M _O for inputting a control input u to generate a _first intermediate operation value v ₁ , and a deviation e
Type and a compensation element L which generates an intermediate calculation value v _2, enter the intermediate calculation value v ₂ and the intermediate calculation value v _1, a subtractor for outputting a comparison value v ₃ of both the comparison value v ₃ type limits the compensation element M _D for outputting a fourth signal v _4, the u = u _SU when the value of the fourth signal v ₄ exceeds a predetermined value u _SU> 0,
A limiter that limits u = u _SL when the value of the fourth signal v ₄ is smaller than a predetermined value u _SL <0, and otherwise sets u = v ₄ and outputs a control input u. M _O ,
The transfer function matrices of M _D and L are expressed as C = D _CL ⁻¹ N _CL using a transfer function matrix D _CL ⁻¹ which may include unstable elements and a transfer function matrix N _CL consisting only of stable elements. When represented, M
_{O = D CL -D M, M} D = D M -1 (D M is a constant matrix portion D _CL), have a relationship of L = N _CL.

[0021] where I is a unit matrix of the same size as the D _{CL,
D CL = Y-RN L,} N CL = X + RD L, R is a stable transfer function matrix of choice for the designer.

[0022] However, the irreducible decomposition representation on a stable rational transfer function matrix of the plant P, at Hidarisunde about decomposition representation (subscript L) and right irreducible decomposition representation (no subscript), P = D _L ^{- 1} N _L = N
D ^-1 . D _L , N _L , N, and D are respectively N _L X _L
+ D _L Y _L = I, a stable transfer function matrices satisfy XN + YD = I, and _{X L, Y L, X,} Y is a stable transfer function matrices.

In order to achieve the above object, in the feedback compensator according to the second aspect, the control input u is controlled by a two-degree-of-freedom control system.
Is expressed as u = −C ₁ y + C ₂ r by the target value r and the output y, the unstable elements of the compensator are replaced by the compensation elements H, M _O , M _D , L of the stable transfer function matrix, A limiter is inserted in a loop having compensation elements M _O and M _D.

That is, in response to the input disturbance d ₁ or the output disturbance d ₂ , the control input u is a controller of the plant P which is input at the saturation at the upper limit u _U and the lower limit u _L and outputs the output y. The target value r of the output y is input and the control input u
Outputs, control inputs u is the target value r, transmission time in the output y linearly related function matrix C _1, C ₂ in u = -C ₁ y + C ₂
In a feedback compensator expressed as r, a control input u is input, a first compensation element M _O for generating a _first intermediate operation value v ₁ and a target value r are input, and an intermediate operation value v is generated. The compensation element H and the output y are input, and the intermediate operation value v ₅
, A comparator that receives intermediate calculation values v and v ₅ and calculates a comparison value v ₂ between them, and a comparison value v ₂
And enter the intermediate calculation value v _1, a subtractor for outputting a comparison value v ₃ of the two inputs the comparison value v _3, a compensation element M _D for outputting a fourth signal v _4, the fourth signal When the value of v ₄ exceeds a predetermined value u _SU > 0, u = u _SU is restricted, and the fourth signal v
_When the value of ₄ is smaller than a predetermined value u _SL <0, the limit is set to u = u _SL ; otherwise, the limiter is set to u = v ₄ and the control input u is output, and the compensation elements H, M _O , M _D , L
Is a transfer function matrix D _CL ^-1 which may include an unstable element and a transfer function matrix N consisting only of stable elements.
C ₁ and C ₂ are calculated using _CL and K, and C ₁ = D _CL ^-1 N _CL and C ₂
= D _CL ^-1 K, H = K, M _O = D _CL −D _M ,
M _D = D _M ^-1 (D _M is a constant matrix part of D _CL ), L = N _CL
Have a relationship.

[0025] where I is a unit matrix of the same size as the D _{CL,
D CL = Y-RN L,} N CL = X + RD L, R is a stable transfer function matrix of choice for the designer.

[0026] However, the irreducible decomposition representation on a stable rational transfer function matrix of the plant P, at Hidarisunde about decomposition representation (subscript L) and right irreducible decomposition representation (no subscript), P = D _L ^{- 1} N _L = N
D ^-1 . D _L , N _L , N, and D are respectively N _L X _L
+ D _L Y _L = I, a stable transfer function matrices satisfy XN + YD = I, and _{X L, Y L, X,} Y is a stable transfer function matrices.

