JP3493340B2 - Method for determining control law of automatic control system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [0001] BACKGROUND OF THE INVENTION 1. Field of the Invention
Actuators installed in airplane stability increase devices
A self-contained design that can be suitably implemented to design the controller
The present invention relates to a method for determining a control law of a dynamic control system. [0002] 2. Description of the Related Art Conventionally, a hydraulic cylinder or the like
The PID (Ratio
Example: Integral / differential) As one of the controller design techniques, LM
There is an I-loop shaping method. This is the PID controller
H∞ control theory framework with robust stability
And a multi-input PID file.
Method that can theoretically design feedback control law
This is a useful controller design technique. [0003] The robust cost obtained by the above design method
A qualitative controller has a large feedback gain.
Control using an actuator with a small stroke.
When applied to control devices, it may cause actuator saturation.
As a result, desired control performance may not be obtained. Said
Example of a control device using a small troke actuator
As an aircraft stability augmentati
on system; abbreviated SAS). [0004] This stability increasing device is, for example, a helicopter.
Flight altitude and speed to the control system of rotorcraft such as
Gain stability in all flight areas as the aircraft increases
To control the control surface by sensing the motion of the aircraft.
It is mounted as one of the stems. The controlled object is
Small strike to drive angular displacement of blade pitch angle etc.
This is a low-key actuator, which is
The attitude of the aircraft detected by the
And adjust the manipulated variable so that this observation value matches the target value.
Output. In such a device for increasing stability, an actuator
By setting the data stroke small,
Minimize impact on pilot control in case of equipment failure
You can stop it. In addition, important evaluation fingers for flight control law
One of the targets, the stability margin, generally increases the gain
Robust stability conflicts with
To make trade-offs
Design using the above LMI loop shaping method
In the method, means to realize this stability margin trade-off
There is a problem that does not have. [0006] SUMMARY OF THE INVENTION The object of the present invention is to
Prevents control performance from deteriorating due to tutor saturation.
System that enables trade-offs between stability and stability margins
An object of the present invention is to provide a method for determining a control law of a control device. [0007] SUMMARY OF THE INVENTION The present invention according to claim 1 is provided.
Is the control given by the state equation and the output equation
The target P and a prefix to shape the open loop frequency characteristic
Extended control target Pw = including the compensator W1 and the post-compensator W2
Robust stability margin is maximum for W1, P, W2
Of an automatic control system that seeks a robust stabilization controller C
In the method for determining a control law, the robust stabilization controller C
Is represented by a linear combination of the components of the right inverse graph,
Specify at least one of the upper and lower gain limits.
Minimize the H∞ norm of a closed loop system
Optimization by simultaneous solving with linear matrix inequalities
Automatic control system characterized by determining a controlled control law
This is the method of determining the control law of the system. According to the present invention, the extended control object Pw and the donkey
The H∞ norm of the closed loop system consisting of the stabilizing controller C
Invert the linear matrix inequality to be minimized and the PID gain of C to the right
Specify the gain range as a linear combination of the components of the graph.
And solving the inequalities in
Causes the stability margin to be insufficient due to the inequality
To avoid excessive gain and robust stability within that range
Determine the gain that maximizes the
Thus, it is possible to prevent the control performance from deteriorating due to factors. [0009] FIG. 1 shows an embodiment of the present invention.
Helicopter to which the control law decision method of the automatic control system is applied
FIG. 2 is a block diagram showing a schematic configuration of a device 1 for increasing the stability of a septum;
is there. In the present embodiment, the control law determination method of the present invention is used.
Of an automatic control system with a controller designed according to
As a control device for the helicopter G, which is the control object.
The mounted stability increasing device 1 will be described. This stability
Stability augmentation system (SAS) 1
Is a device to increase the inherent stability of the aircraft.
To maintain the attitude angle and altitude as set.
Helicopter G, distinguished from autopilot
Depending on the rate gyro mounted on the
Angular velocities around the three axes yaw and yaw are detected, and this signal is
To the adder 4 via the proportional gain setting circuit 3 of the compensation circuit 2
Deriving, differentiator 5 and differential gain setting circuit
6 to the adder 4. Helicopter G
Also, a posture detecting means realized by an inertial reference device or the like.
Is installed to indicate the attitude angle of the aircraft from this attitude detection means.
The attitude signal corresponds to the integral value of the angular velocity, and the compensation circuit 2
Is output to the adder 4 through the integral gain setting circuit 7 of FIG.
It is. The adder 4 includes a proportional gain setting circuit 3 and a differential
Each signal from the gain setting circuit 6 and the integral gain setting circuit 7
The sum of the outputs is obtained, and the sum is sent to the washout circuit 8.
Therefore, while the stabilization device 1 is gradually settled to neutral,
Outputting a control signal of the actuator to the actuator
To respond to disturbances and other responses.
Automatically corrects steering angle and suppresses swing around three axes
Thus, the dynamic stability of the helicopter G is improved. P based on the LMI loop shaping method
The design procedure of the ID controller will be described. First,
As shown in FIG.
