Parametric Robust Control Research Articles

Barrier function-based adaptive neural network sliding mode control of autonomous surface vehicles

In this paper, we consider trajectory tracking control for autonomous surface vehicles (ASVs) with unknown boundary model uncertainties and external disturbances. The neural networks (NNs) and the sliding mode control (SMC) with a switched adaptive law are combined for the first time. The NNs are used to approximate model uncertainties and external disturbances of ASVs. The parameters of the robust SMC term first increase until the sliding variable reaches a quasi sliding mode which bound is associated with the parameter of the barrier function (BF). Then the BF is selected as the parameter of the robust term for the SMC strategy to estimate the NN approximation error and to constrain the sliding variable inside the predefined quasi sliding mode. One salient feature of our approach is that the robust control parameter is no more than approximation error of NNs in sliding and steady phases of SMC. Simulation studies are performed to illustrate the advantage of the proposed control method.

Adaptive Proportional Integral Robust Control of an Uncertain Robotic Manipulator Based on Deep Deterministic Policy Gradient

An adaptive proportional integral robust (PIR) control method based on deep deterministic policy gradient (DDPGPIR) is proposed for n-link robotic manipulator systems with model uncertainty and time-varying external disturbances. In this paper, the uncertainty of the nonlinear dynamic model, time-varying external disturbance, and friction resistance of the n-link robotic manipulator are integrated into the uncertainty of the system, and the adaptive robust term is used to compensate for the uncertainty of the system. In addition, dynamic information of the n-link robotic manipulator is used as the input of the DDPG agent to search for the optimal parameters of the proportional integral robust controller in continuous action space. To ensure the DDPG agent’s stable and efficient learning, a reward function combining a Gaussian function and the Euclidean distance is designed. Finally, taking a two-link robot as an example, the simulation experiments of DDPGPIR and other control methods are compared. The results show that DDPGPIR has better adaptive ability, robustness, and higher trajectory tracking accuracy.

Real-Time Implementation of Robust Loop-Shaping Controller for a VSC HVDC System

Voltage source converter (VSC) based HVDC systems are one of the most promising technologies for high voltage bulk power transmission. The reliability and stability of a VSC-based HVDC system greatly depends on the design of a proper controller for the inner decoupled d-q current loop. One of the major causes of instability in a properly tuned controller is due to system parameter variation. This paper presents the design of a fixed parameter robust controller for the inner decoupled d-q current loop for a VSC-based HVDC system to deal with the uncertainties due to system parameter variations. The method of multiplicative uncertainty is employed in the robust design to model the variations in the system parameters. The robust control design was realized through a graphical procedure known as the loop-shaping technique. The graphical loop shaping technique is a much simpler and more straightforward method compared to the traditional H∞-based algorithms for robust controller design. The designed robust controller was experimentally verified using a real-time hardware in loop (HIL) system and was tested on a VSC HVDC system. The performance of the designed robust controller is compared to that of a traditional PI controller. It has been observed that a classical PI controller is effective for a given operating point, and its performance deteriorates when the operating point changes or when the system parameters change. The studies conducted using real-time hardware in the loop (HIL) system prove that the designed loop-shaping-based robust controller provides very good performance and stability for a wide range of system parameter variations, such as changes in resistance and the inductance of the VSC HVDC system compared to the PI controller tuned using conventional methods.

Part 1: robust adaptive control of quadrotor with disturbance observer

PurposeThe aim of this paper is to design a nonlinear disturbance observer-based control (DOBC) method obtained by patching a control method developed using a robust adaptive technique and a DO.Design/methodology/approachFor designing a DOBC, initially a class of nonlinear system is considered with an external disturbance. First, a DO is designed to estimate the external disturbances. This estimate is combined with the controller to reject the disturbances and obtain the desired control objective. For designing a controller, the robust sliding mode control theory is used. Furthermore, instead of using a constant switching gain, an adaptive gain tuning criterion is designed using Lyapunov candidate function. To investigate the stability and effectiveness of the developed DOBC, stability analysis and simulation study are presented.FindingsThe major findings of this paper include the criteria of designing the robust adaptive control parameters and investigating the disturbance rejection when robust adaptive control based DOBC is developed.Practical implicationsIn practice, the flight of quadrotor is affected by different kind of external disturbances, thus leading to the change in dynamics. Hence, it is necessary to design DOBCs based on robust adaptive controllers such that the quadrotor model adapts to the change in dynamics, as well as nullify the effect of disturbances.Originality/valueDesigning DOBCs based on robust control method is a common practice; however, the robust adaptive control method is rarely developed. This paper contributes in the domain of DOBC based on robust adaptive control methods such that the behavior of controller varies with the change in dynamics occurring due to external disturbances.