[0027]

The operation of the first aspect of the present invention will be described.

For example, when the control input u continues to exceed the limit value due to the influence of disturbances d ₁ and d ₂ , the control input u is input to the first compensation element _MO , and
Intermediate calculation value v ₁ is generated, and in the compensation element L, enter the deviation e between the output y and the target value v, the intermediate calculation value v ₂ is generated, in the subtractor, the intermediate calculation value v ₂ and the intermediate calculation enter a value v _1, both comparison value v ₃ of the output, the compensation element M _D, enter the comparison value v _3, the fourth signal v ₄
When the value of the fourth signal v ₄ exceeds a predetermined value u _SU > 0, the limiter is limited to u = u _SU and the value of the fourth signal v ₄ becomes the predetermined value u _SL <0. When smaller than u
= U _SL .

As described above, in the one-degree-of-freedom control system, the control input u
Is expressed as u = Ce by the deviation e between the target value v and the output y, the unstable element D _CL ^-1 of the compensator is replaced with compensation elements M _O , M _D , L of a stable transfer function matrix, Since the limiter is inserted in the loop having the compensation elements M _O and M _D , even when the state where the control input u exceeds the limit value continues, the calculation result becomes equal to or less than the limit value of the limiter. Overflow due to the divergence of the calculation result of the input u is prevented. Here, the output y also needs to be bounded, but since this output y is a sensor output, it is limited by the sensor saturation value and becomes bounded.

The operation of the second aspect of the present invention will be described.

For example, when the control input u continues to exceed the limit value due to the influence of the disturbances d ₁ and d ₂ , the control input u is input to the first compensation element M _O and the first intermediate An operation value v ₁ is generated, a target value r is input in a compensation element H, an intermediate operation value v is generated, an output y is input in a compensation element L, an intermediate operation value v ₅ is generated, and a comparator in, enter the intermediate calculation value v and v _5, is calculated comparison value of the two v ₂ is, in the subtracter receives the comparison value v ₂ and the intermediate calculation value v _1, comparison value of the two v ₃ is output ,
In compensation element M _D, enter the comparison value v _3, fourth signal v ₄ is output, in the limiter, the fourth signal v ₄
Is limited to u = u _SU when the value exceeds a predetermined value u _SU > 0, and is limited to u = u _SL when the value of the fourth signal v ₄ is smaller than the predetermined value u _SL <0.

As described above, in the two-degree-of-freedom control system, the control input u
There target value r, the output y and the transfer function matrix C _1, C ₂ in _{u = -C 1 y + C 2} r and a feedback compensator that is expressed when a linear relationship, unstable elements D _CL ^-1 Compensator When the compensation elements K, M _O , M _D , L are replaced by stable transfer function matrices and a limiter is inserted in the loop having the compensation elements M _O , M _D , the control input u exceeds the limit value. Even when the state is maintained, the result of the calculation becomes equal to or less than the limit value of the limiter, and overflow due to the divergence of the result of the calculation of the control input u is prevented. Here, the output y also needs to be bounded, but since this output y is a sensor output, it is limited by the sensor saturation value and becomes bounded.

[0033]

Embodiments of the present invention will be described below with reference to the drawings.

(First Embodiment) First, the configuration will be described.

FIG. 1 is a block diagram showing a one-degree-of-freedom control system to which a feedback compensator according to a first embodiment of the present invention is applied.

In the block diagram of FIG. 1, the input disturbance d ₁
And the output disturbance d ₂ , the control input u becomes the upper limit u _U and the lower limit u
_This is a controller of the plant P that is saturated with _L and outputs an output y, receives a deviation e between the output y and a target value v of the output y, outputs a control input u, and outputs a control input u having a deviation e. U = Ce in the transfer function matrix C when there is a linear relationship with
This transfer function matrix C constitutes the feedback compensator of the first embodiment.

