JP2002189501A - Method for deciding control rule of automatic control system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable the trade-off of robust stability and stability margin by preventing the deterioration of control performance due to the saturation of an actuator. SOLUTION: In method for searching a robust stabilization controller C whose robust stability margin is maximized with respect to an extension control object Pw=W1×P×W2 including an object to be controlled P which is given an object to be really controlled through a state equation and an output equation and a pre-compensator W1 and a post-compensator W2 for shaping open loop frequency characteristics, the PID gain of the robust stabilization controller C is expressed with the linear connection of the components of a right inverse graph, and an inequality whose upper limit or lower limit is at least designated is solved simultaneously with a linear matrix inequality minimizing the H∞ norm of the closed loop system so that it is possible to decide a control rule capable of realizing the well-balanced trade-off robust stability and stability margin.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for determining a control law of an automatic control system which can be suitably implemented to design a controller of an actuator provided in, for example, a device for increasing the stability of a rotary wing aircraft.

[0002]

2. Description of the Related Art Conventionally, as one of the design methods of a PID (proportional / integral / derivative) controller for an actuator control device realized by a hydraulic cylinder or the like, LM
There is an I-loop shaping method. This makes it possible to design a PID controller with robust stability in the framework of H∞ control theory, and a method that can theoretically design a PID feedback control law for a multi-input system. This is a useful controller design technique.

A controller having robust stability obtained by the above-described design method has a large feedback gain and, when applied to a control device using an actuator having a small stroke, causes saturation of the actuator, resulting in a desired control performance. May not be obtained. As an example of the control device using the small stroke actuator, a stability augmentati
on system; abbreviated SAS).

[0004] This stability increasing device senses the motion of the airframe in a control system of a rotary wing aircraft such as a helicopter in order to obtain stability in all flight areas with an increase in flying altitude and speed. It is mounted as one of the steering systems for controlling the control surface. The controlled object is
This is a small-stroke actuator that drives the blade pitch angle and other angular displacements.The attitude of the aircraft detected by sensors provided on the aircraft is input as an observation amount, and the observation amount is adjusted to match the target value. , Output the manipulated variable.

In such a device for increasing stability, by setting the stroke of the actuator small,
In case of equipment failure, the effect on pilot control can be minimized. In addition, the stability margin, which is one of the important evaluation indices of the flight control law, generally tends to decrease as the gain is increased, so it is a demand that conflicts with robust stability and requires a trade-off. Nevertheless, the above-described design method using the LMI loop shaping method has a problem that means for realizing a trade-off of the stability margin is not provided.

[0006]

SUMMARY OF THE INVENTION An object of the present invention is to provide a method for determining a control law of a control device which prevents a decrease in control performance due to actuator saturation and enables a trade-off between robust stability and stability margin. It is.

[0007]

According to the present invention, a control target P given by a state equation and an output equation, a pre-compensator W1 for shaping an open-loop frequency characteristic and a post-compensation are provided. Extended control target Pw =
A method for obtaining a robust stabilization controller C having a maximum robust stability margin with respect to W1, P, and W2, wherein a PID gain of the robust stabilization controller C is represented by a linear combination of components of a right inverse graph, And determining an optimized control law by solving an inequality specifying at least one of a lower limit and a lower limit simultaneously with a linear matrix inequality that minimizes the H∞ norm of the closed loop system. Is a method of determining the control law.

According to the present invention, a linear matrix inequality that minimizes the H∞ norm of a closed loop system composed of the extended control object Pw and the robust stabilization controller C, and a linear combination of the PID gain of C and the component of the right inverse graph By solving the inequality with the specified gain range as a simultaneous expression, it is possible to prevent the excessive gain that causes the stability margin to be insufficient due to the inequality with the specified gain range, and to achieve robust stability within that range. By determining the gain to be maximized, it is possible to prevent the control performance from deteriorating due to actuator saturation or the like.

