Multivariable Optimal Control Research Articles

Design of an Optimal Multivariable PID Controller for a Two-Link Robot Arm

Incorporating manipulator robots into various industries has revolutionized automation and manufacturing processes. Manipulator robots are versatile machines equipped with robotic arms and end-effectors, enabling them to handle complex tasks with precision and efficiency. This research aims to design an optimal Mutivariable PID (MPID) controller that ensures precise and accurate movements of two-link robot arm. Theoretical foundations of the MPID controller are discussed together with its relevance to robotic arm systems, and the challenges associated with its implementation. The research methodology involves mathematical modelling of the two-link robot arm dynamics, and the use of an optimization algorithm to determine the optimal MPID controller coefficients. Simulation results demonstrate performance enhancement and productivity of the two-link robot arm through the improved MPID controller.

Optimal Multivariable Control for Wide Output Regulation and Full-Range Efficiency Optimization in LCC–LCC Compensated Wireless Power Transfer Systems

Optimal Multivariable Control for Wide Output Regulation and Full-Range Efficiency Optimization in <i>LCC</i>–<i>LCC</i> Compensated Wireless Power Transfer Systems

A model of sustainable development of science and high technology cities taking into account the area's life cycle

Subject. This article analyzes the cyclical nature of urban development. Objectives. The article aims to identify new areas for the development of cities of science and high technology. Methods. For the study, I used the methods of general systems, logical, comparative, and multivariate analyses, grouping, generalization, expert assessments, and optimal control. Results. The article proposes a methodology for constructing an economic and mathematical model of sustainable development of cities of science and high technology. Conclusions. A self-developing innovation ecosystem will help ensure the sustainable development of science cities in the long term.

Multirate Predictive Control for Diode Clamped Inverters with Data-Based Learning Implementation

Diode clamping is a widely used topology for power inverters due to the low number of components, low cost, and general efficiency of the circuit, but its main drawback is the difficulty in controlling a multilevel configuration. For that, finite-control-set model predictive control was chosen, as it is a multivariable optimal controller that takes into account constraints and deals with multiple objectives. However, it has high computational burden and its control solution is held constant during the sampling period if not using modulation. This work first proposes a multirate enhancement for this control technique to address the latter issue, and then uses a novel learning method to allow the online implementation and overcome the high computation time. This method is tested in simulation in a three-phase, five-level diode-clamped inverter. Comparisons and performance gains of the multirate technique are provided.

Intelligent direct thrust control for multivariable turbofan engine based on reinforcement and deep learning methods

This paper proposes a novel intelligent direct thrust control (IDTC) architecture for a two-spool turbofan engine, in which the thrust is directly controlled by the IDTC architecture with two control variables instead of transforming thrust command to other commands. To realize thrust control, the unmeasurable thrust should be estimated first. A dynamic thrust model (DTM) is proposed to characterize the strong non-linearity of the engine. With the dynamic characteristic data set generation method, the date diversity increases and the thrust under random engine dynamics can be estimated more accurately. For the multi-variable optimal thrust controller, reinforcement learning (RL) method proximal policy optimization (PPO) algorithm is applied in the intelligent controller (IC) design process. Considering the engine characteristics, the reward system and the controller structure are redesigned to realize thrust optimal control and limit protection. The network used in both the DTM and the IC designing are the long short-term memory (LSTM) recurrent neural network (RNN), which can better process the engine time series and get better performance and accuracy. As the traditional evaluation criteria are too conservative to evaluate the overall ability of the proposed IDTC architecture in the full envelope, new criteria are proposed. Numerical simulations shows the satisfactory thrust estimation and control performance of the proposed IDTC architecture in the full envelope above the idle, and verify the superiority against other methods. Also, the strategy selection of the IC under extreme control tasks also shows the intelligence of the controller and gives new ideas for the engine control law design.

