Goal of the work
Familiarize yourself with the construction of step-by-step extremal control systems during control dynamic objects with a delay.
Theoretical part
In any production (at a plant, combine) there is some leading technical and economic indicator (TEI) that fully characterizes the efficiency of this production. It is beneficial to maintain this leading indicator at an extreme value. Such a generalized indicator can be the profit of the enterprise.
For all technological processes (in workshops, departments) that are part of the production, based on the leading TEP, one can formulate their private TEPs (for example, the unit cost of production at a given productivity). In turn technological process can usually be divided into a number of sections (technological units), for each of which it is also possible to find the optimality criterion Q . Reaching the extremum Q will bring the private TEC of the process and the leading TEC of the production as a whole closer to the extremum.
Optimality criterion Q it can be directly some technological parameter (for example, the temperature of the flame of the combustion device) or some function depending on the technological parameters (for example, efficiency, thermal effect of the reaction, useful product yield for a given period of time, etc. ).
If the optimality criterion Q is a function of some parameters of the object, then the system of extreme control (ESR) can be applied to optimize this object.
In the general case, the value of the optimality criterion depends on the change in a number of input parameters of the object. There are many control objects for which the value of the optimality criterion Q depends mainly on changing one input parameter. Examples of such objects are various kinds of furnace devices, catalytic reactors, chemical water treatment at thermal power plants, and many others.
So, extreme control systems are designed to search for optimal values of control actions, i.e. such values that provide an extremum of some criterion Q process optimality.
Extreme control systems, which are designed to optimize an object for one input channel, are called single-channel. Such SERs are most widely used.
When optimizing objects with significant inertia and pure delay, it is advisable to use stepwise extremal systems that act on the controlled input of the object at discrete time intervals.
When studying an extremal system, in most cases it is convenient to represent the optimization object as a series connection of three links: an input linear inertial link, an extremal static characteristic at = F(X) and the output linear inertial link (Fig. 1). Such a structural substitution scheme can be designated LNL.
Rice. 1Scheme of the LNL extremal object
It is convenient to take the gain coefficients of both linear links equal to unity. If the inertia of the input linear link is negligibly small compared to the inertia of the output linear link, the object can be represented by the equivalent circuit of the CL; if the inertia of the output linear link is negligible, - by the LN equivalent circuit. The intrinsic inertial properties of an object are usually represented by an output inertial link; the inertia of the measuring devices of the system belongs to the same link.
The input linear link usually appears in the block diagram of the object when the actuator (IM) of the extremal system acts on the optimization object itself through a link with inertia, for example, if the input parameter of the object being optimized is temperature, and the IM affects its change through the heat exchanger. The inertia of the actuator is also referred to the input linear part.
It should be noted that the coordinates of the control object intermediate between linear and non-linear links in the vast majority of cases cannot be measured; this is easy to implement only when modeling the system.
In some cases, it is possible to determine the structural substitution scheme of an object only experimentally.
To do this, change the input coordinate of the object v 1 corresponding to the output value z 1 , before v 2 (Fig. 2, A), at which the value of the output coordinate of the object as a result of the transient process will be approximately equal to z 1 .
If this perturbation practically did not cause any noticeable change in the output coordinate of the object (Fig. 2, b), then the input inertial link is absent. If the transient process as a result of such a perturbation has a form qualitatively close to that shown in Fig. 2, V, then the inertial link at the input of the object exists.
Rice. 2Characteristics of extreme op amp
The structure of objects LN and LN, in which the linear part is described differential equation of the first order with or without delay, and the static characteristic y=f(x) can be any continuous function with one extremum in the operating range can be approximated sufficiently a large number of industrial facilities optimization.
Extreme control systems:
Automatic optimization systems with extremum storage
In extreme controllers SAO with memorization of the extremum, the difference between the current value of the output signal is fed to the signum relay at object and its value at the previous point in time.
Structural diagram of ACS with extremum memorization is shown in fig. 3 . Object output value ABOUT with static characteristic y=f(X) served on a storage device memory extreme regulator.
Rice. 3Automatic optimization system with extremum memorization
The storage device of such a system should only record the increase in the input signal, i.e. memorization occurs only when increasing y. To decrease at the storage device is not responding. The signal from the storage device is continuously fed to the comparison element ES, where is compared with the current value of the signal y. Difference signal at-u max from the comparison element goes to the signum relay SR. When the difference at-y max reaches deadband value at n signum relay, it reverses the actuator THEM, which affects the input signal X object. After actuation of the signal relay, stored in the memory device memory meaning y reset and signal storage at starts again.
