A simple method for solving the LQG stochastic control problem using a polynomial approach

Decentralised power system load frequency control beyond the limit of diagonal dominance

In real-world industrial processes, achieving self-tuning of control unit parameters using an intelligent optimization algorithm offers significant advantages in adapting to the diverse characteristics of dynamic systems. Conventional controllers often fall short in real-time application scenarios and reliability requirements. In response, adaptable learning algorithms have gained acceptance across various industrial control applications. Handling complex computational tasks, extensive training data, and multivariable demands requires a robust platform to achieve optimal results. In this article, we present a multi-input, multioutput (MIMO) control system that utilizes the Big Bang–Big Crunch optimization algorithm alongside the learning algorithm for multivariate data analysis (LAMDA). Our modifications to the LAMDA controller involve using the ordered weighted average instead of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i>-norm or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-norm as aggregate functions. Additionally, we adopted field-programmable gate array (FPGA) technology to improve execution speed and energy efficiency compared to conventional platforms (e.g., microcontrollers). We modeled the MIMO system for heating, ventilation, and air conditioning system using state space equations. The hardware system was designed with (very high-speed integrated circuit) hardware description language (VHDL). To demonstrate our approach, we implemented the entire system on an AMD/Xilinx Virtex-7 FPGA, and experimental results confirmed the feasibility of our proposed optimization strategy.

Three-phase voltage source converter (VSC) is widely used for interfacing distributed energy resource (DER) units with the ac utility grid. Current vector control in synchronous reference frame is the common approach for these applications. In this frame, system model represents a multi-input multi-output (MIMO) control system. However, decoupling terms are used to split the system into two single-input single-output (SISO) subsystems. Moreover, feed-forward terms are also employed to achieve soft start. In this paper, it is shown that when the grid is weak, the feed-forward terms have stabilizing effect in addition to the soft-start advantage. Nevertheless, the decoupling terms have a destabilizing effect. The paper concludes that, if proportional-integrating (PI) compensators are used (which is a common practice), the decoupling terms can be avoided. However, the feed-forward terms must be taken from the phase-locked loop to have an improved stability. Detailed stability analysis of a grid-connected VSC considering the PLL dynamics and grid impedance is carried out and verified by means of simulations.

The decentralised load-frequency controller design problem concerned is translated into an equivalent problem of decentralised controller design for a multi-input multi-output (MIMO) control system. It is shown that, subject to a condition based on the structured singular values, each local area load-frequency controller can be designed independently. The stability condition for the overall system can be stated as to achieve a sufficient interaction margin and a sufficient gain and phase margin defined in classical feedback theory during each independent design. It is demonstrated by computer simulations that within this general framework, very simple local controllers can be designed to achieve satisfactory performances for a sample two-area power system and a simplified four-area power system. Under the proposed framework based on the structured singular values, other design methods for local area controllers may also be applied. © IEE, 1998.

Advanced control of large-scale wind turbines: Structural load reduction and lifetime control

In wireless communication, multiple signals are utilized to receive and send information in the form of signals simultaneously. These signals consume little power and are usually inexpensive, with a high data rate during data transmission. An Multi Input Multi Output (MIMO) system uses numerous antennas to enhance the functionality of the system. Moreover, system intricacy and power utilization are difficult and highly complicated tasks to achieve in an Analog to Digital Converter (ADC) at the receiver side. An infinite number of MIMO channels are used in wireless networks to improve efficiency with Cross Entropy Optimization (CEO). ADC is a serious issue because the data of the accepted signal are completely lost. ADC is used in the MIMO channels to overcome the above issues, but it is very hard to implement and design. So, an efficient way to enhance the estimation of channels in the MIMO system is proposed in this paper with the utilization of the heuristic-based optimization technique. The main task of the implemented channel prediction framework is to predict the channel coefficient of the MIMO system at the transmitter side based on the receiver side error ratio, which is obtained from feedback information using a Hybrid Serial Cascaded Network (HSCN). Then, this multi-scaled cascaded autoencoder is combined with Long Short Term Memory (LSTM) with an attention mechanism. The parameters in the developed Hybrid Serial Cascaded Multi-scale Autoencoder and Attention LSTM are optimized using the developed Hybrid Revised Position-based Wild Horse and Energy Valley Optimizer (RP-WHEVO) algorithm for minimizing the "Root Mean Square Error (RMSE), Bit Error Rate (BER) and Mean Square Error (MSE)" of the estimated channel. Various experiments were carried out to analyze the accomplishment of the developed MIMO model. It was visible from the tests that the developed model enhanced the convergence rate and prediction performance along with a reduction in the computational costs.

Multi input multi output (MIMO) system with the multiple antennas at both the transmitter and receiver is the emerging technology in the modern wireless system. MIMO systems are well adopted due to its high spectral efficiency and high data rates. For the detection of MIMO systems, a powerful technique called Lattice Reduction (LR) algorithm are used to obtain the better orthogonality in the channel matrices and is aided with the linear and low complexity detectors such as Zero forcing(ZF) and Minimum mean square error (MMSE) for the reduction in complexity. In this paper we propose a new algorithm called Enhanced lattice reduction algorithm to improve the error performance for the linear detectors with the lesser complexity and also it is aided with the non linear precoding called Tomlinson-Harashima precoding (THP) in the presence of channel state information (CSI). Lattice reduction aided with THP improves the performance linearly. BER performance of the proposed algorithm is determined and it is compared with the other LR aided algorithms in the literature.