The feedback compensator C receives a control input u, a first compensation element M _O for generating a _first intermediate operation value v ₁ , and a deviation e, and generates an intermediate operation value v ₂ . a compensation element L which receives the intermediate calculation value v ₂ and the intermediate calculation value v _1, a subtractor for outputting a comparison value v ₃ of the two inputs the comparison value v _3, outputs a fourth signal v ₄ Compensating element M _D
When the value of the fourth signal v ₄ exceeds a predetermined value u _SU > 0, u = u _SU is limited, and the value of the fourth signal v ₄ becomes the predetermined value u.
_{When SL} <0, the limiter is set to u = u _SL , and in other cases, u = v ₄ and a limiter for outputting the control input u is provided.

Next, referring to FIG.
think of.

According to the conventional source "System Control Theory for Advanced Control", all feedback compensators C internally stable for the plant P are expressed as follows when u is not saturated (of course, the above-mentioned). 1 type servo system is also included).

[0040] _{C = (Y-RN L)} -1 (X + RD L), det (Y-RN L) ≠ 0 ... (5) = (X L + DQ) (Y L -NQ) -1, det (Y L −NQ) {0 (6) where RH is a set of stable rational transfer function matrices, and P
Of the irreducible decomposition expression on RH∞ is expressed as P = ND ^-1 = D _L ^-1 N _L D, N, by the left irreducible decomposition expression (subscript L) and the right irreducible decomposition expression (no subscript). _{N L, D L ∈RH∞ ... (} 7) XN + YD = I, N L X L + D L Y L = I X, Y, are [X], Y _L ∈RH∞ ... (8). Also, R {RH} and Q {RH}.

That is, u, y (when u is not saturated)
For example, all feedback compensators C that do not diverge the signal in the feedback loop and stabilize the feedback system use the free parameter R {RH} or Q {RH}, and are expressed by equation (5) or (6). Has been proven to be.

[0042] Here, (5) C ^{_{a, C = D CL -1 N CL}} = N C D C -1 ... (9) D CL = Y-RN L ∈RH∞ from the equation, D _C = Y _L - _{NQ∈RH∞ N CL = X + RD L} ∈RH∞, can be expressed by N _C = X _L + DQ∈RH∞ and coprime factorization.

[0043] (9) Since a N _CL ∈RH∞ in formula, contain some uncertainties, such as an integrator is D _CL ^-1, can lead to internal destabilization in (9) Is _DCL ^-1 .

FIG. 2 is obtained by rewriting FIG. 2 according to the equation (9). However, here, the D _CL ^-1 are represented using positive feedback I-D _CL.

[0045] Here, put a limiter to the position of FIG. 3, I-D _CL ∈R from being a D _CL ∈RH∞ (stable)
H∞ (stable), and it can be easily understood that u becomes equal to or less than the limit value of the limiter even in the situation as shown in equation (4).

Here, it is necessary that y is bounded. However, since y used for the calculation in the controller is a sensor output, y is limited by the saturation value of the sensor and becomes bounded.

Here, the limiter can be set as follows: u = sign (v ₃ ) u _L | v ₃ |> u _L = v ₃ | v ₃ | ≦ u _L (10)

Since the limit value of the limiter can be selected to be equal to the input saturation point of the plant, its setting is easy, and the capability of the control system can be extracted to the limit point of input saturation without waste.

Next, consider the case where the _IDCL has a direct delivery term.

When the _IDCL has a direct term, when implementing FIG. 3 with a digital arithmetic unit, when computing u, the value of v ₁ is required, and when computing the value of v ₁ Then, an algebraic loop is required in which the operation value of u is required, and the operation cannot be performed. This can be solved as follows.

[0051] The D _CL, a transfer without the direct claim function matrix M _O a constant coefficient matrix D _M, expressed as _{D CL = M O + D M} , configured as shown in FIG. 1 to FIG. 3 by equivalently converting the block diagram Then, since the feedback element M _O is a delay element, there is no algebraic loop, and implementation on a digital computer is possible.

FIG. 4 shows a flowchart of the calculation process in the feedback compensator C of FIG. 1, and each step will be described below.

In step 40, a target value v is input.

In step 41, the output y is input.

In step 42, a deviation e is output from the difference between the target value v and the output y.

In step 43, in the compensation element L to which the deviation e is input, the intermediate operation value v is calculated by the equation v ₂ = N _CL e.
₂ is output.

[0057] At step 44, the subtracter for inputting the intermediate calculation value v ₂ and the intermediate calculation value _{v 1, v 3 = v 2} -v
Comparison value v ₃ of both output by the _first equation.

