JPS6191702A - Addaptive control method and system - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention] The present invention relates to an adaptive control system.

An adaptive control system is a closed-loop system that changes the gain of the system depending on the system's response to a disturbing event. Although the response characteristics of most controlled processes vary only slightly over their operating range,
Other systems exist whose operating characteristics vary considerably. for example,
The arms of cranes and robots have different response characteristics depending on the direction of the object being moved. Also, many other controlled systems or processes have different response characteristics at different parts of their operating range. The result is a forward gain that provides a stable response in some parts of the operating range, but makes the thread unstable in other parts of the operating range. For such a controlled system, adaptive control is more desirable than control that keeps the gain constant.

However, most adaptive control systems rely on knowledge of the response characteristics of the controlled system. For this reason, some adaptive controllers add white noise to the input terminal of the controlled system to determine the response characteristics of the controlled system. Other adaptive controllers calculate the response characteristics of the controlled system by adding discrete binary noise to the input terminal of the controlled system.

Still other adaptive controllers use mathematical models of the controlled system. The same control signal is then applied to this model at the same time as the control signal is applied to the actual system.

Then, the response of the actual controlled system is compared with the response of the model system, and the difference is used to adjust the forward gain signal of the actual system until the actual system behaves in the same way as the model.

It is an object of the present invention to provide an adaptive control system that does not require detailed knowledge of the controlled process or mechanism. 'fG real,
Mjli (J) The only condition for a controlled process or system is that reducing the forward gain of the control loop increases the stability of the system.Also, the adaptive control system of the present invention does not respond to the magnitude of the error signal; It only responds to the stability of the overall response of the system.

In practicing the invention, the error signal of a closed loop control system is processed and the results are used to vary the overall gain of the system. In particular, the error signal is first squared and the resulting signal rr:
Spend e minutes. The differentiated signal is then used to trigger the switching device. The switching device produces a selectable positive output when the differentiated signal is positive and produces a selectable negative output when the differentiated signal is negative. The output of this switching device is integrated and used to change the forward gain of the system.

When the yarn is made using an electronic circuit, the switching device is a pulse width modulation circuit. By selecting the ratio between the positive and negative outputs of this pulse width modulation circuit, the damping coefficient and thus the stability of the system are controlled. The present invention adjusts the gain of the controlled system or process to maintain a predetermined stability margin.The pulse width modulation circuit also has a threshold so that the magnitude of the differential signal is minimal, i.e. It is possible to prevent either high or low output from being output until the threshold level is exceeded.

The invention will be explained in detail with reference to the drawings.

The present invention uses Ryabunov's second method, or direct method, to determine the stability of a control system, and uses the forward loop (f
orward 1oop ) (7) Gain M positive L, maintaining a preselected stability margin. This description will first explain how and why the present invention works from a theoretical abreach perspective, and then describe one embodiment of an apparatus for carrying out the present invention. It becomes clear from this theoretical exploration that many other embodiments of the invention are possible. Although the embodiments described with particular reference to the drawings are electronic control systems, the present invention may be used in any other type of control system, including fluid control systems, mechanical control systems, optical control systems, and the like.
It is conceivable to use fml=.

The Lyapunov function has the characteristic that its time derivative can be used to measure the stability of any closed-loop control system.

At this time, the M differential is negative for a stable control system, and positive for an unstable control system. (The Lyapunov function is well known to those skilled in the art, and the criteria for determining that E'', the square of the difference between the measured value and the desired value of the controlled parameter in a closed-loop system, is such a function should be fully explained. (This would only unnecessarily lengthen this specification.) The work of Ryabno7 is broadly applicable to all closed-loop systems, but as can be easily seen, it applies well to systems that behave like damped harmonic oscillators. In such a system, the magnitude of the error signal following a step or unit input is given by:

(”) E = Eo e″″ζ” 5in1:IJt
However, E: Error in the controlled system Eo = Initial error in the controlled system ζ = Attenuation coefficient ω = Unique number of shooting shifts 12 hours In a stable system, ζ is positive, and in an unstable system, it is negative. It is also known that in the design of a control system, this selection provides adaptive control of the system.

When the error signal (E) is squared, the resulting formula satisfies the conditions for the Ryakunov coefficient.

In the case of a damped harmonic oscillator, the equation is as follows.