Evaluation of global techno-socio-economic policies for the FEW nexus with an optimal control based approach

Inordinate consumption of natural resources by humans over the past century and unsustainable growth practices have necessitated a need for enforcing global policies to sustain the ecosystem and prevent irreversible changes. This study utilizes the Generalized Global Sustainability model (GGSM), which focuses on sustainability for the Food-Energy-Water (FEW) Nexus. GGSM is a 15-compartment model with components for the food-web, microeconomic framework, energy, industry and water sectors, and humans. GGSM shows that an increased per capita consumption scenario is unsustainable. In this study, an optimal-control theory based approach is devised to address the unsustainable scenario through policy interventions to evaluate sustainability by employing multiple global indicators and controlling them. Six policy options are employed as control variables to provide global policy recommendations to develop the multi-variate optimal control approach. Seven objectives are proposed to limit the human burden on the environment to ascertain sustainability from a lens of ecological, economic, and social wellbeing. This study observes the performance of the policy options toward seven sustainability indicators: Fisher Information, Green Net Product, Ecological Buffer, Carbon dioxide emissions, Nitrous oxide emissions, and Global Water Stress. The optimal control model assesses these multiple objectives by minimizing the variance in the Fisher Information. One significant result from this study is that optimizing for the Fisher Information based objective is adequate to attain sustainability and manage the other objectives under consideration. Thus, forgoing a multi-objective problem framework. The results show that cross-dimensional policy interventions such as increased vegetarianism and increased penalty on industrial discharge are shown to have a positive impact on scale.

Smart energy savings for aeration control in wastewater treatment

This paper describes control algorithm of minimum energy loss in the aeration process of wastewater treatment in the activated sludge system. The basic equations of the aeration process have been proposed in this paper with the dissolved oxygen concentration (DO) and the amount of sludge discharge (QW) being dual-parameter control variables and the organic matter concentration S and the microbial concentration X in the aeration tank being the state variables. Based on the present study on optimization control of wastewater treatment, the multivariable optimal control model with restriction factors have been presented in the paper. The model with modern control theory and system analysis are introduced into the field of activated sludge wastewater treatment. It takes the two most important control parameters (DO &QW), effluent quality as restriction factor. The minimum energy consumption in the aeration process is used as the objective function. This approach has been carried out and the results show that adopting optimal control strategy in the aeration process can effectively conserve energy with the assurance of effluent water quality.

Comparison of PLL-Based and PLL-Less Vector Current Controllers

This article presents a detailed and rigorous comparison between two vector current control (VCC) approaches for voltage source converters (VSC). A PLL-less VCC (also called the direct power control) has recently been proposed in several major publications with the assumption that it will improve the performance of conventional PLL-based VCC during weak grid conditions. In this article, first, we introduce an enhancement to both the PLL-based and PLL-less VCCs by using an optimal multivariable control design for both of them. Then, we show that both controllers perform equally during normal and weak grid conditions. However, the PLL-less VCC produces errors when the grid frequency variations occur and eventually becomes unstable when the grid is also weakened. Furthermore, the PLL-less VCC cannot produce a clean output current when unbalanced grid disturbances occur. This article proposes a method to address this latter issue. It also proves that the filters used in PLL-less VCC introduce similar dynamics to those of PLL. This article concludes that the PLL-based VCC is still the preferred choice for the grid-interfaced VSCs. Laboratory-scale experimental results are also included to validate the simulation results.

Linear-quadratic optimal control of multi-modal distribution systems with imperfect channels*

The paper examines the perspectives of linear-quadratic (LQ) optimal control in steering the process of goods distribution in logistic systems with multiple transportation options. In the considered class, the distribution centre governs the stock replenishment process of subordinate depots, from which un uncertain market demand is served. The centre is linked with the depots via shared supply channels with different characteristics regarding delay, reliability, and capacity, e.g. train vs truck delivery. The design objective is a rule of dynamical channel allocation – how many goods to send in a period using a given mode – so that balanced, cost-efficient system performance and high customer service rate are achieved. The received goods are inspected for quality defects and rejected when faulty. Thus, one needs to cope with two major sources of uncertainty: unpredictable demand variations and channel imperfections. A multi-variable LQ optimal controller is designed and presented in closed form for detailed analytical and numerical treatment. It is formally shown that despite perturbations, the controller always establishes a non-negative and upper-bounded replenishment signal, and the stock level does not cross the reference value. Conditions for warehouse space selection and obtaining full demand satisfaction at the depots are specified and formally proved.