Systems with extremum memory usually have actuators with a constant travel speed, i.e. dx/dt=±k 1 Where k= const. depending on the signal And Signum-relay actuator changes the direction of movement.
Let us explain the work of the SAO with the memorization of the extremum. Let's assume that at the moment t 1 (Fig. 4), when the state of the object is characterized by the values of the signals at the input and output, respectively X 1 And at 1 (dot M 1), the extreme regulator is turned on. At this point, the memory device stores the signal at 1 . Let us assume that the extreme regulator after being put into operation began to increase the value X, while the value at decreases - the storage device does not respond to this. As a result, a signal appears at the output of the signal relay at-at 1 . In the moment t signal at-at 1 reaches the dead zone of the signal relay at n(dot M 2), which works by reversing the actuator. After that, the stored value at 1 is reset and the memory device stores the new value at 2 . Object entry signal X decreases, and the exit signal at increases (trajectory from the point M 2 To M 3). Because the at increasing all the time, output memory continuously follows the change y.
Rice. 4Search for the optimum in SAO with memorization of the extremum:
A- characteristics of the object; b- changing the output of the object; V- signal at the input of the signum relay; G- changing the input of the object.
At the point M 3 the system reaches an extreme, but the decrease X continues. As a result, after the point M 3 meaning at already decreasing and memory remembers y Max. Now at the input of the signum relay SR difference signal appears again y-y max. At the point M 4 , When y 4 -y max = y n, the signum relay is activated, reversing the actuator and resetting the stored value y max etc.
Oscillations are set around the extremum of the controlled value. From fig. 4 it can be seen that the period of input oscillations T in object is 2 times greater than the oscillation period of the output of the object T out. Signum relay reverses IM when y=y max - y n. The direction of the IM movement after the signum relay actuation depends on the direction of the IM movement before the signum relay actuation.
From the consideration of the work of the SAO with the memorization of the extremum, it can be seen that its name does not quite accurately reflect the essence of the system's operation. The memory device fixes a non-extremum of the static characteristic of the object (its value at the moment the controller is put into operation is unknown). The memory device fixes the values of the output quantity at object when at increases.
Step type automatic optimization systems
The block diagram of the stepping ACS is shown in fig. 5. Output measurement at object in the system occurs discretely (behind the object exit sensor there is a pulse element IE 1), i.e. at certain intervals ∆ t(∆t- repetition period of the impulse element). Thus, the pulse element converts the changing output signal at object into a sequence of pulses, the height of which is proportional to the values at at points in time t=n∆t, called pickup points. Let's denote the values at at the time t=n∆t through at p. Values at n served on the storage device memory (delay element). The storage device supplies to the comparison element ES previous value at p- 1 . On ES arrives at the same time y n. At the output of the comparison element, a difference signal is obtained ∆y n =y n - at p- 1 The next moment t=(n+1) ∆t signal pickup stored value at p- 1 is reset from the memory and the signal is stored at n+ 1 , a signal y n comes from memory on ES and at the input of the signum relay SR signal appears ∆ at n+ 1 = y n + 1 -y n .
Rice. 5The structure of the discrete(stepper)SAO
So, a signal proportional to the increment ∆ at object exit for the time interval ∆ t. If ∆ y>0 then such movement is allowed by the signum relay; if ∆ at<0, then the signal relay is activated and changes the direction of the input signal X.
Between the signal relay SR and executive mechanism THEM(fig. 5) one more impulse element is included IE 2 (working in sync with IE 1), which performs periodic opening of the power circuit THEM, stopping THEM for this time.
The actuator in such ACS usually changes the input X object in steps by a constant value ∆x. It is expedient to change the input signal of the object by a step quickly so that the time for moving the actuator by one step is sufficiently small. In this case, the perturbations introduced into the object by the actuator will approach jumps.
Thus, the signum relay changes the direction of the subsequent step ∆ x n+ 1 actuator, if the value ∆ y n becomes less than zero.
Let us consider the nature of the search for an extremum in a stepping ACS with an inertialess object. Let us assume that the initial state of the object is characterized by the point M 1 on the static dependence y=f(x) (Fig. 6a). Let us assume that the extremal controller is put into operation at the moment of time t 1 and the actuator makes a step ∆ X to increase the object's input signal.
Rice. 6Search in discrete SAO: A - object characteristics; b- change output; V- change input
Object output signal at while also increasing. After time ∆ t(at time t 2) the actuator takes a step in the same direction, since ∆ at 1 =y 2 -y 1>0. In the moment t 3 the actuator makes one more step on ∆ X in the same direction, since ∆ y 2 =y 3 -y 2 is greater than zero, etc. at time t 5 plant output increment ∆ y 3 =y 5 -y 4 , becomes less than zero, the signum relay is activated and the next step ∆ X the actuator will make in the direction of decreasing the input signal of the object X etc.
