О.М. Klymenko, V.G. Tregub

National University of Food Technologies

Dynamic control of objects of periodic action

Automated control systems of objects of periodic action realize logical algorithms and dynamic management. First ensure the transition from stage to stage and from operation to operation, others implement dynamic management, mainly during the working stage. Peculiarity of dynamic objects of periodic action (OPA) compared with the objects of continuous action (OCA) is that transition processes in OPA associated with the transition from the initial state, which is characterized by the vector in the final state, which corresponds to vector are useful and provide a ready product of these objects. In OCA the same transition processes occur under the influence of disturbances and characterize the deviation from the nominal technological regime. If we accept the assumption then can be regarded as a vector-function of transition that sets the trajectory of an object from to .

Development of the system of dynamic control (SDC) of such transition depends on many factors, but primarily on whether the technological regulation (TR) sets the function of transition. The most simple case of solving of such task occurs when TR rigidly defines the transition function, and hence the trajectory of an object from the initial to the final state. In this case, the development of the programmer, the main component of SDC, reduces to the transfer of transition function to machine carriers. If the TR does not set this trajectory, but imposes restrictions on change of the controlled values, then there are two possible variants of the SDC. The first is a system of programming control (SPC), the second is a system of control by constraints (SCC). The most effective way to create a program that implements the transition function is optimizational, which requires solution of the problem of dynamic optimization.

In general, the problem of dynamic optimization of the deterministic process is to find such function or when which ensures optimum of the functionality.

or

and besides restrictions W, which take into account the resource of management for such problems usually have three components:

links inequalities
boundary conditions

where I – criterion of the management; x, x* - variables of state of the object and their optimal values; z - disturbance; u, u* - management and its optimal value; j- objective function; f - mathematical model (MM) of the object; a, b - parameters of the objective function and MM respectively.

Returning to the problem of dynamic optimization, we note that OPA as objects of optimization relate to the objects with incomplete information, so analytical algorithms with forecast models and feedbacks are used to optimize them. Application of pure search algorithms is not possible due to shortage of time. Incompleteness of the information about OPA may have two reasons: the first is the lack of information about all components of the perturbation vector z and the vector of model parameters b; the second is the lack of information about all components of the vector-function of limitation of the inequalities type.

In the first case, we use system with forward mathematical model (FMM), and in the second - with forward physical model (FPM) in the case when the unknowns are the limitations associated with the critical values of the driving force, the excess of which leads to critical situations in the apparatus. Physical-mathematical model is used when incompleteness of information about the object associated with both factors. All of these models can work with constant parameters and with their correction.

One of the variants of the block diagram of multiplanimetric system of programming control (SPC) with additional connection over the change of task and with logical functional unit (LFU) is shown in Figure 1, where the PSD - programming setting device, OC - object of control , - regulated (controlled) value and its set value, y - parameter of the task (for the temporal program the parameter of the task is time τ); - error of the control; - controlling action; , - disturbance at the input and output of the object respectively; - transfer functions of regulator, compensator and object.

Fig.1

The equation for error of regulation of such SPC is as follows:

Contrary to standard combined systems in this system compensator is used not to compensate the perturbation by changing the task but to increase astatizm of the system and to reduce the error of control by reducing the coefficient of . The main advantage of SPC compared with single system consists in that the increase of astatizm with the help of the connection over the tasks change does not affect the margin of stability of the system due to the fact that this connection is not included in the closed circuit of the system. LFU is designed to change the settings for the transfer function of the regulator depending on the type of the area of transition function. Logical condition of such change is the achievement of coordinates that define the completion of a certain area of function. The best choice as a parameter of the task is not the time, but a state variable that more accurately describes the degree of completion of a periodic process. Comparative assessment of the reduced system and the single SPC without LFU at programming management of sterilizer of periodic action with different types of transition functions demonstrated reduction of integral modular criterion of regulation in 7-8 times. Implementation of the program 25-05-25 (min) by the single SPC without LFU and by the combined SPC with LFU is shown in Figures 2 and 3 respectively.

Fig.2

Fig.3

In case when transition function is not set by the technological regulations, and critical constraints are imposed on the driving force of the process, for the construction of SDC can be applied control system with FPM. As FPM can be uses device, located inside or outside the machine, which continuously receives little part of the product from the reaction zone. Considering the small space of FPM, in this model through the intensification of the process is created the regime of warning changes of the driving force of the process.

Conclusion:

For dynamic control of OPA is used programming control or control by constraints. The most effective SPC is a system with additional connection over the change of task and with logical functional unit. In case when transition function is not set by the technological regulations, and critical constraints are imposed on the driving force of the process, for the construction of SDC can be applied control system with FPM.

References:

Трегуб В.Г. Автоматизація периодических процессов в пищевой промышлености / В.Г.Трегуб. – К.: Техніка, 1982. – 158 с.

Трегуб В.Г. Оптимальне керування періодичними процесами з міжфазними переходами / В.Г.Трегуб, Ю.О.Чорна // Восточно-европейский журнал передовых технологий – 2010 – №6/4(48) – С.7– 9.