A Robust Circuit and Controller Parameters’ Identification Method of Grid-Connected Voltage-Source Converters Using Vector Fitting Algorithm

This article presents a vector fitting (VF) algorithm-based robust circuit and controller parameters’ identification method for grid-connected voltage-source converters (VSCs). The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain impedance frequency responses (IFRs) of the VSCs are first measured using the frequency scanning method, based on which the corresponding measured phasor-domain IFRs are calculated. Then, polynomial transfer functions are generated by applying the VF algorithm on the measured phasor-domain IFRs, from which the circuit and controller parameters, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LCL$ </tex-math></inline-formula> filter parameters, digital sampling time, current controller parameters, and phase-locked loop parameters, are identified. The influence of measurement noise on parameters’ identification accuracy and corresponding countermeasure to mitigate the adverse influence are also theoretically investigated. The proposed method is able to identify the circuit and controller parameters when detailed parameters are missing due to industrial secrecy or parameters variation caused by operating condition change, temperature fluctuation, or aging. The effectiveness of the proposed circuit and controller parameters’ identification method is validated by theoretical demonstration, OPAL-RT-based real-time simulation, and experimental validation.

Vehicles robust scheduling of hazardous materials based on hybrid particle swarm optimisation and genetic algorithm

This paper takes the vehicles scheduling of hazardous materials as the research object. First, considered the four objectives of risk minimization, cost minimization, risk equilibrium value minimization, and duration minimization, the vehicles robust scheduling of hazardous materials in multiple distribution centers with risk balance is constructed. Then, uncertain models are transformed into peer-to-peer models through the idea of robust discrete optimization. By introducing the crossover and mutation operators of genetic algorithm into particle swarm algorithm, a hybrid particle swarm algorithm is constructed, and three-stage coding rules are adopted. Finally, case study is exemplified to prove the feasibility of the model and algorithm. The results show that the obtained scheduling scheme for the vehicles of hazardous materials minimizes the risk value and makes the risk distribution more balanced for the government regulatory department, and the vehicle can avoid certain road sections with relatively large risk values. For transportation enterprises, the vehicle scheduling scheme for transporting hazardous materials minimizes the cost and shortens the task duration at the same time. In the case of risk uncertainty, different robust control parameters are introduced to make the vehicles robust scheduling of hazardous materials have different degrees of stability.

Parameter identification and robust vibration control of a truck driver’s seat system using multi-objective optimization and genetic algorithm

This paper has developed a 5-DOF driver and seat suspension system model for active vibration control. A novel fast system parameter identification method from vibration measurement data has been proposed for the seat-occupant system based on the multi-objective Genetic Algorithm optimization (GA). This system parameter identification method can identify the seat system parameters of a 5-DOF lumped mass-spring-dashpot biodynamic seat-occupant model from vibration test results quickly and accurately. Without calculation and measurement of materials, the physical parameters of the seat suspension system such as masses (m), stiffness (k), and damping coefficients (c) are estimated through matching the measured resonant frequency and transmissibility amplitude at a specific frequency with the simulated ones. This is one of the main contributions of this paper. The characteristics of the human body vibration in the low-frequency range are analyzed through the seat to head transmissibility (STHT) ratio. The experimental and simulation results of the STHT values have been calculated and compared to verify each other. The sensitivity analysis of the seat effective amplitude transmissibility (SEAT) values over the seat system parameters have been conducted and validated by the measured results of the transmissibility ratios. A full state feedback controller has been developed to reduce the human body vibration in the seat suspension system, which is another new contribution of this paper. The simulation results show that the proposed controller has better vibration attenuation performance than the conventional PID controller.