The last three decades have seen rapid development in modern control theory and microprocessors. Application of newly developed control algorithms in Industrial process control has gained popularity due to microprocessor based control systems. In this chapter all categories of control algorithms which have gained popularity amongst industrial users or which are industrially implementable are covered. We have first covered control algorithms for single-input single-output (SISO) systems and then multi-input multi-output (MIMO) systems. Three term controllers, time delay compensation techniques and fuzzy logic controllers, etc., have been discussed for SISO plants. Predictive, adaptive, optimal and state feedback controllers have been covered for both SISO and MIMO plants. We have discussed auto tuning techniques for SISO PID controllers and also briefly expert control systems. Algorithms have been described in their digital implementation form. Implementation of control algorithms in industrially available distributed digital control system has been discussed. A brief report has been given for actual implementation of some algorithms in industrial plants and benefits due to this implementation have been highlighted. In particular applications of optimal control and optimal filtering in power industry in UK and power, cement and steel industry in Japan and predictive control techniques in petroleum industries in North America have been mentioned while describing the particular algorithm. Recent research results to pool resources of linear quadratic gaussian design popular in power, cement and steel industry and predictive control (model algorithmic control and internal model control) popular in petroleum industries to evolve a better approach to controller design have been highlighted.

An optimal control problem with an infinite horizon quadratic cost functional for a linear system with point-wise and distributed time delays in the state variables is considered. The case, where the cost functional does not contain a control cost, is analyzed. The latter means that the solution (an optimal control) of the considered problem is singular. This control problem is solved by a regularization method. Namely, it is associated with a new optimal control problem for the same equation of dynamics. The cost functional in this new problem is the sum of the original cost functional and an integral of the square of the control with a small positive weighting coefficient. Due to the smallness of this coefficient, the new problem is a cheap control problem. Using the singular perturbation technique, an asymptotic analysis of this cheap control problem is carried out. Based on this analysis, the infimum of the cost functional in the original problem is obtained, and a minimizing control sequence is constructed.

Multi-input multi-output (MIMO) radar systems have taken considerable attention among radar community in recent years. As stated in some publications MIMO radars have serious performance advantages compared to single-input single-output (SISO) radars. Although MIMO radars perform well theoretically, they have some practical problems. One of these problems is the data transmission rate required by MIMO radars. Quantization directly affects the amount of data to be transmitted. In this paper effects of quantization on MIMO radar performance is covered.

This paper presents a method of continuous-time simple-adaptive control (SAC) for multi-input multi-output (MIMO) nonlinear systems using multifraction neural networks. The control input is given by the sum of the output of the simple adaptive controller and the output of the multifraction neural network is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the multifraction neural network is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems.

In previous works, density evolution schemes have been used to design an irregular low-density parity-check (LDPC) code for the multi-input multi-output (MIMO) systems. However the code design based on the density evolution can be used only for simple code structure like LDPC codes and repeat-accumulate (RA) codes. Recently simple and accurate irregular LDPC code design method based on the extrinsic information transfer (EXIT) chart was introduced for an AWGN channel. This code design scheme is much flexible, therefore it can be used for any kind of code structure like turbo codes. In this paper we design an irregular LDPC code for a MIMO system using the EXIT chart based scheme. The EXIT charts are used to obtain the optimal edge degree distribution of the irregular LDPC code combined with the MMSE-SIC MIMO detector. This scheme can be generalized for designing the optimal iterative MIMO detector combined with any kind of channel codes including turbo codes.

This paper presents an investigation into the modelling and control of a one-degree-of-freedom (1 DOF) twin-rotor multi-input multi-output (MIMO) system (TRMS). The behaviour of the TRMS in certain aspects resembles that of a helicopter. Hence, it is an interesting identification and control problem. A dynamic model characterizing the TRMS in hover is extracted using a black-box system identification technique. The extracted model is employed in the design of a feedback linear quadratic Gaussian compensator, namely the stability augmentation system (SAS). This has a good tracking capability but requires high control effort and has inadequate authority over residual vibration of the system. These problems are resolved by further augmenting the system with a command path prefilter, resulting in the command and stability augmentation system (CSAS). The combined feedforward and feedback compensator satisfies the performance objectives and obeys the actuator constraint. The control law is implemented in realtime on the TRMS platform.

This paper presents a neural-network-based predictive control (NPC) method for a class of discrete-time multi-input multi-output (MIMO) systems. A discrete-time mathematical model using a recurrent neural network (RNN) is constructed and a learning algorithm adopting an adaptive learning rate (ALR) approach is employed to identify the unknown parameters in the recurrent neural network model (RNNM). The NPC controller is derived based on a modified predictive performance criterion, and its convergence is guaranteed by adopting an optimal algorithm with an adaptive optimal rate (AOR) approach. The stability analysis of the overall MIMO control system is well proven by the Lyapunov stability theory. A real-time control algorithm is proposed which has been implemented using a digital signal processor, TMS320C31fromTexasInstruments.Twoexamples,includingthecontrolofa MIMO nonlinear system and the control of a plastic injection molding process, are used to demonstrate the effectiveness of the proposed strategy. Results from both numerical simulations and experiments show that the proposed method is capable of controlling MIMO systems with satisfactory tracking performance under setpoint and load changes.

For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis problem is amenable to a convex programming approach. In this paper, we show that a strictly broader class of problems we call internally quadratically invariant, also yields an affine set of achievable closed-loop maps. We treat systems represented by rational as well as proper rational transfer functions and present an illustrative example.