Analysis, control, and modeling of the three‐port converter without port voltage constraint for photovoltaic/battery system application

AbstractFor a photovoltaic (PV)/battery power system consisting of PV module, energy storage system, and local load, using a three‐port converter (TPC) instead of several single‐input converters is more desirable, such as simpler circuit, higher efficiency, lower cost, and centralized control without communication circuit. In this paper, a TPC is proposed and analyzed, which includes operating modes, steady‐state performance, and parameter design. Compared with other converters, the proposed TPC has a low cost, compact structure, and a more flexible voltage relationship among all ports. Moreover, energy management and control methods are further proposed for PV/battery systems based on the proposed converter, which can achieve maximum power point tracking (MPPT) of PV module and constant output voltage. In order to design the control loop and realize multivariable optimal control, a small‐signal model of the converter is obtained in each operation mode. Then a detailed decoupling design approach based on a small‐signal model is provided to allow a separate controller design for the proposed converter. Finally, the validity of the proposed converter and its energy management and control method are verified by experimental results.

Optimal Multivariable MMC Energy-Based Control for DC Voltage Regulation in HVDC Applications

The penetration of renewable energy resources is changing the way the power system is understood and operated. With an increasing number of power electronics devices integrated into the power system, the modular multilevel converter (MMC) is arising as one of the key technologies for HVDC applications. While several control strategies for MMCs have been proposed in the last years, designing controls for MMCs remains a challenging and non-trivial problem due to its large number of degrees of freedom. In this paper, a general multivariable control structure is proposed that generalizes and improves upon previously reported approaches. Moreover, to fully exploit the degrees of freedom offered by this control, a model-based tuning methodology is presented that extends results from optimal $\mathcal {H}_2$ structured control design to MMC applications. A case study using an HVDC link is used to illustrate and analyze the performance of the MMC using the proposed approach in different scenarios.

An Optimal Multivariable Control Strategy for Inductive Power Transfer Systems to Improve Efficiency

Efficiency of wireless power transfer systems, based on inductive power transfer (IPT) technology, suffers significantly due to coil misalignment and load variations. Although numerous control strategies have been proposed in the past to improve the efficiency under these conditions, a technique that utilizes all freedoms of control simultaneously to maximize efficiency is yet to be reported. This article therefore proposes a multivariable control strategy that uses the optimal combination of all control variables to maximize the efficiency of IPT systems when regulating power and even under large coil misalignments and load variations. The article presents a comprehensive mathematical model, describing the underlying theory of the proposed optimal control philosophy, and investigates the performance and limitations of the proposed technique under wide range of operating conditions. To demonstrate the improvement in performance, theoretical results are presented in comparison to those obtained from a 1-kW prototype bidirectional IPT system, and also benchmarking against conventional control techniques. Results convincingly indicate that the proposed optimal control strategy regulates power at maximum efficiency despite large coil misalignments and load variations.

Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs.

Optimal Robust Control of a Robots Group

The article focuses on the development of an on-board system design method for optimal control of an autonomous mobile group of objects. It is assumed that the group consists of a leader and some agents. A new method for the synthesis of an optimal multivariable control system, which is needed for preserving desired position of the agent relatively to the leader, was substantiated in the article. The leader passes along a random trajectory and measurement of the agent position with respect to the leader is accompanied with random noise. All group members experience the action of random disturbances.

Cross Regulation Reduced Optimal Multivariable Controller Design for Single Inductor DC-DC Converters

Single Inductor (SI) converters with the advantage of using one inductor for any number of inputs/outputs find wide applications in portable electronic gadgets and electrical vehicles. SI converters can be used in Single Input Multiple Output (SIMO) and Multiple Input Multiple Output (MIMO) configurations but they need controllers to achieve good transient and steady state responses, to improve the stability against load and line disturbances and to reduce cross regulation. Cross regulation is the change in an output voltage due to change in the load current at another output and it is an added constraint in SI converters. In this paper, Single Input Dual Output (SIDO) and Dual Input Dual Output (DIDO) converters with applications capable of handling high load current working in Continuous Conduction Mode (CCM) of operation are taken under study. Conventional multivariable PID and optimal Linear Quadratic Regulator (LQR) controllers are developed and their performances are compared for the above configurations to meet the desired objectives. Generalized mathematical models for SIMO and MIMO are developed and a Genetic Algorithm (GA) is used to find the parameters of a multivariable PID controller and the weighting matrices of optimal LQR where the objective function includes cross regulation as a constraint. The simulated responses reveal that LQR controller performs well for both the systems over multivariable PID controller and they are validated by hardware prototype model with the help of DT9834® Data Acquisition Module (DAQ). The methodologies used here generate a fresh dimension for the case of such converters in practical applications.