GRU-Type LARC Strategy for Precision Motion Control With Accurate Tracking Error Prediction

To simultaneously achieve accurate tracking error prediction, rigorous motion accuracy, and certain robustness to parameter variations and unknown disturbances, this article proposes a data-based learning adaptive robust control (LARC) strategy based on gated recurrent unit (GRU) neural network. Firstly, parameter adaptive control and robust control are utilized to guarantee the robustness against parametric uncertainties and unknown disturbances. A GRU neural network is then constructed and capable of precisely predicting the tracking error after training with data collected from a linear-motor-driven stage. Essentially, the GRU network can be viewed as a data-based model, which captures the tracking error dynamic characteristics and provides a prediction even before implementing the real trajectory. Consequently, a reference modification and a feedforward compensation part can be formed, which is the significant part of the whole LARC control structure. Comparative experimental investigation not only validates the effectiveness of the tracking error prediction ability, but also demonstrates the practically satisfactory transient/steady-state tracking performance of the proposed control strategy.

Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule

When consumers faced with the choice of competitive chain facilities that offer exclusive services, current rules cannot describe these customers’ behaviors very well. So we propose a partially proportional rule to represent this kind of customer behavior. In addition, the exact demands of customers in many real-world environments are often difficult to determine. This is contradicting to the assumption in most studies of the competitive facility location problem. For the competitive facility location problem with the partially proportional rule, we establish a robust optimization model to handle the uncertainty of customers’ demands. We propose two methods to solve the robust model by studying the properties of the counterpart problem. The first method MIP is presented by solving a mixed-integer optimization model of the counterpart problem directly. The second method SAS is given by embedding a sorting subalgorithm into the simulated annealing framework, in which the sorting subalgorithm can easily solve the subproblem. The effects of the budget and the robust control parameter to the location scheme are analyzed in a quasi-real example. The result shows that changes in the robust control parameter can affect the customer demands that were captured by the new entrants, thereby changing the optimal solution for facility location. In addition, there is a threshold of the robust control parameter for any given budget. Only when the robust control parameter is larger than this threshold, the market share captured by the new entering firm increases with the increases of this parameter. Finally, numerical experiments show the superiority of the algorithm SAS in large-scare competitive facility location problems.

Control Strategies on Path Tracking for Autonomous Vehicle: State of the Art and Future Challenges

Autonomous vehicle technology aims to improve driving safety, driving comfort, and its economy, as well as reduce traffic accident rate. As the basic part of autonomous vehicle motion control module, path tracking aims to follow the reference path accurately, ensure vehicle stability and satisfy the robust performance of the control system. This article introduces the representative control strategies, robust control strategies and parameter observation-based control strategies on path tracking for autonomous vehicle. Furthermore, the implementations and disadvantages are summarized. Most importantly, the critical review in this article provides a list and discussion of the remaining challenges and unsolved problems on path tracking control.

Robust Optimization of a Distribution Network Location-Routing Problem Under Carbon Trading Policies

Taking carbon emissions into account in decision-making on distribution network operations contributes to achieving the goal of promoting energy conservation and emissions reduction. The focus of this paper is to research multicapacity hierarchical location-routing robust optimization in distribution network design under carbon trading policies. First, this problem is described as a mixed integer nonlinear programming model. Then, based on strong duality theory, the nonlinear model is transformed into a linear robust equivalent model. Finally, GUROBI software is used for numerical calculation and analysis. The results suggest the following: carbon trading policies have a carbon abatement effect; with a decrease in the carbon emissions cap and an increase in carbon trading prices, carbon emissions undergo a ladder-like downward trend; uncertain fluctuations in freight units will influence the optimal decision-making patterns of enterprises; and making more vehicles available will reduce carbon emissions. The government should set a reasonable carbon emissions cap according to market conditions. Enterprises could adopt robust control parameters on the basis of their decision-making preferences and consider the impact of carbon trading policy in formulating and adjusting an optimal decision-making scheme.