(2) λ== Eo2e-2ζ(=)t(-2ζωs
in”a+t+2ωsinωtcO8ωt)t Examining this equation, you can see why it is used to measure the stability of a system.The term outside the parentheses on the right side of equation (2) becomes smaller with time when the damping coefficient is positive. It gives an exponential curve that stabilizes the system. When the system is unstable, that is, when the damping coefficient is negative, the exponential curve increases with time. The term in parentheses in Equation (2) has two components. The first term is negative whenever ζ is positive, that is, when the system is stable.The second term in parentheses oscillates evenly above and below the time axis.The sum of these two terms is , when averaged over time, the sum is negative when ζ〉0. Thus, whenever the system described by equation (1) is stable, the time integral of equation (2) is negative, It is proportional to the damping coefficient.As is clear from the above, the time average value of equation (2) is a measure of the stability of the system.

Note again that for any controlled system, whether linear or nonlinear, the square of the difference between the actual output and the desired output satisfies the conditions of the 7-function function. Therefore, although the above explanation has been made for damped harmonic oscillators, the results are the same for other systems, including nonlinear systems.

It is desirable that the adaptive gain control be sensitive only to changes in system stability and not to the magnitude of the error signal.

When the left side of equation (2) is transformed, the following equation holds true.

This equation is clearly directly proportional to the magnitude of the error signal.

Controlling the total gain of the system using the time integral of equation (2) has the disadvantage that it depends on the amplitude of the error signal E.

This drawback can be overcome by using a pulse width modulation circuit. Such a circuit has two output states, positive and negative, and the equation (2
) is switched between two output states when the value changes sign. The result alternates between predetermined positive and negative values, the width of which is proportional to the time derivative of the square of the error signal, i.e. the length of time during which equation (2) is positive or negative, respectively. It becomes a square wave pulse train. The pulse train thus obtained is independent of the magnitude of the error signal.

When the output rectangular wave train from the pulse width modulation circuit is time-integrated, the result is the time integral of the time derivative of the square of the error signal.
t), but is a positive or negative signal that is completely independent of the magnitude of the error signal (E).

This signal is proportional to the damping coefficient ζ and provides a measure of thread stability and can be used to adjust the gain of the controlled process to maintain stability. For example, in response to some inputs to a controlled process, the output of a pulse lll11 modulation circuit is
When the divided value is positive, indicating that the system is unstable, the gain signal of the controlled process is lowered so that the integrated value of the output of the pulse width modulation circuit becomes zero.

Although the system described above will operate with a full margin of stability, it is usual to allow some margin, i.e. the damping coefficient should be set to a very slightly positive value, typically between 0.5 and 1.5. It is desirable to operate the controlled process in an intermediate state. This can be achieved in several ways. One method is to add a selectable amount to the integrated output of the pulse width modulation circuit, but the stability margin this provides depends on how the amount added is chosen. Another method, as detailed below, is to vary the ratio between the amplitudes of the positive and negative outputs of the pulse width modulation circuit. In this way, the ratio between the damping coefficient and the output power is not linearly related;
It is related via a transcendental function, giving any desired specific margin.

The invention described above can be implemented in the embodiment shown in FIG.

System 10 includes a controlled system or process 12;
The controlled system 12 may be a mechanical system such as the position control of a missile or aircraft wing, or a robot arm that must work in a changing environment such as underwater or out of water. be able to. Controlled system 12 may be a process, such as a chemical process, where the chemistry at the outlet side of the process is measured and the controlled variables are flow control valves, reactant temperatures, or reaction mixer speeds.

The controlled system 12 has input terminals 14 which control several input parameters of the controlled system 12 to bring the output parameter or response to a selected value and maintain it there. This value is 2
It can represent a particular physical relationship between individual parts, the chemical composition or concentration of an effluent from a chemical process, or almost any other measurable physical property. Measuring the value of the parameter to be controlled, feedback line 1
6 to the input terminal.

A comparator 18 (shown as a summing point) determines the difference between the signal at input terminal 14 representing the desired value of the controlled parameter and the actual value of the controlled parameter coming from feedback line 16. The measured error signal E
is sent to the controlled system 12 via the amplifier 20.

Amplifier 20 may be a conventional electronic amplifier whose output is approximately proportional to the input. However, this specification (patent Hu
The term amplifier as used in FF (including the range of FF) is a broad concept that includes any system or group of elements that receives an input signal and produces a larger or modified output signal.

- Example B Taking a hydraulic system, this includes a source of fluid under pressure and a proportional flow control valve. In such yarns the gain can be controlled according to the principles of the present invention. In the above example, the gain is obtained by adjusting the pressure upstream of the proportional flow control valve FJ,'l. It can be changed.

The response of the controlled system 12 to a unit or step input, as indicated by the error signal E, takes the shape of curve A in FIG.
Comparator 18 and amplifier i20 together form a conventional feedback control system, with the gain of amplifier 20 controlling the damping coefficient of the system and thus the stability of the system. A further requirement necessary to ensure that the invention can be applied to controlled system 12 is that lowering the gain of amplifier 20 increases the stability of system 1o. And a large number of systems of practical interest satisfy this criterion.

