JP2001312301A - Controller - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a controller which reduces a follow-up deviation with a simple configuration. SOLUTION: Concerning a controlled system such as motor controller 2 expressed with r0/ δ2+p1δ} and δ=z-1, a stable polynomial having desired closed loop characteristics m(δ)=δ2+m1δ+m0 and an observer polynomial q(δ)=δn+qn-1δn-1+...+q0, where n=2+d, which is stabilized when an out-of- estimation disturbance degree is defined as (d), are selected, and when the equalities k(δ)=kn-1δn-1+...+kd+1δd+1+qdδd+...+q0 and h(δ)=hnδn+...+h0 are established, equalities kj=qj and j=0 to (d) are established. Further, ki, i=d+1 to n-1, hi and i=0 to (n) are selected so as to satisfy k(δ)r0+h(δ) δ2+p1δ}=q(δ) p(δ)-m(δ)} and a closed loop control system is configured for applying a control input such as u(k)= k(δ)/q(δ)}u(k)+ h(δ)/q(δ)}y(k)+(m0/r0x(k). Further, feedforward compensation such as x(k)= m(δ)/m0z2}v(k) is applied.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a control device. More specifically, the present invention relates to a control device with a small following deviation for shortening a settling time of positioning of a controlled object.

[0002]

2. Description of the Related Art Conventionally, as a method of shortening a positioning settling time of a motor control device or the like and improving a trajectory error, there is a configuration of insertion of a feedforward loop and finite settling control of a discrete time. In addition, regarding suppression of disturbance and the like to the control target,
Many compensation methods using disturbance observers have been implemented.

[0003]

However, insertion of a feed-forward loop into a conventional PID controller or the like has a disadvantage that overshoot occurs when feedforward is applied too much, and it is practical to apply 100% compensation. Is impossible. In addition, when there is a load fluctuation or mismatch, over-compensation or under-compensation due to feed forward becomes an increasingly large factor, which is a hindrance to increase a practical effect.

In addition, since discrete-time finite settling control is constituted by a closed loop, the closed-loop gain becomes equivalently large,
In many cases, a desired effect cannot be actually obtained due to the influence of noise, mismatch, and the like.

Further, in a method using a disturbance observer or a conventional method using a two-degree-of-freedom control system, a main controller is formed in addition to a disturbance compensator, or a pre-compensator is formed. However, the configuration becomes complicated for the effect obtained.

Further, the disturbance compensation characteristic basically suppresses a step-like disturbance, and there is no simple control of a configuration including a compensator capable of coping with acceleration or a change in acceleration.

Accordingly, the present invention provides a control device which has a simple configuration of the controller, can minimize the following deviation while keeping the entire control system stable, and can cope with acceleration or a change in acceleration. The purpose is to do.

[0008]

In order to achieve the above object, according to the first aspect of the present invention, a discrete time system is used to approximate r
₀ / {δ ² + p ₁ δ}, a stable polynomial having a desired closed-loop characteristic for a control target such as a motor control device represented by δ = z−1: m (δ) = δ ² + m ₁ δ + m ₀
And the assumed disturbance order to be compensated is d, a stable observer polynomial: q (δ) = δ ⁿ + q _n-1 δ ^n-1 + ...
+ Q ₀ , n = 2 + d, and k (δ) = k _n−1 δ
^n-1 +... + k _{d + 1} δ ^{d + 1} + q _d δ ^d +... + q ₀ ,
_{h (δ) = h n δ} n + ... + when the _{h 0, k} j =
q _j , j = _{0 to} d, and k (δ) r ₀ + h
(Δ) ｛δ ² + p ₁ δ｝ = q (δ) ｛p (δ) -m
([Delta])} so as to _{satisfy, k i, i = d +} 1~n-1 and _h i, choose i = 0~n, u (k) = {k (δ) /
q (δ)｝ u (k) + ｛h (δ) / q (δ)｝ y (k)
+ (M ₀ / r ₀ ) x (k) to form a closed loop control system that gives a control input, and further, x (k) =
It is characterized by providing feedforward compensation such as ｛m (δ) / m ₀ z ² ｝ v (k).