[0009]

FIG. 1 is a block diagram showing a schematic configuration of a helicopter stability increasing device 1 to which a control law determining method of an automatic control system according to an embodiment of the present invention is applied. In the present embodiment, as an example of an automatic control system including a controller designed by the control law determination method of the present invention, a stability increasing device 1 mounted on a steering control device of a helicopter G to be controlled will be described. This stability augmentation system (SAS) 1
Is a device for increasing the stability inherent in the airframe, which is distinguished from an autopilot that maintains an attitude angle and an altitude as set, and a helicopter G.
The rate gyro mounted on the sensor detects the angular velocities around the three axes of pitch, roll, and yaw.
It is derived to the adder 4 via the proportional gain setting circuit 3 of the compensation circuit 2 and to the adder 4 via the differentiator 5 and the differential gain setting circuit 6. The helicopter G is also provided with attitude detecting means implemented by an inertial reference device or the like. The attitude signal indicating the attitude angle of the aircraft from the attitude detecting means corresponds to an integral value of the angular velocity.
Is output to the adder 4 via the integral gain setting circuit 7 of the above.

The adder 4 calculates the sum of the outputs from the proportional gain setting circuit 3, the differential gain setting circuit 6, and the integral gain setting circuit 7, and the value is gradually and neutrally settled by the washout circuit 8 while being neutralized. The control signal of the actuator of the stability increasing device 1 is output to operate the actuator, whereby the steering angle is automatically corrected in response to a disturbance or the like, the swing around three axes is suppressed, and the helicopter G It is to improve the dynamic stability.

P based on the LMI loop shaping method
The design procedure of the ID controller will be described. First, as shown in FIG. 2 to be described later, a pre-compensator W1 and a post-compensator W for shaping the open-loop frequency characteristic of the control target P.
The left graph of the extended control object Pw = W2 · P · W1 to which

[0012]

(Equation 1)

[0013] Here, G〜, M〜, and N〜 indicate a dynamic system, and the above equation 1 indicates that the dynamic system G〜 is expressed by the following linear differential equations (2) and (3).

[0014]

(Equation 2)

The pre-compensator W1 and the post-compensator W2 are
The H∞ loop shaping method can take the form of any dynamic or static system, but in this method the shape is determined as in equation 17 below. The right inverse graph of the control rule C = N _C M _C ⁻¹ obtained using the same notation as the above,

[0016]

(Equation 3)

[0017] Here, in the case of PID control, P
Taking into account that the pole does not change due to the adjustment of the ID gain, it is assumed that the pole among the characteristics of the control law C is given in advance. This means that in Equation 3 above, two indeterminate elements are C _K2 and D _K2 . Also,
Using the normalized right inverse graph K _N of C, Q is defined as follows.

[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 ## Further, T at the right shoulder of the symbol represents a transposed matrix. X is a symmetric positive definite solution of the following Riccati equation:

[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 fixed K _N ... (16-2)

The specific form of the PID control law is expressed by the following equation (17).

[Equation 11]

Here, s is a Laplace operator, τ is a time constant of pseudo differentiation, K _P is a proportional gain, K _I is an integral gain, and K _D
Indicates a differential gain. The time constant τ of the pseudo differentiation is set to a sufficiently small value (| τ | ≪1). In consideration of designing by the LMI loop shaping method, the control law is pre-compensator W1, the part C designed by the above method, the post-compensator W
Divide into two.

[0030]

(Equation 12)

Here, T _W is a parameter for adjusting the open-loop crossover frequency. Moreover, those _{K P W, K IW, K} DW where each K _P, K _I, and K _D divided by w ₁ × w _2.

FIG. 2 is a block diagram showing a procedure for realizing the controller C. FIG. 2A shows the configuration of a closed-loop mathematical model at the time of design, and FIG. 2 shows the configuration of a mathematical model. In determining the ranges of the above-mentioned proportional gain K _P , integral gain K _I , and differential gain P _D , the part C to be designed is expressed by the following equation.

[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 follows.

[0035]

(Equation 15)

From Equations 24 and 26, the parameters K _P , K _I , and K _D of the PID controller are all expressed by linear combinations of the components of the right inverse graph as shown in Equations 27 to 29.

[0037] _{K P = w 1 × {-τC} K21} × w 2 ... (27) K I = w 1 × {C K22 + C K2 / τ + C K21} × w 2 ... (28) K D = w 1 × { τD _K2 + τ ² C _K21 ｝ × w ₂ … (29)

Therefore, the upper limit value K of each gain
_{When P (UPPER)} , KI _(UPPER) , _{KD (UPPER)} and the lower limit values KP _(LOWER) , KI _(LOWER) , _{KD (LOWER)} are given, the following equations (30 ₎ , ₍ 31 ₎ are obtained. The three inequalities of Equation 32 are expressed by Equation 1
The PID gain can be optimized within a specified range by solving it simultaneously with 6-1.