The adaptive control system of the present invention varies the gain of amplifier 20 in response to error signal E so that a selectable margin of stability of the system lo is maintained. For this purpose, conductor 24 is connected to system 10.
An amplifier 22 is provided which receives an error signal E from and 26 and squares the error signal E. The result E obtained is, for example, as shown in the song WB of FIG. This E2 signal is then time differentiated by a differentiator 28. At this time, the signal is inverted. The corner frequency of the differentiator 28 is selected to be one or two orders of magnitude larger than the corner frequencies of any other elements of the controlled system 12.

Therefore, does the response of the differentiator itself have a negative effect on the thread control? It will not affect you. Curve C in FIG. 2 shows the inversion of the time differential of the square of the error signal. The output signal of the differentiator 28 oscillates above and below zero as shown in FIG. When the system 10 is stable and the damping coefficient is positive, it spends a lot of time on the positive side of zero.

The output of differentiator 28 is sent to a pulse width modulation (PWM) circuit 30. This circuit has two output levels, one with a positive voltage B and the other with a negative voltage A.

When the output of the differentiator 28 is negative, the output of the PWM circuit 30 is A.
When the output of the differentiator 28 is positive, the output of the PWM circuit 30 is B. The resulting rectangular wave pulse train is shown by the curved line in FIG.

PWM circuit 30 also has a dead zone where the output is zero. PWM circuit 30 does not respond at all unless the absolute value of the signal received from differentiator 28 exceeds a minimum value. This dead zone is shown by two imaginary lines that intersect curve C in FIG. 2 and a horizontal portion that coincides with the X-axis of the curve. This dead zone reduces the stability of the system to a predetermined minimum h
The system gain of the amplifier 20 does not change unless it changes by 1 or more.

The output of PWM circuit 30 is sent to integrator 32. Integrator 32
The output of represents the algebraic sum of the areas under the curves of FIG. 2, ie, the positive area minus the negative area. Integrator 82
The break point frequency of is selected to be approximately 1 of the break point frequency of the fracture system 12. This allows one integration to be performed over a sufficient period of time to accurately reflect the average of the rectangular pulse train. Integrator 82
System 10 is stable when the output of integrator 82 is positive, and system 10 is unstable when the output of integrator 82 is negative.

The degree to which the output of integrator 32 is above or below zero is a measure of the stability or instability of system 10. The output of integrator 82 is provided through limiter 34 which limits the maximum and minimum gain of amplifier 20.

An error signal is generated in response to changes in the signal at input terminal 14. Oscillations in the error signal indicate that the system is becoming less stable. In this case, the output of the integrator a2 becomes small because the time during which the output of the differentiator 28 is below the zero axis is negative. This reduction reduces the gain numerator of amplifier 20. amplifier 20
The gain continues to decrease until the time during which the time differential output is in the positive region is equal to the time during which it is in the negative region. If the oscillations in the error signal indicate increased stability, the gain of amplifier 20 will be higher.

PWM circuit 80 also serves to margin the stability of system 1o. In particular, the ratio of the values of A and B as the output of the PwM circuit 80 controls the stability margin through controlling the damping coefficient 3 of the system IO. As can be seen from FIG. 2, the output of the PwM circuit 80 has a vector ωt of 1.
It has a waveform that repeats every 800 rotations. This unit of turning consists of two parts, the positive one has a width of 90° + δ with δ as the offset angle, and the negative one has a width of 90'-
has δ. For a single repeating unit, the area above the curve is B(90'+δ) and the area under the curve is A(90'+δ).
0°−δ). The adaptive control circuit is (4)B(90°+
The gain of the amplifier 20 is changed until δ)=A(90'-δ).

This relationship with δ can be derived fairly easily.

(5) Era (2)==0 when ωt = 90'-δ. Therefore, at that time (6) 2
ζω5in2ωt = 2ωsinωtoO8ωt. This becomes as follows (7) Substituting equation (5) into equation (7) with ωt' = tan-1'' and solving, (8) δ = jan-1ζ Therefore, when δ = 0, ζ = 0, which represents a state of zero stability and is usually highly undesirable.

By combining equations (4) and (8), the following equation is obtained.

(9) tan ζ = 90° (Friend 1A + B Equation (9) shows that any desired attenuation coefficient can be obtained by changing A and B. The gain of amplifier 2o is expressed by curve D
(Figure 2) The progress in which the areas above and below the zero axis become equal continues to change. However, this equation occurs when there is some stability margin represented by choosing a positive damping coefficient.

System 10 has been described as an electronic system.