Therefore, the disturbance compensation characteristic makes it possible to make the control system robust against disturbances and mismatches.
Primary, secondary,... Further, the pole arrangement characteristic causes the closed-loop control characteristics to be pole-arranged such that the characteristic equation has a desired characteristic m (δ). By matching the disturbance compensation characteristic with the pole arrangement characteristic, the characteristic of the closed loop control system can be equal to m (δ) even if there is disturbance or mismatch. Further, the above m (δ) can be compensated by feedforward compensation, and the characteristic from the command to the output can have a finite settling characteristic of z− ² .

[0010] The present invention according to claim 2 is a discrete time
Approximately in the system, r₀/ ｛Δ²+ P₁δ｝, δ = z-1
Desired for controlled objects such as motor controllers
Stable polynomial with closed loop characteristics: m (δ) = δ
²+ M₁δ + m₀And the assumed disturbance order to be compensated is d.
Then, a stable observer polynomial: q (δ) = δⁿ+ Q
_n-1δ^n-1+ ... + q₀, N = 2 + d, and k
(Δ) = k_n-1δ^n-1+ ... + k_{d + 1}δ^{d + 1}+ Q
_dδ^d+ ... + q₀, H (δ) = h_nδⁿ+ ... + h₀age
When k_j= Q_j, J = 0 to d, and k
(Δ) r₀+ H (δ) ｛δ²+ P₁δ｝ = q (δ) ｛p
(Δ) −m (δ)｝_i, I = d + 1
~ N-1 and h_i, I = 0 to n, and u (k) =
｛K (δ) / q (δ)｝ u (k) + ｛h (δ) / q
(Δ)｝ y (k) + (m₀/ R₀) X (k)
A closed loop control system that provides input
Furthermore, the two poles of the closed-loop control system,
Let the roots of the term m (δ) be F₁And F₂Compensate by
X (k) = F so that the ratio can be adjusted₂[｛Z^-1v
(K) + F ₁(V (k) -z^-1v (k))｝-z^-1
｛Z^-1v (k) + F₁(V (k) -z^-1v
(K))｝ + z^-1｛V (k) -z^-1v (k)｝] +
z^-1[Z^{− 1}v (k) + F₁｛V (k) -z^-1v
(K) 与 え る]
It is characterized by.

Therefore, the compensation for the first pole of m (δ) can be performed independently by F ₁ and the compensation for the second pole can be performed independently by F ₂ .

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The configuration of the present invention will be described below in detail based on an embodiment shown in the drawings.

FIGS. 1 and 2 show an embodiment of a control device according to the present invention.
One form is shown. The control device 1 approximately includes a discrete time system,
r₀/ ｛Δ²+ P₁A mode represented by δ｝, δ = z-1,
For the control object such as the
Stable polynomial with loop characteristics: m (δ) = δ²+ M₁δ
+ M₀And d is the assumed disturbance order to be compensated.
Observer polynomial: q (δ) = δⁿ+ Q_n-1δ
^n-1+ ... + q₀, N = 2 + d, and k (δ) =
k_n-1δ^n-1+ ... + k_{d + 1}δ^{d + 1}+ Q_dδ ^d+
… + Q₀, H (δ) = h_nδⁿ+ ... + h₀And when
k_j= Q_j, J = 0 to d, and k (δ) r₀+
h (δ) ｛δ²+ P₁δ｝ = q (δ) ｛p (δ) -m
(Δ) ｋ_i, I = d + 1 to n−1 and
H_i, I = 0 to n, u (k) = ｛k (δ) /
q (δ)｝ u (k) + ｛h (δ) / q (δ)｝ y (k)
+ (M₀/ R₀) Close to give a control input like x (k)
A loop control system is configured, and x (k) =
｛M (δ) / m₀z²フ ィ ー ド Feed form like v (k)
Word compensation is provided.