[0058] At step 45, the compensation element M _D to enter the comparison value _{v 3, v 4 = D M} -1 v fourth signal v ₄ by equation ₃ is output.

[0059] At step 46, the limiter for inputting a fourth signal v _4, the value of the fourth signal v ₄ is limited to u = u _SU when exceeding a predetermined value u _SU> 0, the fourth signal v
_When the value of ₄ is smaller than a predetermined value u _SL <0, the control is limited to u = u _SL , and in other cases, the control input u is output as u = v ₄ .

In step 47, v ₁ = (D _CL -D _M ) u in the first compensation element M _O receiving the control input u.
The first intermediate operation value v ₁ is output by the following equation.

Also, the above equation (6) can be used to construct as shown in FIG. 5. In this case, however, the limit value of the limiter is generally set to the input saturation of the plant as shown in the equation (10). It cannot be the same as a point.

When the above-described feedback compensator C of the first embodiment is applied to a PID control system, the following is obtained, and when shown in a block diagram, it becomes as shown in FIG.

C = K _P + K _I / s + K _Ds / (1 + τs) = {(K _D + K _P τ) s ² + (K _P + K _I τ) s + K _I } / s (1 + τs) (11) _{, N CL = {(K D} + K P τ) s 2 + (K P + K I τ) s + K I} / (s 2 + as + b) D CL = s (1 + τs) / (s 2 + as + b) = τ - {(aτ -1) s + bτ｝ / (s ² + as + b) (a> 0, b> 0) Therefore, M _O = − {(aτ−1) s + bτ} / (s ² + as + b) D _M = τ.

Next, the effects will be described.

In a feedback compensator in which a control input u is expressed as u = Ce by a deviation e between a target value v and an output y in a one-degree-of-freedom control system, an unstable element of the compensator C is compensated for by a stable transfer function matrix. Since elements are replaced by elements M _O , M _D , and L and a limiter is inserted in a loop having compensation elements M _O , M _D , if the control system to be implemented is linear, the input saturation of the plant will be increased in all cases. Thus, it is possible to prevent the calculation of the control input u from overflowing.

(Second Embodiment) First, the configuration will be described.

FIG. 7 is a block diagram showing a two-degree-of-freedom control system to which the feedback compensator of the second embodiment according to the second aspect of the present invention is applied.

In the block diagram of FIG. 7, the input disturbance d ₁
And the output disturbance d ₂ , the control input u becomes the upper limit u _U and the lower limit u
A controller of a plant P that is saturated with _L and outputs an output y, receives an output y and a target value r of the output y, outputs a control input u, and outputs the control input u as the target value r and the output When there is a linear relationship with y, u = −C _{1 in the} transfer function matrices C ₁ and C ₂
y + C ₂ r = [C ₁ C ₂ ] [yr] ^T = C [-y
r] ^T (T represents transposition), and this C constitutes the feedback compensator of the second embodiment.

The feedback compensator C receives a control input u, receives a first compensation element M _O for generating a _first intermediate operation value v ₁ , and a target value r, and generates an intermediate operation value v. a compensation element H for inputs the output y, inputs the compensation element L which generates an intermediate calculation value v _5, the intermediate calculation value v and v _5,
Enter a comparator for calculating a comparison value v ₂ of both type the comparison value v ₂ and the intermediate calculation value v _1, a subtractor for outputting a comparison value v ₃ of both the comparison value v _3, 4 a compensation element M _D for outputting a signal v _4, the value of the fourth signal v ₄ a predetermined value u _SU
> Limited to u = u _SU when exceeding 0, it is limited to u = u _SL when the value of the fourth signal v ₄ is smaller than a predetermined value u _SL <0, otherwise and u = v ₄ Control A limiter for outputting an input u.

Next, according to FIG.
think of.

According to the conventional reference "System Control Theory for Advanced Control", the control input u is determined by the target value r and the output y. When u is not saturated, the internally stable two-degree-of-freedom compensator C for the plant P is expressed as follows.

[0072] _{C = [C 1 C 2]} = (Y-RN L) -1 [(X + RD L) K] _{where, D CL = Y-RN L} , putting the _{N CL = X + RD L,} C 1 = ^{_{D CL -1 N CL C 2 =}} D CL -1 K ... (12) where, K∈RH∞ are free parameters.