A New Hill Climbing Maximum Power Tracking Control for Wind Turbines With Inertial Effect Compensation

Finding and tracking maximum power point are two important dynamics in the control of variable-speed wind turbines since they determine the efficiency of wind turbines. The conventional hill climbing possesses the problems of wrong directionality and low performance since it does not take the inertial effect into account. In this paper, a novel hill climbing method is proposed by considering the inertial effect to solve these problems. Besides, employing the exact model knowledge of the generator in the maximum power tracking control deteriorates the efficiency considerably; therefore, it is required to design a parameter independent and robust control system if possible. Thus, the third-order super-twisting sliding mode and continuous integral sliding mode controllers are designed for the control of generator and grid-side converters to track the maximum power trajectory accurately, and they are compared to each other for the chattering in experimental results. A comparison is also performed between the conventional and proposed hill climbing methods based on the captured energy from the wind. Experimental results, with a wind turbine emulator, demonstrate that the proposed hill climbing method relaxes the wrong directionality and sluggish performance of the conventional one.

Tuning Multi-Objective Evolutionary Algorithms on Different Sized Problem Sets

Multi-Objective Evolutionary Algorithms (MOEAs) have been applied successfully for solving real-world multi-objective problems. Their success can depend highly on the configuration of their control parameters. Different tuning methods have been proposed in order to solve this problem. Tuning can be performed on a set of problem instances in order to obtain robust control parameters. However, for real-world problems, the set of problem instances at our disposal usually are not very plentiful. This raises the question: What is a sufficient number of problems used in the tuning process to obtain robust enough parameters? To answer this question, a novel method called MOCRS-Tuning was applied on different sized problem sets for the real-world integration and test order problem. The configurations obtained by the tuning process were compared on all the used problem instances. The results show that tuning greatly improves the algorithms’ performance and that a bigger subset used for tuning does not guarantee better results. This indicates that it is possible to obtain robust control parameters with a small subset of problem instances, which also substantially reduces the time required for tuning.

Parametric Robust Control of the Multivariable 2 × 2 Looper System in Steel Hot Rolling: A Comparison between Multivariable QFT and H∞

Two robust mutlivariable controllers, H∞ and a decentralized quantitative feedback theory (QFT), are designed in the frequency domain for the 2 × 2 looper system in a steel hot rolling mill to keep stability in the presence of parametric uncertainties. The H∞ controller is designed by using the mixed sensitivity approach, while the multivariable decentralized QFT is designed by the extension of the sequential loop closing method presented elsewhere. Stability robustness conditions are verified in the frequency domain, while simulations in time domain are carried out to evaluate the controllers and compare their performance along with that of proportional + integral (PI) and single input single output (SISO) QFT controllers designed earlier. The QFT controller shows the best balance among the performance indicators analyzed here; however, at the expenses of using higher power in one of the control inputs.

A Hybrid Adaptive Control Strategy for Industrial Robotic Joints

This paper presents a hybrid adaptive approximation-based control (HAAC) strategy for a class of uncertain robotic joints' system. The proposed control structure consists of a robust sliding mode controller and an adaptive approximation-based controller. The robust sliding mode controller is designed by using the super-twisting algorithm, which is a particularly effective method to decrease the chattering caused by the traditional sliding mode control (SMC) and compensate the disturbances. Another improvement of the robust sliding mode controller is that the robust control parameters only subject to the upper bound of the derivative of the external disturbances, rather than choosing a relatively large value. Moreover, the designed adaptive approximation-based controller has the following two distinctive features: 1) the control parameters are designed to be adjusted in real time and 2) the prior knowledge of actual robotic model is not required to be known. These features contribute to compensating the uncertainties. The stability of the closed-loop system is proved by using the Lyapunov theory, and the simulation results demonstrate the effectiveness of the proposed control method. Finally, the proposed HAAC could apply in the experiments of industrial robotic joints' system.

Robust optimization based optimal chiller loading under cooling demand uncertainty

Optimization of electrical power consumption in multi-chiller system leads to save more energy in building or industrial locations. Also, this optimization problem is one of the most important issues in multi-chiller system. Furthermore, uncertainty modeling of cooling demand is necessary because of variation in cooling demand should be considered. Therefore, this work proposes a robust optimization approach for uncertainty modeling of cooling demand in order to obtain robust chiller loading in the uncertain environment which cooling demand is supplied by multi-chiller system. Minimizing of electrical power consumption in multi-chiller system is considered as objective function. The proposed robust scheduling of multi-chiller system is modeled as non-linear programming which is solved via CONOPT solver under General Algebraic Modeling System (GAMS) optimization software. The proposed optimization model is studied in the deterministic and robust optimization strategies and obtained results are compared with each other. Also, the effects of changes in the robust control parameter are analyzed on optimal chiller loading which decision maker can select the decision without risk as risk-neutral strategy via deterministic method or the most robust decision as risk-averse strategy via robust optimization approach. Comparison results show that capability of proposed approach in the uncertain environment.

