LQG control of linear lossless positive-real systems: the continuous-time and discrete-time cases

Lossless positive-real systems have been widely studied in the literature. They are systems in which the energy is entirely transferred between input and output. In this paper, new aspects related to the linear quadratic gaussian (LQG) control of lossless positive-real systems are reported including both the continuous-time and the discrete-time cases. Direct formulas for the calculation of the optimal gains will be introduced and the properties of the different structures of the LQG compensator obtained for the continuous-time and the discrete-time cases will be emphasized, also in view of designing positive-real LQG compensators. Numerical examples related to low-damped structures are also discussed to verify the possibility to design the LQG compensator on the basis of a lossless approximation.

Comparative Study of DE, PSO and GA for Position Domain PID Controller Tuning

Gain tuning is very important in order to obtain good performances for a given controller. Contour tracking performance is mainly determined by the selected control gains of a position domain PID controller. In this paper, three popular evolutionary algorithms are utilized to optimize the gains of a position domain PID controller for performance improvement of contour tracking of robotic manipulators. Differential Evolution (DE), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are used to determine the optimal gains of the position domain PID controller, and three distinct fitness functions are also used to quantify the contour tracking performance of each solution set. Simulation results show that DE features the highest performance indexes for both linear and nonlinear contour tracking, while PSO is quite efficient for linear contour tracking. Both algorithms performed consistently better than GA that featured premature convergence in all cases.

Comparative Study of DE, PSO and GA for Position Domain PID Controller Tuning

Gain tuning is very important in order to obtain good performances for a given controller. Contour tracking performance is mainly determined by the selected control gains of a position domain PID controller. In this paper, three popular evolutionary algorithms are utilized to optimize the gains of a position domain PID controller for performance improvement of contour tracking of robotic manipulators. Differential Evolution (DE), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are used to determine the optimal gains of the position domain PID controller, and three distinct fitness functions are also used to quantify the contour tracking performance of each solution set. Simulation results show that DE features the highest performance indexes for both linear and nonlinear contour tracking, while PSO is quite efficient for linear contour tracking. Both algorithms performed consistently better than GA that featured premature convergence in all cases.

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

Iterative learning control with forgetting factor (ILCFF) is widely used in control engineering. However, choosing the optimal parameters of ILCFF to improve system-output characteristics has been a challenging issue for controller designers. This paper proposes an iterative learning control (ILC) algorithm that involves a variable forgetting factor based on optimal gains for a class of discrete linear time-invariant systems with aperiodic disturbances. The convergence of the algorithm is analyzed, and the necessary and sufficient condition for its convergence is derived in terms of proportional–integral–derivative coefficients. A design method based on optimal gains is established to determine the algorithm coefficients and to accelerate system convergence. Furthermore, the influence of the forgetting factor on both the system-output error and the scope of the proposed algorithm is analyzed. Additionally, the most suitable system type for the application of the forgetting factor is determined. The effectiveness of the algorithm is verified by performing a theoretical analysis and a case-based simulation. The proposed iteration-varying optimal forgetting-factor-based ILC algorithm undergoes fast convergence with a small system-output error. The findings disrupt the conventional view that the use of the forgetting factor increases system-output error. In fact, in a system with small trajectory and increased disturbances, the error induced by the forgetting factor may be smaller than that of the traditional optimal ILC algorithm.

Current Control Optimization for Grid-tied Inverters Using Cuckoo Search Algorithm

One of the most decisive factors for a smooth and stable operation of an DC / AC converter connected to the power grid are the gains used in the current controllers. This paper proposes the use of the Cuckoo Search optimization algorithm via Lévy Flights to facilitate the determination of the optimal gains of the grid connected DC/ AC converters. With the proposed algorithm, it becomes possible to determine the optimal gains of the current controllers of the DC / AC converters connected with the grid thus improving their stability, accuracy and response time. Keywords: DC/AC converters, Cuckoo search, Optimization, Current controllers

Design of PI Controller for Voltage Controller of Four-Phase Interleaved Boost Converter Using Particle Swarm Optimization

This article introduces voltage feedback controlling using the PI controller tuned gains by metaheuristic optimizations for a four-phase interleaved boost converter. The metaheuristic optimizations, particle swarm optimization (PSO), genetic algorithm (GA), and Tabu search (TS) are applied to find the optimal gains for the proposed control system. In experiment, the designed control system is implemented on the DSP board TMS320F28335 with MATLAB/Simulink. In this paper, there are two conditions of the control system in the test, without load and with load. The response result of the proposed control system tuned gains by PSO is no overshoot and approaches to the steady state better than GA and TS methods. Moreover, it is able to maintain the output voltage feedback at a constant level according to the control signal both without load and with load conditions. As a result, the four-phase interleaved boost converter is regulated by the PI controller tuned gains with PSO which could efficiently maintain the voltage of both levels.

PID Controller Tuning using ACO Algorithm for AVR Systems

This paper features an effective technique to device the parameters of PID controllers for utilization together with an Automatic Voltage Regulator System (AVR). The quintessential goal is to acquire a good load disturbance response by minimizing the performance index/(Integral time square error). Simultaneously, the transient response is assured by limiting maximum overshoot, settling time and rise time of the step response to minimal values. For achieving these goals, optimum and quick tuning of the parameters (Kp, Ki, and Kd) is essential. In an effort to accomplish the aforementioned, the paper put forth an algorithm developed based on the Ant Colony Optimization technique (ACO) to decide optimal gains of PID controller and for getting optimal performance within an AVR system. Simulation results establish superior control response may be accomplished in comparison with methods like conventional tuning method (trial and error) and built-in genetic algorithm (GA) took-kit.e.

Combining Pole Placement and Online Empirical Mode Decomposition Methods to Adaptive Active Control of Structural Vibration

Using a combination of the pole placement and online empirical mode decomposition (EMD) methods, a new algorithm is proposed for adaptive active control of structural vibration. The EMD method is a time-frequency domain analysis method that can be used for nonstationary and nonlinear problems. Combining the EMD method and Hilbert transform, which is called Hilbert–Huang transform, achieves a method that can be implemented to extract instantaneous properties of signals such as structural response dominant instantaneous frequencies. In the proposed algorithm, these estimated instantaneous properties are utilized to improve the pole-placement method as an adaptive active control technique. The required active control gains are obtained using a genetic algorithm scheme, and optimal gains are calculated corresponding to preselected excitation frequencies. An algorithm is also introduced to choose excitation frequencies based on online EMD method resolution. In order to investigate the efficiency of the proposed method, some case studies that include a discrete model, continuous samples of beam and plate structures, and experimental cantilevered beam are carried out, and the results of the proposed method are compared with the preset (nonadaptive) optimal gains conditions.

Fingering instability on curved substrates: optimal initial film and substrate perturbations

We investigate the stability of a thin Newtonian fluid spreading on a horizontal cylinder under the action of gravity. The capillary ridge forming at the advancing front is known to be unstable with respect to spanwise perturbations, resulting in the formation of fingers. In contrast to the classic case of a flow over an inclined plane, the gravity components along a cylindrical substrate vary in space and the draining flow is time-dependent, making a modal stability analysis inappropriate. A linear optimal transient growth analysis is instead performed to find the optimal spanwise wavenumber. We not only consider the optimal perturbations of the initial film thickness, as commonly done in the literature, but also the optimal topographical perturbations of the substrate, which are of significant practical relevance. We found that, in both cases, the optimal gains are obtained when the perturbation structures are the least affected by the time horizon. The optimal spanwise wavenumber is found to be dependent on the front location, due to the dependence of the characteristic length of the capillary ridge on its polar location.