In step-by-step SAOs, to ensure stability, it is necessary that the movement of the system to the extremum be nonmonotonic.
There are stepping CAO, at which change the signal at the input in one step ∆ X variable and depends on the value y.
Automatic optimization systems with derivative control
Automatic optimization systems with derivative control use the property of the extreme static characteristic that the derivative dy/dx is equal to zero at the value of the input signal of the object x=x wholesale(See Fig. 7).
Rice. 7Graph of the change in the derivative of the unimodal characteristic
The block diagram of one of such ACS is shown in fig. 8. The values of the input and output signals of the object O are fed to two differentiators D 1 And D 2 , at the output of which signals are obtained, respectively dx/dt And dy/dt. The derivative signals are fed to the dividing device DU.
Rice. 8Structure of the SAO with the measurement of the derivative of the static characteristic
At the exit DU a signal is received dy/dx, which is fed to the amplifier At with gain k 2. The signal from the output of the amplifier goes to the actuator THEM with a variable speed of movement, the value of which is proportional to the output signal of the amplifier And. Gain THEM equals k 1 .
If the static characteristic of the object y=f(x) has the shape of a parabola y=-kx 2 , then the SAO is described by linear equations (in the absence of perturbations), since dy/dx=-2kx, and the remaining links of the system are linear. A logical device for determining the direction of movement towards an extremum is not used in such a system, since it is purely linear and it would seem that the value of the extremum is known in advance (since dy/dx= 0 for x=xoiit).
At the time of inclusion of the CAO into operation on THEM some signal is given to set it in motion, otherwise dx/dt= 0 And dy/dt= 0 (in the absence of random perturbations). After that, the ACS works like a conventional ACS, in which the task is the value dy/dx= 0.
The described system has a number of shortcomings that make it almost inapplicable. First, at dx/dt → 0 derivative dy/dt also tends to zero - the problem of finding the extremum becomes uncertain. Secondly, real objects have a delay, so it is necessary to divide by each other not simultaneously measured derivatives dy/dt And dx/dt, and shifted in time exactly by the signal delay time in the object, which is quite difficult to do. Thirdly, the absence of a logical device (signum relay) in such an ACS leads to the fact that under certain conditions the system loses its operability. Let us assume that the CAO started working at x
In addition, even if such a system moves to an extremum at the initial moment, then it loses its operability with an arbitrarily small drift of the static characteristic without a verification reverse switch.
Rice. 9Optimization system with the measurement of the derivative of the output of the object:
A - system structure; b- characteristics of the object; V- change output; G- input signal d - changing the entry of an object.
Consider another type of ACS with derivative measurement and actuator THEM constant speed of movement, the block diagram of which is shown in fig. 9.
Let us consider the nature of the search for the SAO extremum with the measurement of the derivative with the block diagram shown in fig. 9, A.
Let the inertialess object of regulation ABOUT(Fig. 9, a) has a static characteristic shown in fig. 9, b. The state of the ACS at the moment of turning on the extreme controller is determined by the values of the input signals x 1 and exit at 1 - dot M 1 on the static feature.
Let us assume that the extremal controller after putting it into operation at the moment of time t 1 changes the input signal X in the direction of increase. In this case, the signal at the output of the object at will change in accordance with the static characteristic (Fig. 9, V), and the derivative dy/dt when moving from a point M 1 before M 2 decreases (Fig. 9, G). At the point in time t 2 the output of the object will reach an extremum at max, and the derivative dy/dt will be equal to zero. Due to the insensitivity of the signum relay, the system will continue to move away from the extremum. At the same time, the derivative dy/dt changes sign and becomes negative. In the moment t 3 , when the value dy/dt, remaining negative, will exceed the dead zone of the signum relay ( dy/dt)H the actuator will reverse and the input signal X will start to decrease. The output of the object will begin to approach the extremum again, and the derivative dy/dt becomes positive when moving from the point M 3 before M 4 (Fig. 9, V). At the point in time t 4, the output signal again reaches an extremum, and the derivative dy/dt=0.
However, due to the insensitivity of the signum relay, the movement of the system will continue, the derivative dy/dt becomes negative and at the point M 5 will reverse again, etc.
In this system, only the output signal of the object is differentiated, which is fed to the signal relay SR. Since when the system passes through the extremum, the sign dy/dt changes, then to find the extremum it is necessary to reverse THEM, when the derivative dy/dt becomes negative and exceeds the dead band ( dy/dt)H signal relay.