Pre-compensator W1 and post-compensator W for shaping
2 to which extended control object Pw = W2 · P · W1
Rough, [0012] (Equation 1) [0013] Here, G ~, M ~, N ~ are dynamic
Equation 1 above shows that the dynamic system G〜
This is represented by the linear differential equations of Expressions 2 and 3. [0014] (Equation 2) The pre-compensator W1 and the post-compensator W2 are
In H∞ loop shaping, any dynamic system or static system
It can take the form of a stem, but this method
As in equation 17, the shape is determined. Notation similar to the above
Control rule C = N_CM_C ^-1The right inverse graph of [0016] (Equation 3) [0017] Here, in the case of PID control, P
Considering that the pole does not change by adjusting the ID gain
The poles of the characteristics of control law C are given in advance.
And This means that in Equation 3 above,
Is C_K2And D_K2Means two. Also,
Right normalized inverse graph K of C_NIs defined as follows using
I do. [0018] (Equation 4) Here, * on the right shoulder of the symbol indicates conjugate transposition.
The normalized right inverse graph is obtained as follows. [0020] (Equation 5) Here, (Equation 6) ## EQU1 ## T on the right shoulder of the symbol indicates the transposed matrix.
Represent. X is the symmetric positive definite of the following Riccati equation
It is a solution. [0023] (Equation 7) Here, (Equation 8) It is. Using the elements of the above equations 1, 4 and 5,
The following four matrices are defined. (Equation 9)When these are used, the linear line of the following equation 16-1 is obtained.
Convex optimization problem expressed by column inequality and algebra of the following equation 16-2
Equations are solved alternately to find Q and K, and the optimal control law element C
_K2D _K2Can be requested. [0027] (Equation 10)       Q = (GK_N)^*for fixedK_N                            … (16-2) The specific form of the PID control law is given by the following equation (17).
Is shown. (Equation 11) Where s is a Laplace operator and τ is a pseudo fine
Minute time constant, K_PIs the proportional gain, K_IIs the integral gain, K_D
Indicates a differential gain. The time constant τ of the pseudo differentiation is sufficient
Set a small value (| τ | ≪1). LMI Loopche
Consider the design by the iping method,
Compensator W1, part C designed by the above method, post-compensator W
Divide into two. [0030] (Equation 12) Where T_WAdjusts the open-loop crossover frequency.
Parameters to be adjusted. Also, K_{P W}, K_IW, K_DWHaso
Each K_P, K_I, K_DTo w₁× w_TwoDivided by FIG. 2 is a block diagram showing a procedure for realizing the controller C.
FIG. 2A is a lock diagram, and FIG.
Fig. 2 (2) shows the configuration of the mathematical model of
1 shows a configuration of a closed-loop mathematical model. Above proportional gay
K_P, Integral gain K_I, Differential gain P_DDetermine the range of
In this case, the part C to be designed is expressed by the following equation.
You. [0033] (Equation 13) Here, between the part C to be designed and Equation 4,
The following formula, [Equation 14] Utilizing that there is a relationship indicated by PID
Each element of the right inverse graph of the controller can be represented as
it can. [0035] (Equation 15)From equations 24 and 26, the parameters of the PID controller
Data K_P, K_I, K_DAre the same as in equations 27 to 29
It is represented by a linear combination of the components of the right inverse graph. [0037]       K_P= W₁× ｛-τC_K21｝ × w_Two                        … (27)       K_I= W₁× ｛C_K22+ C_K2/ Τ + C_K21｝ × w_Two            … (28)       K_D= W₁× ｛τD_K2+ Τ^TwoC_K21｝ × w_Two                  … (29) Therefore, the upper limit value K of each gain
_{P (UPPER)}, K_{I (UPPER)}, K_{D (UPPER)}And lower limit
K_{P (LOWER)}, K_{I (LOWER)}, K_{D (LOWER)}Was given
Then, the following three inequalities of Expression 30, Expression 31, and Expression 32 are expressed by Expression 1.
Solving in conjunction with 6-1 gives the PID gain
It can be optimized within the specified range. [0039] (Equation 16) Equations (30) to (32) are used to calculate the gain K_P,
K_I, K_DBoth upper and lower limits are specified.
However, if necessary, only the upper limit or only the lower limit
May be specified. Any one of Expressions 30 to 32
Only books or a combination of two equations may be used. FIG. 3 shows a control provided in the stability increasing device 1.
6 is a flowchart for explaining a design procedure of controller C.
You. First, in step a1, the expanded control target Pw
In order that the outline of the open loop frequency characteristic becomes the desired shape,
Pre-compensator W1 connected to both sides of controller C and post-compensator
Determine the compensator W2. Specifically, P_w= W_Two・ P ・ W
₁Check the diagram representing frequency characteristics such as the Bode diagram of
Scalar amount W₁, W_Two, T_WTo adjust. Next,
In step a2, the time constant τ of the pseudo-differentiation is determined.
3. From Equation 25, the fixed element A of the control law_K, B_K, C_K1, D_K1
Ask for. In step a3, the initial value of the PID gain is
From the equations 24 and 26, the control element C_K2,
D_K2Ask for. In step a4, control is performed from Equations 6 to 11.