Internal stability means that the transfer function matrix V from d ₁ , d ₂ , r to y, u in FIG. 8 is V {RH}.

That is, when d ₁ , d ₂ , and r are bounded, it means that signals such as y and u do not diverge.

The above equation (12) is similar to the first embodiment, in which DC _L ^-1
It was implemented by positive feedback of I-D _CL, 7
It can be configured as follows.

In the two-degree-of-freedom compensator, u = D _CL ^-1 Kr-D _CL ^-1 N _CL y (13) corresponding to the equation (4), but K {RH}, ID _CL ∈RH∞, N _CL ∈RH
From ∞, it can be seen that if there is a limiter at the position in FIG. 7, u is bounded even in the situation of equation (13).

However, also here, the fact that y is a sensor output in the controller and is bounded is used.

Next, the effects will be described.

In a feedback compensator in which a control input u is expressed by a target value r and an output y as u = −C ₁ y + C ₂ r in a two-degree-of-freedom control system, an unstable element of the compensator is converted into a stable transfer function matrix. Compensation elements H, M _O , M _D , and L were replaced, and a limiter was inserted in a loop having compensation elements M _O and M _D. Therefore, if the control system to be implemented was linear, plant Of the control input u can be prevented from overflowing due to the input saturation.

[0080]

According to the first aspect of the present invention, there is provided a feedback compensator in which a control input u is expressed as u = Ce by a deviation e between a target value v and an output y in a one-degree-of-freedom control system. Since the unstable element of the compensator C is replaced with the compensation elements M _O , M _D , L of the stable transfer function matrix and the limiter is inserted in the loop having the compensation elements M _O , M _D , the control to be implemented is performed. If the system is linear, it is possible to prevent the calculation of the control input from overflowing due to the input saturation of the plant in all cases.

According to the second aspect of the present invention, in the two-degree-of-freedom control system, the control input u is set to u = − by the target value r and the output y.
In a feedback compensator expressed as C ₁ y + C ₂ r, the unstable elements of the compensator are replaced with compensation elements H, M _O , M _D , L of a stable transfer function matrix, and compensation elements M _O , M
_{Since the} limiter is inserted in the loop having _D , if the control system to be implemented is linear, it is possible to prevent the calculation of the control input from overflowing due to the input saturation of the plant in all cases. The effect is obtained.

This technique is particularly useful in application to an auxiliary steering angle control system mounted on a vehicle.

[Brief description of the drawings]

FIG. 1 is a block diagram corresponding to a claim showing a feedback compensator of a first embodiment corresponding to the present invention according to claim 1 by the equivalent transformation of FIG.

FIG. 2 is a block diagram showing a feedback compensator of a first embodiment in a one-degree-of-freedom control system.

FIG. 3 is a block diagram illustrating a feedback compensator according to a first embodiment implemented using positive feedback.

FIG. 4 is an operation flowchart of the feedback compensator of the first embodiment.

FIG. 5 is a block diagram showing a modified type feedback compensator of the first embodiment.

FIG. 6 is a block diagram in which the feedback compensator of the first embodiment is applied to a PID control system.

FIG. 7 is a claim correspondence block diagram showing a feedback compensator according to a second embodiment corresponding to the second aspect of the present invention.

FIG. 8 is a block diagram showing a feedback compensator of a second embodiment in a two-degree-of-freedom control system.

FIG. 9 is a block diagram showing a conventional feedback compensator in a one-degree-of-freedom control system.

[Explanation of symbols]

d ₁ input disturbance d ₂ output disturbance u control input y output P plant v target value e deviation v ₁ first intermediate calculation value M _O first compensation element v ₂ intermediate calculation value L compensation element v ₃ comparison value v ₄ second 4 signal M _D compensating element

──────────────────────────────────────────────────続 き Continuation of front page (58) Surveyed field (Int.Cl. ⁶ , DB name) G05B 11/36-13/04 JICST file (JOIS)

Claims (2)