Sign responsive system dy/dt, according to the principle of operation, it is close to the stepping ACS, but less noise-resistant.
Automatic optimization systems with auxiliary modulation
In some works, such automatic optimization systems are called systems with a continuous search signal or, according to the terminology of A.A. Krasovsky simply by continuous systems of extreme regulation.
In these systems, the property of a static characteristic is used to change the phase of the object's output signal oscillations in comparison with the phase of the object's input oscillations by 180° when the object's output signal passes through an extremum (see Fig. 10).
Rice. 10The nature of the passage of harmonic oscillations through a unimodal characteristic
In contrast to the ACS considered above, systems with auxiliary modulation have separate search and working movements.
The block diagram of the ACS with auxiliary modulation is shown in fig. 11.Input signal X object O with characteristic y=f(x) is the sum of two components: x=xo(t)+a sin ω 0 t, Where A And ω 0 - constant values. Component a sin ω 0 t is a trial movement and is produced by a generator G, component x o(t) is a labor movement. When moving to an extremum, the variable component a sin ω 0 t the input signal of the object causes the appearance of an alternating component of the same frequency ω 0 =2π/T 0 in the output signal of the object (see Fig. 10). The variable component can be found graphically, as shown in Fig. 10.
Rice. elevenSAO structure with auxiliary modulation
It is obvious that the variable component of the signal at the output of the object coincides in phase with the variable component of the signal at the input for any value of the input, when x 0 =x 1
Amplitude A search fluctuations should be small, since these fluctuations pass into the output signal of the object and lead to an error in determining the extremum.
Quantity component y, frequency ω 0 , separated by a bandpass filter F 1 (Fig. 11). Filter task F 1 is not to miss the constant or slowly changing component and the components of the second and higher harmonics. Ideally, the filter should pass only the component with frequency ω 0.
After filter F 1 variable component of quantity y, frequency ω 0 , fed to the multiplying link MOH(synchronous detector). The reference value is also fed to the input of the multiplier link v 1 =a sin( ω 0 t + φ ). Phase φ reference voltage v 1 selected depending on the filter output phase F 1 , since filter f 1 introduces an additional phase shift.
Multiplier output voltage u=vv 1 . With a value x<x wholesale
u = vv 1 = b sin( ω 0 t+ φ ) a sin( ω 0 t+ φ ) = ab sin 2 ( ω 0 t + φ )==ab/ 2 .
When the value of the signal at the input x>X 0PT signal value at the output of the multiplier link MOH is:
u = vv 1 = b sin( ω 0 t + φ + 180°) a sin( ω 0 t + φ ) = - ab sin 2 ( ω 0 t + φ )= = - ab/ 2 .
Rice. 12The nature of the search in the CAO with auxiliary modulation:
A - object characteristics; b- change of a phase of fluctuations; V- harmonic oscillations at the input; G- total input signal; d - signal at the output of the multiplier link.
After the multiplier signal And applied to a low pass filter F 2 , which does not pass the variable component of the signal And. DC signal and=and 1 after filter F 2 is applied to the relay element RE. The relay element controls the actuator at a constant travel speed. Instead of a relay element in the circuit, there may be a phase-sensitive amplifier; then the actuator will have a variable speed of movement.
On fig. Figure 12 shows the nature of the search for an extremum in the ACS with auxiliary modulation, the block diagram of which is shown in fig. 11. Suppose that the initial state of the system is characterized by signals at the input and output of the object, respectively X 1 And y 1 (dot M 1 in fig. 12a).
Because at the point M 1 meaning x 1 <х опт then when the extreme controller is turned on, the phases of the input and output oscillations will coincide. Let us assume that in this case the constant component at the filter output F 2 is positive ( ab/2>0), which corresponds to the movement with increasing X, i.e. dx 0 /dt>0. In this case, the SAO will move towards an extremum.
If the starting point M 2 , which characterizes the position of the system at the moment of turning on the extremal controller, is such that the input signal of the object x>x opt (Fig. 12, a), then the oscillations of the input and output signals of the object are in antiphase. As a result, the constant component at the output F 2 will be negative ( ab/2<0), что вызовет движение системы в сторону уменьшения X (dx 0 /dt<0 ). In this case, the SAO will approach the extremum.
Thus, regardless of the initial state of the system, the search for an extremum will be provided.