FIG. 1 is a block diagram to which the control device 1 is applied. In the above equation, h (δ), k (δ), q
(Δ) are H (z), K (z) and Q in FIG. 1, respectively.
(Z). Note that in the figure, δ = z
It is assumed that the conversion from −1 to δ → z has been performed.

FIG. 2 shows an example of a hardware configuration for realizing control by the control device 1. The hardware configuration according to the present embodiment includes an MPU 11 (microprocessor), a RAM 12, a ROM 13, a flash ROM 1
4, a shared memory 15, a DA converter 9 (digital-analog converter) to which the motor 3 is connected via the PWM driver 5, and a DI / D receiving an input of the sensor 16.
O17 (digital input / digital output), a counter 8 to which an encoder 7 for detecting the position of the motor 3 is connected, an SCI 18 (serial communication interface), and a host controller connected to the SCI 18 via the shared memory 15 19 etc. Motor 3
Is connected to a load 4 such as a robot. 1 and 2 are examples, and the application of the present invention is not limited to such a system.

The motor control device 2 includes, for example, a motor 3, a load 4, a DA converter 9, a PWM driver 5, a position detector 6, an encoder 7, and a counter 8, as shown in FIG. Generally, when the motor control device 2 configured as described above is discretized at a constant sampling period T (second) in consideration of discrete control by a microcomputer, approximately It is represented as

R ₀ / {δ ² + p ₁ δ}, δ = z−1 where z is a leading operator for a discrete-time system. Further, r ₀ and p ₁ are constant coefficients of the motor control device 2.

In such a controlled object, the input signal is u (k) and the position output signal is y (k). On the other hand, the following closed-loop controller is configured.

First, let d be the assumed disturbance order to be compensated.
A stable observer characteristic polynomial expressed by Expression 2 is selected.

[Mathematical formula-see original document] q ([delta]) = [delta] ⁿ + qn _{-1 [} delta] ^n-1 + ... +
q ₀ , n = 2 + d When a stable polynomial having a desired closed-loop characteristic is used as a characteristic polynomial represented by Equation 3 and the polynomials represented by Equations 4 and 5 are used, Equation 6 is satisfied. ,
_{k i, i = d + 1~n} -1 and _h i, choose the i = 0~n.

M (δ) = δ ² + m ₁ δ + m ₀

K (δ) = k _n−1 δ ⁿ⁻¹ +... + K _{d + 1} δ
^{d + 1} + q _d δ ^d + ... + q ₀

## EQU5 ## h (δ) = h _n δ ⁿ +... + H ₀

K (δ) r ₀ + h (δ) {δ ² + p ₁ δ} = q
(Δ) {p (δ) −m (δ)} p (δ) is a control target, that is, a denominator polynomial of the transfer function of the motor control device 2 in the present embodiment. Here, by setting k _j = q _j , j = 0 to d, a unique solution is given to the equation of Expression 6, and a disturbance suppression function described later can be provided independently of the command response. This is the first feature of the control device 1. According to the first feature, the control system can be made robust against disturbance and mismatch, and d, that is, the disturbance compensation order can be set to 0th order, 1st order according to the purpose.
Next, second ...

Next, the thus obtained q
Using (δ), k (δ), and h (δ), a closed-loop control system that provides a control input represented by Expression 7 is configured.
Where x (k) represents the input to the closed loop control system,
v (k) represents a reference position command input to the entire control system configured.

U (k) = ｛k (δ) / q (δ)｝ u (k) +
{H (δ) / q (δ)} y (k) + gx (k), g = m
₀ / r ₀ This point is the second feature of the control device 1. According to the second feature, the control characteristics of the closed loop are poled such that the characteristic equation has a desired characteristic m (δ). That is, the entire control system can be a pole arrangement system, and the poles can be arranged at a feasible position.