[0039]

(Equation 16)

Equations (30) to (32) represent the gains K _P ,
K _I, although in the form specified both upper and lower limits of K _D, may specify an upper limit only, or lower only when necessary. Any one of Expressions 30 to 32
Only books or a combination of two equations may be used.

FIG. 3 shows the control provided in the stability increasing device 1.
6 is a flowchart for explaining a design procedure of the container C.
You. First, in step a1, the expanded control target Pw
So that the specific shape of the open loop frequency is 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 the 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 determined, and the adjustment factors C _K2 ,
_Find D _K2 . In step a4, a normalized right inverse graph K _N of the control law is obtained from Expressions 6 to 11, and Q is obtained from Expression 16-2. Next, in Step a5, Expressions 16-1 and 30 to
The optimal adjustment factors C _K2 and D _K2 are obtained by simultaneously combining Expression 32. In step a6, if γ in Expression 16-1 converges,
In step a7, a PID gain is obtained from Expressions 27 to 29. If it does not converge, the process returns to step a4,
The operation of obtaining the normalized right inverse graphs Kn and Q again and repeating the operation of obtaining the optimum adjustment elements C _K2 and D _K2 in the step a5 until the convergence is reached, and determining the PID gains K _P , K _I and K _D in the step a7. I do.

By solving the inequalities for designating the gain range simultaneously with the PID control law design method based on the LMI loop shaping method in this manner, the gain is prevented from becoming excessive, and the control performance due to the saturation of the actuator is reduced. It is possible to prevent a drop and to make a trade-off between robust stability and stability margin.

In particular, in the above-described embodiment, the upper limit values K _{P (UPPER)} , K _{I (UPPER)} , and K _{D (UPPER) are} set as the range of the PID gain of the compensation circuit in the aircraft stability increasing device.
And gain lower limit values K _{P (LOWER)} , K _{I (LOWER)} , K
As a result of the setting of _{D (LOWER)} , the magnitude of the actuator operation input by the feedback signal is suppressed. Therefore, as shown in FIG. As shown by the solid line in FIG. 4 (2), [inch] can avoid reaching the saturated state, and suppresses an excessive reaction as compared with the broken line where the range of the gain is not restricted. Also, for the pitch rate [deg / sec] shown in FIG. 4 (3), the gain-constrained solid line is more stable than the dashed line where the gain is not constrained, and is further shown in FIG. 4 (4). Pitch attitude angle [deg]
Similarly, compared to the dashed line that does not constrain the gain,
It has been confirmed by the present inventor that the solid line with the gain restricted is stabilized.

In the above embodiment, a method of determining a control law by PID control using all elements of proportional, integral, and differential is described as an application example of a helicopter stability increasing device as a rotary wing aircraft. In another embodiment of the present invention, the control law determination method according to the present invention is applied to any one of the three elements of the above-described proportional, integral, and derivative or a combination of any two of them. Can be applied.

[0046]

According to the first aspect of the present invention, the PID gain of the robust stabilization controller C is represented by a linear combination of components of a right inverse graph, and an inequality specifying at least one of an upper limit and a lower limit is represented by: Simultaneously solving a linear matrix inequality that minimizes the H∞ norm of the closed-loop system prevents an excessive gain in which the stability margin is insufficient due to the inequality specifying the gain range, and maximizes the robust stability within that range. Thus, it is possible to prevent the deterioration of the control performance due to the saturation of the actuator or the like.

[Brief description of the drawings]

FIG. 1 is a helicopter stability increasing device 1 to which a method for determining a control law of a stability increasing system according to one embodiment of the present invention is applied
FIG. 2 is a block diagram showing a schematic configuration of the.

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;

4A and 4B are diagrams illustrating a response of a control target when a disturbance is input to an actuator when a gain is limited and when the gain is not limited, and FIG. 4A illustrates 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.
Indicates a pitch attitude angle signal from a pitch attitude angle detector provided in the control target.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 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

Claims (1)

[Claims] 1. An extended control object Pw = W1 · P including a control object 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. Regarding a method for obtaining a robust stabilization controller C having a maximum robust stability margin for W2, a PID gain of the robust stabilization controller C is represented by a linear combination of components of a right inverse graph, A control law for an automatic control system characterized in that an optimized control law is determined by simultaneously solving at least one of the specified inequalities with a linear matrix inequality that minimizes the H ム norm of a closed loop system. Decision method.