Right normalized inverse graph K_NIs calculated, and Q is obtained from Expression 16-2.
Ask. Next, in step a5, the expressions 16-1 and 30 to
Equation 32 and the optimum adjustment element C_K2, D_K2Seeking
I will. In step a6, if γ in Expression 16-1 converges,
In step a7, the PID gain is calculated from Expressions 27 to 29.
I will. If not converged, the process returns to step a4,
The normalized right inverse graphs Kn and Q are obtained again, and
Optimum adjustment element C for a5_K2, D_K2Operation to ask for
Is repeated until convergence, and in step a7, the PID gain
K_P, K_I, K_DTo determine. Thus, LMI loop shaping
Specify the gain range in the PID control law design method
Solving the inequalities of
Control due to actuator saturation
Tray with robust stability and stability margin
Dooff can be enabled. In particular, in the above embodiment,
Range of the PID gain of the compensation circuit
And the gain upper limit K_{P (UPPER)}, K_{I (UPPER)}, K_{D (UPPER)}
And gain lower limit K_{P (LOWER)}, K_{I (LOWER)}, K
_{D (LOWER)}Is set as a result of the feedback signal
As the size of the actuator operation input is suppressed,
As shown in 4 (1), a disturbance [inch] is input.
Also, the operation amount [inch] of the actuator is as shown in FIG.
Avoid reaching saturation as shown by the solid line.
And the gain range is
Excessive reactions are suppressed. Also shown in FIG. 4 (3)
The gain is also restricted for the pitch rate [deg / sec].
The solid line with the gain constrained is more stable than the
And the pitch attitude angle [deg] shown in FIG.
Similarly, compared to the dashed line that does not constrain the gain,
The fact that the solid line that constrains the gain stabilizes
Therefore, it has been confirmed. In the above embodiment, the rotary wing aircraft
Helicopter stability increase device
・ Control law by PID control using all elements of differentiation
Has been described, but in addition to the practice of the present invention,
In the form, the three elements of proportional, integral, and differential
One or any combination of the two
However, as described above, the control law determination method according to the present invention
Can be applied. [0046] According to the first aspect of the present invention, a robust device is provided.
The PID gain of the stabilization controller C is
Expressed as a linear combination, with less of upper and lower gain limits
The inequality that specifies one of them is the H∞ norm of the closed-loop system
By solving a set of linear matrix inequalities that minimize
Therefore, the stability margin is given by the inequality that specifies the gain range.
To prevent excessive gain from running out of
Determine the gain that maximizes
To prevent deterioration of control performance due to
it can.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a helicopter stability increasing device 1 to which a control law determination method for a stability increasing system according to an embodiment of the present invention is applied.
It is a block diagram which shows schematic structure of. FIG. 2 is a block diagram showing a procedure for realizing the controller C. FIG. 2A shows a configuration of the controller C at the time of design, and FIG. 2B shows a configuration of the controller C at the time of mounting. Show. FIG. 3 is a flowchart for explaining a design procedure of a controller provided in the stability increasing device 1; FIG. 4 is a diagram showing a case where a gain is limited and a case where a gain is not limited in response of a control target when a disturbance is input to an actuator. FIG. 4A shows a disturbance signal input to the control target. 4 (2) shows an operation amount of the actuator, and FIG. 4 (3) shows a pitch rate signal output from a rate gyro provided to the control object.
Represents a pitch attitude angle signal from a pitch attitude angle detector provided in the control target. [Description of Signs] 1 Stability increasing device 2 Compensation circuit 3 Proportional gain setting circuit 4 Comparator 5 Differentiator 6 Differential gain setting circuit 7 Integral gain setting circuit 8 Washout circuit

Continuation of the front page (56) References JP-A-11-110003 (JP, A) JP-A-7-79585 (JP, A) Shinichi Miyamoto, Fixed structure H∞ control based on irreducible decomposition expression and LMI optimization Design, system / control / information, Japan, 1999, VOL. 43, No2, pp80-86, 16-22 Shinichi Miyamoto, Satoshi Iwasaki, Masaaki Shibata, Katsuhiko Takada, Control System Design by LMI Loop Shaping Method and Application to Boom Damping Problem, Transactions of the Society of Instrument and Control Engineers, Japan , 1999, Vol 35, No. 12, 157-1574 (58) Fields investigated (Int. Cl. ⁷ , DB name) G05B 13/02

Claims (1)

(57) [Claims 1] A control target P given by a state equation and an output equation, and a pre-compensator W1 and a post-compensator W2 for shaping an open-loop frequency characteristic. In a method for determining a control law of an automatic control system for finding a robust stabilization controller C having a maximum robust stability margin with respect to an extended control target Pw = W1 · P · W2, the PID gain of the robust stabilization controller C Is represented by a linear combination of the components of the right inverse graph, and by solving an inequality specifying at least one of the upper limit value and the lower limit value of the gain with a linear matrix inequality that minimizes the H∞ norm of the closed loop system, A method for determining a control law of an automatic control system, characterized by determining an optimized control law.