Further, by adopting a structure having such first and second features, the characteristics of the closed-loop control system can be equal to m (δ) even if there is disturbance or mismatch. . As a result, the configuration of the controller can be simplified, that is, the amount of calculation can be reduced, as compared with a conventional control system using a disturbance observer. That is, the transfer function of the control system from the position command input x (k) to the position output y (k) is m ₀
/ M (δ) is a closed-loop shape given in a pole-arranged form.

Further, feedforward compensation as shown in Expression 8 is given to this closed loop.

X (k) = ｛m (δ) / m ₀ z ² ｝ v (k) This point is the third feature of the control device 1. According to the third feature, the poles arranged in the closed loop control system described above can be compensated, and the characteristic from the command to the output can be given a finite settling characteristic of z- ² , and the tracking error can be reduced while the entire control system is stable. It can be minimized.

The above-mentioned first and second characteristics are as follows: m ₀ / r ₀ , H (z), K (z), 1 / Q
It is constituted by the controller of (z). The third feature is constituted by the feedforward compensator 20.
The input to the control target, that is, the motor control device 2 is:
This is performed via the limiter 15.

According to the control device 1 configured as described above, the closed loop coordinate system is configured as a pole arrangement system,
Even if the poles of 100% are compensated by the feedforward, no overshoot occurs, and by realizing the control device 1 in a discrete time system, a substantial finite enactment can be achieved. Further, by performing the feasible pole arrangement, a realistic configuration can be performed without increasing the closed-loop gain unlike the ordinary finite settling control.

Furthermore, since the control device 1 has a structure in which the observer includes a disturbance compensation function, the overall order of the control device 1 can be reduced, that is, disturbance can be suppressed while simplifying the structure.

Here, for example, when a position command with acceleration / deceleration is applied, or when there is a mismatch or disturbance of the object to be controlled normally, the pole arrangement characteristic as the second characteristic and the feed characteristic as the third characteristic are used. Slow parts,
A follow-up deviation occurs in the acceleration / deceleration portion and the portion where the acceleration / deceleration changes.

Therefore, by adding a disturbance compensation characteristic, which is the first characteristic, even if there is a mismatch or disturbance of the controlled object, the deviation at the constant speed when d = 0 and the deviation at d = 1 when d = 1. The deviation between the constant speed and the acceleration is compensated for, and when d = 2, the deviation between the constant speed, the acceleration and the acceleration change is compensated, and the finite settling is performed.

That is, by setting the disturbance compensation order to the 0th order, the 1st order, the 2nd order, etc. according to the purpose, even when a position command with acceleration / deceleration is applied, some mismatch or disturbance of the controlled object, etc. , The steady-state position deviation in the low-speed part, the acceleration / deceleration part, and the part where the acceleration / deceleration changes,
It is possible to be.

The above embodiment is an example of a preferred embodiment of the present invention, but the present invention is not limited to this, and various modifications can be made without departing from the gist of the present invention.

For example, the feedforward compensator 20,
That is, the third characteristic portion is represented by Expression 9.

X (k) = F ₂ [｛z ⁻¹ v (k) + F ₁ (v
(K) −z ⁻¹ v (k))｝ − z ⁻¹ ｛z ⁻¹ v (k)
+ F ₁ (v (k) −z ⁻¹ v (k))｝ + z ⁻¹ ｛v
(K) −z ⁻¹ v (k)｝] + z ⁻¹ [z ⁻¹ v (k)
+ F ₁ {v (k) −z ⁻¹ v (k)}] Here, F ₁ represents a feedforward compensation coefficient for the first pole of the above-described closed loop control system, and F ₂ represents a feedforward compensation coefficient for the second pole. Represents the forward compensation coefficient. In this case, it can be adjusted independently compensation rate for the first pole of the desired closed-loop control system of the characteristic polynomial m ([delta]) in F _1, the compensation rate for the second pole in the F _2.

