Ladieva L., Stashkevich P., Shostak R.

National Technical University of Ukraine "Kyiv Polytechnic Institute", Ukraine

RESEARCH SYSTEM OF AN OPTIMUM STATE OF A CONTROL OBJECT

The solution of an optimum control object’s state search task is proposed to be resolved by means of the microprocessor controller "Remicont R-130".

Statement of the problem

It is very important for many control objects to have optimum conditions while maintaining the technological process. The optimum conditions of maintaining the technological process are changing as well with changing input parameters and characteristics of these objects. The search for such optimum conditions can be done by using special technical means, for example, created on the basis of the programmed microprocessor controllers.

The search of an optimum state of a control object or guiding the optimum technological process by means of the programmed microprocessor controllers are very urgent issues and an interest to the solution of the problem in this manner will increase over time, because quantity of these controllers are rising and it’s cost are getting lower. Furthermore, the device which carries search of an optimum state of a control object and the regulator which will be able to support such state can be created in a single controller. That is why this system has to consist of a device that searches an optimum state of a control object or technological process and a PID controller that maintains this process (fig. 1).

Using the search system of the optimum state of the control object allows providing a necessary quality of object management during maintaining the appropriate technological process.

Main information

A structural scheme of operation algorithm of the technical device that can find the optimum state of the control object is in the fig. 1. The device which implements this algorithm can be created, for example, on the basis of the microcontroller “Remicont R-130”. Such device works as follows.

A signal ∆₁ that is aliquot, for example, to a sensitivity threshold of an analog-to-digital converter of the controller is given on an input of the multiplier unit K. The multiplier unit multiplies this signal on a coefficient K that can take values +1 or -1 depending on a control effect. This effect is created by the logic unit, signal of which depends on a sign of the first derivative of the so-called objective function. The optimum state of the control object depends on parameters of the objective function. Because of the fact that many technological objects have convex extrema of objective function, for such objects in the simplest case this function can be approximated by means of parabolic function. Parameter a that itself can depend on many other parameters that have an influence on the optimum state of the control object is a part of this function.

Fig. 1. Structural scheme of the search algorithm of the control object’s optimum state

It is known that to find the optimum point of the function that is suspected to be an extremum, it is necessary to equate the first derivative of the objective function by the parameter (or all its partial derivatives by appropriate parameters) to zero and to make a research of the extrema in the found point. That is why one of lead nodes of the device that searches the optimum state of a control object has to be a node that defines the first derivative of function and equates it to zero. This node is called as a node which solves the problem:

Such node can be created, for example, for controller “Remicont R-130”, using two algorithms of a moving average (No. 49 in computer libraries of this controller), two algorithms of a summarizing with scaling (No. 43), an algorithm of multiplication and division (No. 44) and an algorithm of comparing numbers (No. 86). A structural scheme of this node is in the fig. 2.

Fig. 2. Structural scheme of the node that defines the first derivative of an output value from input value and its sign

Such node works as follows. An input signal of the target function applies to the input 01 of the first logic block with a moving-average algorithm (designation 1 in the fig. 2). The signal passes through time delay elements 1, 2, ...m with stroking frequency that depends on features of the controller or an external source and applies to the input 02 with a time delay that depends on quantity of the selected elements in the form of signal. After every time delay element, signal value applies to the input of an adder-determinant of the mean value. The signal applies to the input 01 of this logic block No. 1 in the form of signal from the adder’s output. The information about signal in is newer comparing with , that is why difference of signals can be taken for a signal . This difference can be received by applying signals on inputs 01 and 02 of the summarizing-with-scaling block (des. 3 in the figure No. 2). For obtaining the negative signal’s value can be multiplied on a scaling coefficient . An increment of the input value x can be obtained analogically using another logic block with a moving-average algorithm (des. 2) and another summarizing-with-scaling block (des. 4).

As it was said before, it is necessary to equate this signal to zero and to find the point that is suspected to be an extrema. This procedure can be done firstly by defining a sign of the target function’s first derivative and determine where exactly this target function is situated at present time in relation to a point of an optimum state. Next, it is possible to come nearer to the point of the optimum state as close as far as it is allowed by increasing or reducing value of an incoming signal . The tracking integrator can be used for this purpose. It is possible to determine is the maximum or the minimum of the target function is situated in the found optimum point by taking the second derivative of this function and defining its sign. It can be realized analogically.

To define the first derivative’s sign of the target function, for example, for controller “Remicont R-130”, the algorithm of comparing numbers (des. 6 in the fig. 2) is used. For this purpose the signal of the first derivative from the output 01 of the logic block No. 5 applies to inputs 01 and 04 of the logic block with the numbers-comparing algorithm and where the written values of numbers are appropriate. Zero values are written on another two inputs (02 and 03) of this logic block, which means . The signal of the first derivative will be compared with this zero values for defining its sign. If then signal will be on the output 01 of the numbers-comparing algorithm, and signal on the output 02, that must correspond to the positive value of the first derivative. If then the signal will be on the output 01, and the signal on the output 02, that must correspond to the negative value of the first derivative. In this way, having two control signals and it is possible to determine is the target function situated either left or right of the optimum point . As it was told above, it is possible to come nearer to the optimum point as close as far as it is allowed by increasing or reducing value of an incoming signal .

So, the signal will fluctuate near the optimum value on the output of the integrator during all the time. Next, this signal applies at the regulator’s input as a task signal , having an influence on the general input signal x(t) in a way that it obtains the optimum value (fig. 1).

Conclusion

The conducted research showed that this device is capable to maintain the optimum value of the control object’s work in the neighborhood of the certain area justified by technical characteristics of the object and the controller that is used.