A novel technique for optimal integration of active steering and differential braking with estimation to improve vehicle directional stability

This study deals with the enhancement of directional stability of vehicle which turns with high speeds on various road conditions using integrated active steering and differential braking systems. In this respect, the minimum usage of intentional asymmetric braking force to compensate the drawbacks of active steering control with small reduction of vehicle longitudinal speed is desired. To this aim, a new optimal multivariable controller is analytically developed for integrated steering and braking systems based on the prediction of vehicle nonlinear responses. A fuzzy programming extracted from the nonlinear phase plane analysis is also used for managing the two control inputs in various driving conditions. With the proposed fuzzy programming, the weight factors of the control inputs are automatically tuned and softly changed. In order to simulate a real-world control system, some required information about the system states and parameters which cannot be directly measured, are estimated using the Unscented Kalman Filter (UKF). Finally, simulations studies are carried out using a validated vehicle model to show the effectiveness of the proposed integrated control system in the presence of model uncertainties and estimation errors.

Tuning Multivariable Optimal PID Controller for a Continuous Stirred Tank Reactor Using an Evolutionary Algorithm

In this work a multivariable optimal PID controller for a continuous stirred tank reactor was designed in order to obtain optimal system performance without decoupling. The tuning of this controller is obtained by using an evolutionary algorithm (MAGO). This solution is compared with classical methods for multivariable control. The results of this study showed that the controller designed rejects the effect of disturbances and follows the external reference signal efficiently. Evolutionary tuning overcomes broadly the classical methods.

Wind Turbine Multivariable Optimal Control Based on Incremental State Model

AbstractThe multivariable optimal control of a wind turbine by an approach based on incremental state model is proposed. The advantages of incremental state model in comparison with the non incremental one are that the control action cancels steady state errors and incremental state solves the problem of computing the target state, choosing zero as an objective. Linear Quadratic Regulator (LQR) and optimal state observer are applied. The effectiveness of the proposed control method, over the non incremental one, is examined by applying the linear controllers to the nonlinear wind turbine model. The results show that incremental LQR control presents good transient response and zero steady state errors, even in presence of disturbances, nonlinearities and modelling errors.

Improve Linear Quadratic Regulator by Particle Swarm Optimization Algorithms for Two Wheeled Self Balancing Mobile robot

The aim of this paper is to suggest a methodical smooth control method for improving the stability of two wheeled self-balancing robot under effect disturbance. To promote the stability of the robot, the design of linear quadratic regulator using particle swarm optimization (PSO) method and adaptive particle swarm optimization (APSO). The computation of optimal multivariable feedback control is traditionally by LQR approach by Riccati equation. Regrettably, the method as yet has a trial and error approach when selecting parameters, particularly tuning the Q and R elements of the weight matrices. Therefore, an intelligent numerical method to solve this problem is suggested by depending PSO and APSO algorithm. To appraise the effectiveness of the suggested method, The Simulation result displays that the numerical method makes the system stable and minimizes processing time.

Fuzzy Scheduled Optimal Control of Integrated Vehicle Braking and Steering Systems

The safe hard braking of a turned vehicle requires short stopping distance while maintaining the vehicle in the path. To achieve the first aim, a wheel slip controller is designed to calculate the maximum braking force of each wheel according to the tire/road conditions. For the second aim, a new optimal multivariable controller for integrated active front steering and direct yaw moment control is analytically developed to control the vehicle directional stability directly. Since the required stabilizing external yaw moment has to be produced by reducing the maximum achievable braking forces of one side wheels, it leads to increase the stopping distance and should be kept as low as possible. In an effective way to manage the integrated control inputs, a fuzzy logic is defined to determine the weight factor of each control input in the integrated optimal control law. This logic is defined using the stability index obtained by the phase plane analysis of nonlinear vehicle model. Therefore, the proposed controller can be tuned automatically for different driving conditions. The simulation results carried out using a validated vehicle model demonstrate that the integrated control system has a better performance compared with stand-alone braking and steering systems to attain the desired purposes.