[0030]

As is apparent from the above description, according to the control device of the first aspect, the disturbance is suppressed by the disturbance compensation characteristic, and the characteristics of the closed loop control system are arranged as desired by the pole arrangement characteristics. By giving the finite settling characteristic of the closed-loop control system by feedforward compensation, it is possible to minimize the following deviation while keeping the entire control system stable,
It can respond to acceleration and changes in acceleration. As a result, a control device with a small following deviation can be realized with a simple configuration.
That is, it can be realized without increasing the cost.

Further, according to the control device of the second aspect, the compensation ratio for the first pole and the compensation ratio for the second pole of the control device can be independently adjusted.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an example to which a control device of the present invention is applied.

FIG. 2 is a schematic diagram illustrating an example of a hardware configuration to which the control device of the present invention is applied.

[Explanation of symbols]

 1 controller 2 motor controller

Claims (2)

[Claims] 1. Approximately in a discrete time system, r₀/ ｛Δ²+
p₁δ｝, δ = z-1
Stable with desired closed-loop characteristics for the controlled object
Polynomial: m (δ) = δ²+ M₁δ + m₀And compensate
When the assumed disturbance order is d, a stable observer polynomial
Formula: q (δ) = δⁿ+ Q_n-1δ^n-1+ ... + q₀, N
= 2 + d, and k (δ) = k_n-1δ^n-1+ ... +
k_{d + 1}δ^{d + 1}+ Q_dδ^d+ ... + q₀, H (δ) = h
_nδⁿ+ ... + h₀And k _j= Q_j, J = 0 to d
And k (δ) r₀+ H (δ) ｛δ²+ P
₁δ｝ = q (δ) {p (δ) -m (δ)}
And k_i, I = d + 1 to n−1 and h_i, I = 0 to n
Select u (k) = {k (δ) / q (δ)｝ u (k) +
｛H (δ) / q (δ)｝ y (k) + (m₀/ R₀) X
Constructs a closed-loop control system that provides a control input as in (k)
X (k) = ｛m (δ) / m ₀z
²Give feedforward compensation like｝ v (k)
A control device characterized in that: 2. Approximately in a discrete time system, r₀/ ｛Δ²+
p₁δ｝, δ = z-1
Stable with desired closed-loop characteristics for the controlled object
Polynomial: m (δ) = δ²+ M₁δ + m₀And compensate
When the assumed disturbance order is d, a stable observer polynomial
Formula: q (δ) = δⁿ+ Q_n-1δ^n-1+ ... + q₀, N
= 2 + d, and k (δ) = k_n-1δ^n-1+ ... +
k_{d + 1}δ^{d + 1}+ Q_dδ^d+ ... + q₀, H (δ) = h
_nδⁿ+ ... + h₀And k _j= Q_j, J = 0 to d
And k (δ) r₀+ H (δ) ｛δ²+ P
₁δ｝ = q (δ) {p (δ) -m (δ)}
And k_i, I = d + 1 to n−1 and h_i, I = 0 to n
Select u (k) = {k (δ) / q (δ)｝ u (k) +
｛H (δ) / q (δ)｝ y (k) + (m₀/ R₀) X
Constructs a closed-loop control system that provides a control input as in (k)
And the two of the closed loop control system
Let the poles, the roots of the characteristic polynomial m (δ), be F₁as well as
F₂X (k) so that the rate of compensation can be adjusted by
= F₂[｛Z^-1v (k) + F₁(V (k) -z^-1v
(K))｝-z^-1｛Z^-1v (k) + F₁(V (k)
-Z^-1v (k))｝ + z^-1｛V (k) -z^-1v
(K)｝] + z^-1[Z^-1v (k) + F ₁｛V (k)
-Z^-1v (k)｝]
A control device characterized by giving