In systems with a variable speed actuator, the speed of the system movement to the extremum will depend on the amplitude of the output oscillations of the object, and this amplitude is determined by the deviation of the input signal X from the value X wholesale
Tuning (extreme control)
Extreme control got its name from the specific purpose of this control. The task of extremal control is to achieve an extremal goal, i.e., in extremization (minimization or maximization) of some indicator of the object, the value of which depends on the controllable and uncontrollable parameters of the object. A very common tuning operation leads to extreme control.
Any customization consists in building such a system of actions that provide the best mode of operation for the custom object. To do this, it is necessary to be able to distinguish between the states of an object and to qualify these states in such a way as to know which of the two states should be considered “better” than the other. This means that a measure of the quality of the tuning must be determined during the tuning process.
For example, when setting up a technological process, the number of defective parts in a batch can serve as an indicator of its quality; in this case, the goal of process tuning is to minimize waste. However, not all extreme objects allow such a simple quantitative representation of the tuning quality index. So, for example, when tuning radios or televisions, such measures of tuning quality can be sound quality and quality
images of the received transmission. It is already quite difficult to quantify the tuning quality index here. However, as will be shown below, in order to solve extreme control problems, it is often important to know not the absolute value of the quality indicator, but the sign of its increment in the control process. This means that for management it is enough to know whether the quality indicator has increased or decreased. In the case of tuning radio equipment, a person solves this problem quite well when it comes to sound or image quality.
Rice. 1.3.1.
Thus, in the future it is assumed that there always exists such an algorithm for processing the information of a customizable object that allows you to quantify the quality of the customization of this object (or the sign of the change in this quality in the control process). The quality of the setting is measured by the number Q , which depends on the state of the controlled parameters of the object:
. (1.3.1)
The purpose of the setting is the extremization of this indicator, i.e., the solution of the problem
where the letter S denotes the area of permissible change in the controlled parameters.
On fig. 1.3.1 shows a block diagram of an extreme object. It is formed from the customization object itself with controlled inputs and observable outputs that carry information about the state of the object, and a converter that, based on the information received, forms a scalar quality indicator of the object.
An example of an extreme object is a radio receiver in the process of searching for a station. If the audibility of the station decreases (as they say, the station “floats away”), then in order to obtain the best sounding transmission, i.e. to tune the receiver, it is necessary to adjust the circuit. The tuning control in this case consists in determining the direction of rotation of the tuning knob. The level of audibility of the station here is an indicator of the quality of the tuning. It does not carry the necessary
Rice. 1.3.2.
control information, i.e. does not indicate which direction to turn the tuning knob. Therefore, to obtain the necessary information, a search is introduced - a trial movement of the tuning handle in an arbitrary direction, which provides additional and necessary information for tuning. After that, you can already tell exactly in which direction you should turn the knob: if the audibility has decreased, you need to turn it in the opposite direction, if it has already increased, you should turn the tuning knob in the same direction to the maximum audibility. Such a simple search algorithm used when tuning a radio receiver, which is a typical example of an extreme object.
Thus, the objects of extreme control are distinguished by the lack of information at the output of the object, the presence of a kind of informational “hunger”. To obtain the necessary information in the process of controlling extreme objects, it is necessary to introduce a search in the form of specially organized trial steps. The search process distinguishes tuning and extreme control from all other types of control.
As a more "serious" example of a one-parameter extremal object, consider the problem of optimal damping of a second-order tracking system (Fig. 1.3.2). The driving perturbation is applied to the input of this servo system y*(t), defining the output state of y(t). Concerning the nature of the behavior y* (t) nothing is known. Moreover, the statistical properties of the perturbation y*(t) may change in unexpected ways.
Rice. 1.3.3.
The task of tuning is to choose such a damping that makes this servo system optimal in terms of the minimum of the functional:
The quantity Q is an estimate of the variance of the residual o(t)=y(t)-y*(t) on the base T. Obviously, when adjusting the servo system, one should seek to minimize the value of Q.
Here, the specified servo system acts as the object of adjustment, the output information for determining the quality of the object's operation is its input and output, and the converter forms the quality indicator according to the formula (1.3.3). The resulting extreme object has the characteristic shown in Fig. 1.3.3. The nature of dependence Q ( O) expresses the obvious fact that too little damping is just as bad as too much damping. As can be seen, the characteristic (1.3.3) has a pronounced extremal character with a minimum corresponding to the optimal damping O*. In addition, the characteristic depends on the properties of the perturbation y*(t). Therefore, the optimal state O*, minimizing Q ( O), also depends on the nature of the driving perturbation y*(t) and changes along with it. This makes us turn to the creation of special automatic tuning systems that maintain the object in a tuned (extreme) state, regardless of the properties of disturbances. These automatic devices that solve the tuning problem are called extremal controllers or optimizers (i.e., devices for optimizing an object).