Design of Robust Controller for Higher Order Interval System using Differential Evolutionary Algorithm

This paper describes the design of the robust PI/PID controller for the higher order interval system via its reduced order model using the differential evolution (DE) algorithm. A stable reduced interval model is generated from a higher order interval system using the DE in order to minimize the cost and reduce the complexity of the system. This reduced order interval numerator and denominator polynomials are determined by minimizing the Integral Squared Error (ISE) using the DE. Then, using reduced order interval model, a robust PI/PID controller is designed based on the stability conditions for determining robust stability of interval system. Finally, using these stability conditions, a set of inequalities in terms of controller parameters is obtained from the reduced order closed loop characteristic polynomial. Then these inequalities are solved to obtain robust controller parameters with the help of a DE algorithm. The designed, robust controller from the reduced order interval model will be attributed to the higher order interval system. The designed PI/PID controller from our proposed method not only stabilizes the reduced order model, but also stabilizes the original higher order system. The viability of the proposed methodology is illustrated through the numerical example of its successful implementation. The efficacy of the proposed methodology is also evaluated against the available approaches presented in the literature and the results were successfully implemented.

A Short-Term Decision Model for Electricity Retailers: Electricity Procurement and Time-of-Use Pricing

This paper establishes a short-term decision model, based on robust optimization, for an electricity retailer to determine the electricity procurement and electricity retail prices. The electricity procurement process includes purchasing electricity from generation companies and from the spot market. The selling prices of electricity for the customers are based on time-of-use (TOU) pricing which is widely employed in modern electricity market as a demand response program. The objective of the model is to maximize the expected profit of the retailer through optimizing the electricity procurement strategy and electricity pricing scheme. A price elasticity matrix (PEM) is adopted to model the demand response. Also, uncertainty in spot prices is modeled using a robust optimization approach, in which price bounds are considered instead of predicted values. Using a robust optimization approach, the retailer can adjust the level of robustness of its decisions through a robust control parameter. A case study is presented to illustrate the performance of the model. The simulation results demonstrate that the developed model is effective in increasing the expected profit of the retailer and flattening the load profiles of customers.

A Multiobjective Route Robust Optimization Model and Algorithm for Hazmat Transportation

Aiming at route optimization problem of hazardous materials transportation in uncertain environment, this paper presents a multiobjective robust optimization model by taking robust control parameters into consideration. The objective of the model is to minimize not only transportation risk but also transportation time, and a robust counterpart of the model is introduced through applying the Bertsimas-Sim robust optimization theory. Moreover, a fuzzy C-means clustering-particle swarm optimization (FCMC-PSO) algorithm is designed, and the FCMC algorithm is used to cluster the demand points. In addition the PSO algorithm with the adaptive archives grid is used to calculate the robust optimization route of hazmat transportation. Finally, the computational results show the multiobjective route robust optimization model with 3 centers and 20 demand points’ sample studied and FCMC-PSO algorithm for hazmat transportation can obtain different robustness Pareto solution sets. As a result, this study will provide basic theory support for hazmat transportation safeguarding.

Robust optimization for day-ahead market participation of smart-home aggregators

This paper proposes an optimization model to participate in day-ahead energy markets when PV generation, thermal and electro-chemical storage devices are aggregated at the residential level. The model includes uncertainty in energy prices, PV and load; and adjustable robust optimization is used to determine a tractable counterpart of the problem. By means of robust control parameters, solutions with different levels of conservatism can be found and analyzed. In addition, the presented model includes explicit representation of battery degradation by means of special ordered sets. This equivalent cycling aging calculation takes into account the non-linear relation between depth of discharge and total life cycles of the battery by piecewise linearization. Performance analysis shows the advantage of the proposed approach when compared to the deterministic solution in terms of average cost and risk. For the analyzed real-life test system, the robust formulation achieves cost reduction of up to 5.7% and standard deviation decreases as much as 36.4%.