However, other types of elements can clearly be used. For example, and without limitation, hydraulic elements are known that perform each of the functions required in the block diagram of FIG. System 10 can then be constructed using such hydraulic elements. Mechanical elements can also be used to create the system 1o, and optical elements or any other combination of elements can be used to suit a particular controlled system 12 and control it and its environment.

In this way, the adaptive control system of the present invention has a forward gain of the controlled system 12? to keep the stability margin at the desired value.

Unlike other adaptive control systems, it is not necessary to know the details of the frequency response of the controlled system 12. Instead, the stability of the system is measured using the square of the error signal (E) that satisfies the conditions of the Lyapunov function. In particular, the square of the error signal is differentiated with respect to time, and the differential thus obtained is used in the pulse width modulation (PWM) circuit 30.
, and make its output a constant positive value when the time derivative is positive, and a constant negative value when the time derivative is negative. The output of the PWM circuit 80 is then integrated by an integrator 82 to obtain a signal representing the difference between the length of time when the time derivative of E is positive and the length of time when it is negative, and in this way Lyapunov's Obtain a measure of the stability of the system established under the theory. The output of integrator 32 is used to control the forward loop gain, returning controlled system 12 to a stability margin defined by the constant positive and negative output values of P4M circuit 80.

[Brief explanation of the drawing]

FIG. 1 is a block diagram of a system embodying the invention, and FIG. 2 is a waveform diagram of four curves representing signals at various locations within the first system. lO...System (system) 12...Controlled system 14
...Input terminal 16...Feedback line 18...Comparator 20...Amplifier 22
...Square amplifier 24.26...Conductor wire 28...
・Differentiator 80...Pulse width modulation circuit (PWM circuit) 82...
Integrator 84...Limiter

Claims (1)

[Claims] 1. To control parameters of a process or mechanism,
measuring the value of this parameter; comparing this measured value with a desired value to obtain an error signal; squaring this error signal; and determining that the time derivative of the squared error signal is positive. comparing the length of time during which the error signal has a negative value with the length of time during which the time derivative of the squared error signal has a negative value to obtain a gain control signal; an adaptive control method, comprising the step of: applying a parameter to the system via an amplifier to adjust the parameter to a desired value. 2. The step of comparing the length of time during which the time differential of the squared error signal is positive and the length of time during which the time differential is negative is performed when the absolute value of the time differential of the squared error signal is determined in advance. Claim 1, characterized in that the method comprises the steps of: triggering the pulse width modulation circuit using the time differential of the squared error signal only when the error signal exceeds the value; and integrating the output of the pulse width modulation circuit. adaptive control method. 3. further multiplying the length of time during which the time derivative of the squared error signal is positive by a preselected constant;
3. The adaptive control method according to claim 2, further comprising the step of comparing this result with the length of time during which the time derivative of the squared error signal is negative. 4. The adaptive control method according to claim 1, further comprising the step of limiting the maximum gain and minimum gain of the amplifier in the middle of providing the error signal to the system. 5. A process including a controlled parameter, an error signal representing the difference between an actual value and a desired value of the controlled parameter, and a variable gain amplifier that applies the error signal to the process to vary the controlled parameter. wherein the method for controlling the gain of the amplifier includes changing the gain of the amplifier in response to an integral of a pulse width modulation circuit triggered by changing the sign of the time derivative of the square of the error signal. A gain control method characterized by: 6. limiting the maximum and minimum gain of said amplifier and multiplying the amplitude of the positive part of the output of the pulse width modulation circuit by a factor selected to obtain the desired margin of system stability; A gain control method according to claim 5, comprising: 7. A dead zone is provided in the pulse width modulation circuit so that the pulse width modulation circuit does not respond until the absolute value of the time derivative of the squared error signal exceeds a selected value. Gain control method described. 8. For controlling a process having an input, a forward gain, and an output, means for measuring the value of said output, and means for comparing the value of said output with a desired value of said output to obtain an error signal. and means for squaring the error signal; means for taking the time derivative of the squared error signal; and calculating the sum of the length of time for which the time derivative is positive and the length of time for which the time derivative is negative. An adaptive control system comprising: means for calculating; and means for controlling a forward gain of the controlled process in response to the sum. 9. The means for calculating the sum comprises a pulse width modulation circuit having two output states, one positive and the other negative, and means for limiting the maximum and minimum values of the forward gain. 9. The adaptive control system according to claim 8, characterized in that: 10. triggering said pulse width modulation circuit by changing the sign of said time derivative, providing said pulse width modulation circuit with means for adjusting the ratio between said two output states, and further providing a dead zone, thereby said 10. The adaptive control system according to claim 9, wherein the pulse width modulation circuit changes its output state only when the absolute value of the time differential exceeds a predetermined value.