A distinctive feature of extreme objects is the non-monotonicity (extremality) of the characteristic, which makes it impossible to use the control method to control such objects. Indeed, observing the output value Q of the object in the above example (see Fig. 1.3.3), it is impossible to build a control, i.e., determine in which direction the controlled parameter should be changed O. This uncertainty is connected, first of all, with the possibility of two situations and, the way out of which to the goal O* produced in the exact opposite way (in the first case, one should increase O, and in the second - to reduce). Before managing such an object, it is necessary to obtain additional information - in this example, this information consists in determining which branch of the characteristic the object is on. To do this, for example, it is enough to determine the value of the quality index at a neighboring point o + ? O, Where? O is a fairly small deviation.
It should be noted that automation of the tuning process is justified only if the extreme characteristic of the object changes in time, i.e., when the extreme state wanders. If the characteristic of the object does not change, then the process of searching for an extremum is of a one-time nature and, therefore, does not need automation (it is enough to stabilize the object in a once defined extreme state).
On fig. 1.3.4 for illustration shows a block diagram of extreme damping control of a servo system that tracks the position of a target. at(t), the nature of the behavior of which changes.
Rice. 1.3.4.
Here, the extremal controller solves the tuning problem, i.e. maintains such a damping value O, which minimizes the quality index of the servo system.
The optimization problem usually consists in finding and maintaining such control actions that provide an extremum of a certain criterion for the quality of the operation of the control object. This problem can be solved automatically with the help of extremal controllers, which search for optimal control actions in the course of operation. Systems that implement automatic search and maintenance of an extremum of a certain indicator of the quality of an object's operation are called extreme control systems or automatic optimization systems. Automatic optimization systems, due to the implementation of optimal control search algorithms in them, have a number of advantages, the main of which is their ability to function normally under conditions of incomplete a priori information about the object and the perturbations acting on it. The use of extreme control systems is advisable in cases where the quality criterion of the object has a pronounced extremum and there are opportunities to search for and maintain its optimal (extreme) mode of operation. The development of the theory and technology of extreme control systems has now reached a significant level. Industry produces typical extreme controllers (automatic optimizers) for a number of technological processes.
Extreme control systems constitute one of the most theoretically and practically developed classes of adaptive systems. Extremal objects are called automatic control objects in which the static characteristic has an extremum, the position and magnitude of which are not known and can change continuously.
Usually, the extremal controller searches for and maintains such values of the coordinates of the object , at which the output 
reaches an extreme value. This mode of operation of the object and the system as a whole is optimal in terms of the minimum or maximum of the quality criterion. An airplane can serve as an example of a one-dimensional extremal object. Dependence of kilometer fuel consumption y from flight speed x characterized by the presence of an extremum, the value and position of which change when the weight of the aircraft changes due to fuel consumption.
Depending on the number of extrema, objects are divided into single-extremum and multi-extremum, and in the latter case, the control problem is to find a global extremum, i.e. highest maximum or lowest minimum. Depending on the number of control actions generated in the extremal controller, one-dimensional and multidimensional extremal control systems are distinguished. By the nature of work in time, extremal systems can be continuous and discrete. Depending on the nature of the search signal, extremal systems with deterministic and random search signals are distinguished.
The need for adaptive (adaptable) control systems arises in connection with the complication of control problems in the absence of the practical possibility of a detailed study and description of the processes occurring in control objects in the presence of changing external disturbances. The effect of adaptation is achieved due to the fact that part of the functions for receiving, processing and analyzing processes in the control object is performed during the operation of the system. This division of functions contributes to a more complete use of information about ongoing processes in the formation of control signals and can significantly reduce the impact of uncertainty on the quality of control. Thus, adaptive control is necessary in cases where the influence of uncertainty or "incompleteness" of a priori information about the operation of the system becomes significant to ensure the specified quality of control processes. Currently, there is the following classification of adaptive systems: self-adjusting systems, systems with adaptation in special phase states, and learning systems.
The class of self-adjusting (extreme) automatic control systems is widespread due to a fairly simple technical implementation. This class of systems is due to the fact that a number of control objects or technological processes have extreme dependencies (minimum or maximum) of the operating parameter on control actions. These include powerful DC electric motors, technological processes in the chemical industry, various types of furnaces, aircraft jet engines, etc. Let us consider the processes occurring in the furnace during fuel combustion. With insufficient air supply, the fuel in the furnace does not burn completely and the amount of heat generated decreases. With excess air supply, part of the heat is carried away with the air. And only with a certain ratio between the amount of air and heat, the maximum temperature in the furnace is reached. In a turbojet aircraft engine, by changing the fuel consumption, it is possible to obtain the maximum air pressure behind the compressor, and, consequently, the maximum engine thrust. At low and high fuel consumption, the air pressure behind the compressor and thrust drops. In addition, it should be noted that the extreme points of control objects are "floating" in time and space.