(57) [Claims] A control input u is a controller of a plant P which receives an input disturbance d ₁ or an output disturbance d ₂ and saturates at an upper limit u _U and a lower limit u _L and outputs an output y.
And the error e between the output y and the target value v of the output y, outputs the control input u, and when the control input u has a linear relationship with the deviation e, a feedback compensator expressed as u = Ce in the transfer function matrix C , A control input u, and a first intermediate operation value v
First and compensating element M _O for generating _1, enter the deviation e,
A compensation element L for generating an intermediate operation value v ₂ and an intermediate operation value v
Type ₂ and the intermediate calculation value v _1, a subtractor for outputting a comparison value v ₃ of the two inputs the comparison value v _3, a compensation element M _D for outputting a fourth signal v _4, the fourth When the value of the signal v ₄ exceeds a predetermined value u _SU > 0, the limit is set to u = u _SU, and when the value of the fourth signal v ₄ is smaller than the predetermined value u _SL <0, the limit is set to u = u _SL. , And in other cases, u = v ₄ and a limiter for outputting a control input u. The transfer function matrix of the compensation elements M _O , M _D , L is a transfer function matrix D which may include an unstable element. Using a transfer function matrix N _CL consisting of only _CL ⁻¹ and a stable element, C = D _CL ⁻¹ N
When expressed as _CL , M _O = D _CL −D _M , M _D = D _M ⁻¹ (D
_M is a constant matrix portion D _CL), it has a relationship of L = N _CL. Where I is a unit matrix of the same size as the _{D CL, D CL = Y-} RN
_L and N _CL = X + RD _L and R are stable transfer function matrices selected by the designer. Here, the irreducible decomposition expression on the stable rational transfer function matrix of the plant P is represented by a left irreducible decomposition expression (subscript L).
And the right irreducible decomposition expression (with no subscript), P = D _L ^-1 N _L =
ND ^-1 . D _L , N _L , N, and D are respectively N _L X
_{L + D L Y L = I} , a stable transfer function matrices satisfy XN + YD = I, and _{X L, Y L, X,} Y is a stable transfer function matrices. A feedback compensator characterized by the above. 2. A controller P of a plant P which receives an input disturbance d ₁ or an output disturbance d ₂ , saturates at an upper limit u _U and a lower limit u _L and inputs and outputs an output y.
And the target value r of the output y, output the control input u,
When the control input u has a linear relationship with the target value r and the output y, the feedback compensator expressed as u = −C ₁ y + C ₂ r in the transfer function matrices C ₁ and C ₂ receives the control input u, A first compensation element M that generates an intermediate operation value v ₁ of 1
Type and _O, and the target value r, the input and the compensation element H to produce an intermediate calculation value v, receives the output y, a compensation element L which generates an intermediate calculation value v _5, the intermediate calculation value v and v ₅ and a comparator for calculating a comparison value v ₂ both, a subtracter enter a comparison value v ₂ and the intermediate calculation value v _1, and outputs a comparison value v ₃ therebetween,
Enter the comparison value v _3, to limit the compensation element M _D for outputting a fourth signal v _4, the u = u _SU when the value of the fourth signal v ₄ exceeds a predetermined value u _SU> 0, A limiter that limits u = u _SL when the value of the fourth signal v ₄ is smaller than a predetermined value u _SL <0, and otherwise sets u = v ₄ and outputs a control input u. The transfer function matrices of H, M _O , M _D , and L are represented by C ₁ , C transfer using transfer function matrix D _CL ^-1 which may include unstable elements and transfer function matrices N _CL , K consisting only of stable elements.
The C _2, when expressed ^{_{C 1 = D CL -1 N CL}} , and ^{_{C 2 = D CL -1 K,}} H = K, M O = D CL -D M, M D = D M -1 (D M the constant matrix portion D _CL), have a relationship of L = N _CL. Where I is a unit matrix of the same size as the _{D CL, D CL = Y-} RN L,
N _CL = X + RD _L , R is a stable transfer function matrix selected by the designer. However, the irreducible decomposition expression on the stable rational transfer function matrix of the plant P is expressed as P = D _L ⁻¹ N _{L by a} left irreducible decomposition expression (subscript L) and a right irreducible decomposition expression (no subscript). = ND
^Set to ^-1 . D _L , N _L , N, and D are respectively N _L X _L +
D _L Y _L = I, a stable transfer function matrices satisfy XN + YD = I, and _{X L, Y L, X,} Y is a stable transfer function matrices. A feedback compensator characterized by the above.