Number Of Controlled Switches Research Articles

A new computational approach for optimal control of switched systems

The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples.

Three-Phase Three-Level Isolated DC-DC Soft Switching Converter For Solar Applications

Three-level isolated DC-DC converter is an attractive topology in high input voltage applications, which can provide the voltage stress of the power devices to only a half of the dc voltage and also reduce the size of dc filter requirement. But major limitations in the existing three level ZVS converter topologies are brought out with an increased inductance in the primary side and it required to provide complete ZVS of all primary devices down to light loads. By employing an external inductance in the primary of the transformer, total leakage inductance of the transformer increases which is required for realization of soft switching of the converter switches but there are some disadvantages of connecting external inductance in the primary of the transformer. To overcome all these drawbacks, the three-phase three-level isolated DC-DC soft switching converter has been proposed in order to reduce voltage and current stresses. This converter topology requires less number of control switches and operates with an asymmetrical duty cycle control. The proposed three level DC-DC converters provide two- level voltage waveform before dc output filter, which significantly reduce the size of dc output filter. The proposed work has been implemented using MATLAB/SIMULINK and the performance of the proposed converter is verified through simulation results.

Синтез оптимального двопозиційного регулятора із мінімальною кількістю перемикань

. A method of synthesis of optimal on-off controllers with a minimum number of switchings is developed in the work. The essence of the method is in reducing the original problem to the problem of minimizing the function of the generalized criterion in the parameter domain of the controller. The topology of the latter makes it possible to sequentially find sets of controller parameters that ensure the fulfillment of ranked problem conditions. An on-off-PI-controller has been proposed in the paper. Its parameters (gains of proportional and integral components of the controller, as well as the threshold at which switching of the control function is carried-out) have been found in the article. In order to prove the effectiveness of the developed method, calculations were performed for four second- and third-order plants (one plant has a time delay). The quality of controlled processes was compared in terms of: average normal error, module of average control, overshoot, settling time and number of switchings. The results of the comparative analysis on these indicators showed that ceteris paribus the synthesized PI-controller has the least number of control switchings. This result extends the duration of use of the automatic control system actuators. The calculations showed that the method of minimizing the number of switchings can be successfully applied within the methodology of synthesis of optimal regulators, which had been developed in the previous author’s researches. Key words: on-off controller, synthesis, criterion, optimization, switching

Complexity of the Minimum-Time Damping of a Physical Pendulum

We study the minimum-time damping of a physical pendulum by means of a bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a finite number of control switchings from the maximal to the minimal value. If one considers simultaneously all optimal trajectories with any initial state, the number of switchings can be arbitrary large. We show that for the nonlinear pendulum there is a uniform bound for the switching number for all optimal trajectories. We find asymptotics for this bound as the control amplitude goes to zero.

An Open Problem of Optimal Control Theory

It is well known that in certain optimal control problems with saturating control the solution trajectory is subjected to an infinite number of control switchings within a finite interval of time. This phenomenon is called chattering and was studied by a number of authors over the past 40 years (see, e.g., the survey paper [3]). The chattering was discovered by A. T. Fuller in 1960 [8] when he considered the optimal control system