In the general case, we can state that there is an extremum, and at what values of the control action it is reached is a priori unknown. Under these conditions, the automatic control system during operation must form a control action that brings the object to an extreme position and keep it in this state under conditions of disturbances and the “floating” nature of extreme points. In this case, the control device is an extremal regulator.
According to the method of obtaining information about the current state of the object, extreme systems are non-search and search systems. In searchless systems, the best control is determined by using analytical relationships between the desired value of the operating parameter and the controller parameters. In search engines that are slow, finding the extremum can be done in a variety of ways. The most widespread method is synchronous detection, which is reduced to estimating the derivative dy/du, where y is the controlled (working) parameter of the control object, u is the control action. A block diagram illustrating the method of synchronous detection is shown in fig. 6.1.
Rice. 6.1 Synchronous detection structure
At the input of the control object, which has an extreme dependence y(u), together with the control action U, an insignificant perturbation is applied in the form of a regular periodic signal f(t) = gsinwt, where g is greater than zero and sufficiently small. At the output of the control object, we get y = y(u + gsinwt). The resulting value of y is multiplied by the signal f(t). As a result, signal A will take on the value
A =yf(t) = y(u+gsinwt)gsinwt.
Assuming that the dependence y(u) is a sufficiently smooth function, it can be expanded into a power series and, with a sufficient degree of accuracy, is limited to the first terms of the expansion
Y(u+gsinwt)=y(u)+gsinwt(dy/du) + 0.5g 2 sin 2 wt(d 2 y/du 2) + ….. .
Since the value of g is small, then we can neglect the terms of higher order and as a result we get
Y(u + gsinwt) » y(u) + gsinwt(dy/du).
Then, as a result of multiplication, signal A will take on the value
A \u003d y (u) sinwt + g 2 sin 2 wt (dy / du).
At the output of the low-pass filter F, we get the signal B
.
If the filter time constant T large enough, we get
.
Therefore, the signal B at the output of the filter is proportional to the derivative dy/du
The scope of XPM is not limited to software development. Extreme project management will be effective for experienced teams that implement innovative projects, start-ups, work in chaotic, unpredictable conditions.
What is Extreme Project Management?
The XPM concept was developed in 2004. But to consider him the only developer would be unfair. Doug was inspired by a number of techniques from other authors:
- model of radical project management Rob Thomseth,
- APM Jim Highsmith,
- extreme programming concept Kent Back.
DeCarlo invested in Extreme Project Management chaos theory And complex adaptive systems.
Chaos theory is a mathematical field devoted to the description and study of the behavior of nonlinear dynamic systems, which, under certain conditions, are subject to the so-called dynamic chaos.
A complex adaptive system is a system of many interacting components that meets a number of conditions (fractal structure, ability for adaptive activity, etc.). Examples of CACs include the city, ecosystems, the stock market.
Doug compares extreme project management to jazz.
Although jazz can sound chaotic, it has its own structure, thanks to which musicians have the opportunity to improvise and create real masterpieces.
Instead of following the beaten path, in Extreme Project Management, project managers discuss the best alternative with the client, experiment, learn from the results, and apply that knowledge to the next project cycle.
One of the properties of some chaotic systems,
which are the objects of consideration of chaos theory - the "butterfly effect",
made popular by Ray Bradbury's "Thunder Came Out"
Brian Warnham, author of the book "", outlined five steps that an extreme project management team must follow in order to successfully complete a project:
- See- clearly define the vision of the project before starting extreme project management
- create- involve the team in creative thought process and brainstorming to create and select ideas to achieve the established vision of the project
- Refresh— stimulate the team to test their ideas through the implementation of innovative solutions
- overestimate- as the development cycle approaches the end, the team should re-evaluate their work
- Distribute- After completing the training, it is important to disseminate knowledge and apply it to future stages of the project, as well as to new projects in general.
Since people are at the forefront of Extreme Project Management, this also determines the specifics of measuring the success of an XPM project:
- users are satisfied with the progress and intermediate deliveries - there is a feeling that the project is moving in the right direction, despite the surrounding instability.
- users are satisfied with the final delivery.
- team members are satisfied with the quality of their lives while working on the project. If you ask them if they would like to work on a similar project, most of them will say yes.
Pros and cons of XPM
Among the main advantages of the methodology, the following should be noted:
- integrity- Despite the fact that Extreme Project Management includes a variety of methods, tools and templates, they only make sense when applied to the entire project as a whole. You, as a project manager, can see the entire project as a single system without having to analyze its individual parts
- human orientation- In XPM, the emphasis is on the dynamics of the project. It allows stakeholders to interact and communicate, and ultimately meet the needs of the client.
- focus on business- once the result is achieved, you will have a clear vision of how the project can benefit your client. The team is constantly focused on early and frequent product delivery
- humanism is one of the principles of Extreme Project Management. It consists in taking into account the quality of life of the people involved in the project. Being an integral part of the project, the passion for work and the corporate spirit strongly influence the business, therefore, during the work on the project, the physical and moral condition of the team is important
- reality as a basis- extreme project management allows you to work in an unpredictable, chaotic environment. You cannot change reality to fit the project. The opposite happens: you adapt the project to external factors.
There were some downsides as well. They can be counted:
- uncertainty- this feature cuts off a large sector of projects, starting with those with a critical risk (military facilities, nuclear power plants, Internet banking applications, etc.), ending with tender projects with a strictly stipulated budget, deadlines and other project properties;
- high requirements for the experience and qualifications of the project team- it is necessary to constantly adapt to changes in the project environment, establish effective communication with each other, stakeholders and the project manager, and work in short iterations (the latter is relevant for the IT sphere);
- the need to change the way of thinking- unlike traditional project management, in which work on the project proceeds according to the usual stages, according to the approved plan and roles, in XPM the team needs to rebuild and be prepared for the impossibility of full control over the project;
- impossibility of long-term planning- yesterday's plan for relevance will not be fresher than the news for the last month. For the correct work of the team to achieve the goal of the project, it is necessary to show the qualities of flexibility and self-organization.
- the project is being created in a dynamic environment- there is a constant change of circumstances, speed, requirements;
- application possible trial and error method in the work on the project;
- An experienced team is working on the project- unlike traditional project management, people are at the forefront, not processes;
- develop an application— during the development life cycle, the software in most cases manages to change the functionality or expand the list of available platforms. The more users use the software, the more changes can be made, which is what extreme project management is great for.
- this is a meta project- that is, which is divided into many small projects. XPM in this case will help to cope with the delay in the start of work;
- the business owner is ready to participate in the work on the project from start to finish. Connections must be made "project manager - businessman",
« project manager— stakeholder,
"project manager - business owner - stakeholder".
Stakeholders are people and organizations that influence the project in one way or another. This includes those actively involved in it (project team, sponsor), and those who will use the results of the project (customer), and people who can influence the project, although they are not involved in it (shareholders, partner companies).
Extreme project management requires the team to quickly adapt to the unusual, constantly changing environment in which they have to work. Therefore, there are several key rules that are mandatory for the effective use of Extreme Project Management:
A real example of the difference classical project management from extreme. In the first, the planned result is achieved, in the second, the desired one.
eXtreme Project Management:
Using Leadership, Principles, and Tools to Deliver Value in the Face of Volatility Doug DeCarlo
#1 for anyone who wants to master Extreme Project Management. Based on experience with more than 250 project teams, the author has written a detailed guide to extreme project management. Project managers of the largest international organizations rave about the book: Management Solutions Group, Inc., Zero Boundary Inc., Guru Unlimited, etc.
Effective Project Management: Traditional, Adaptive, Extreme,
Third Edition Robert K. Vysotsky
After reading which you can get an idea not only about extreme project management, but also adaptive. Of the interesting - at the end of each chapter, questions are given to streamline the submitted material, which is saturated with real case studies of projects from different areas.
Radical Project Management Rob Thomsett
Extreme Project Management is presented from "A" to "Z", each tool and technique is disassembled, with the help of which Extreme Project Management is implemented. Maximum practical information with case studies.
Architectural Practices: Extreme Project Management for Architects
Not a book, but, but it’s impossible not to include it in the selection because of its uniqueness. This is a comprehensive resource on the use of XPM in architecture and construction. Unfortunately, the author of the site no longer updates it, but the page is still suitable as a cheat sheet.
Verdict
the art and science of facilitating and managing the flow of thoughts, emotions and actions in such a way as to obtain maximum results in difficult and unstable conditions.
The reasons for the success of XPM among other management methods lie in three planes:
- Extreme Project Management makes it possible continuous self-correction and self-improvement in real time;
- XPM focuses on defining and following the mission of the project by instilling confidence in stakeholders and the project team;
- human orientation, humanism and the priority of people over processes as key features of the methodology.
