Large Parameter Uncertainties Research Articles

Control method and applications of robust trajectory linearization via nonlinear differentiators

Considering the lack of enough robustness against uncertainties in conventional trajectory linearization control( TLC) method,an improved robust control method was proposed,based on the design principle of nonlinear differentiators. Firstly,via introducing the concept of second-order linear differentiator( SOLD),it was indicated that peaking phenomenon which was similar with using high-gains in SOLD would emerge during the transient profile of differentiation of the nominal command in the existing TLC. And then,tracking differentiator( TD) was used to produce the nominal command and its derivative,peaking phenomenon was totally eliminated and the ability of adjusting the response speed of closed-loop system under the physical limitations was endowed simultaneously. Secondly,by constructing the desired tracking error dynamics of closed-loop system,the control law of the linear time-varying( LTV) system could be directly obtained,PDspectrum theorem and real time tuning of the time varying bandwidth( TVB) of TLC were both avoided.Meanwhile,by utilizing the non-perturbation form of hybrid differentiator( HD) as the desired error dynamics of closed-loop system,the robustness of the system was thus enhanced. In addition,the boundedness of the tracking error in interference system was proved by Lyapunov theory. Finally,the proposed method was applied to the attitude tracking problem of hypersonic vehicle. The simulation results demonstrate the proposed method can still exhibit better control performance and anti-interference capability even if there exist large uncertainties in the aerodynamic parameters,thus the effectiveness and robustness of the control scheme is validated.

Sensitivity of chemical cement alteration – modeling the effect of parameter uncertainty and varying subsurface conditions

AbstractTo ensure the safety of a CO2 storage site and containment of CO­2 in the subsurface, the integrity of wellbore materials must be maintained. Field and laboratory studies have shown CO2‐induced reactivity of wellbore cement, but these results have to be extrapolated to the extended time span of CO2 storage. Geochemical modeling provides a tool for the prediction of cement alteration; however, large uncertainties in input parameters exist and significant variation in subsurface conditions is expected. This asks for a systematic investigation of the sensitivity of modeled cement alteration towards these factors. In this paper we report PHREEQC simulations of CO2 diffusion into cement and subsequent chemical reactions. The sensitivity of cement alteration toward reaction rates, initial porosity, temperature/mineralogy and flow/no flow conditions were investigated. The base case model indicated that intact cement and tight interfaces between the reservoir and the cement would yield less than 1% porosity change after 300 days of diffusion. For porosity increase or degradation to occur at the cement interface, leaching/flow along the wellbore was required. The sensitivity scenarios yield CO2 penetration depths between 0.3 cm and 1.4 cm after 300 days of diffusion. The maximum was reached for the high porosity (fast diffusion) scenario that facilitates CO2 transport through the cement matrix. The minimum CO2 penetration was for enhanced calcium silicate hydrate (C‐S‐H) decalcification, which increases calcite precipitation, CO2 consumption, and hence decelerates CO2 penetration. This is related to high temperatures (and more crystalline C‐S‐H) or to higher kinetic rate constants used. © 2015 Society of Chemical Industry and John Wiley & Sons, Ltd

Bi-directional risk assessment in carbon capture and storage with Bayesian Networks

The complex system required for carbon capture and storage (CCS) encompasses numerous sub-systems with inter-dependencies and large parameter uncertainties that propagate throughout the system. Exploring and understanding these inter-dependencies and uncertainties is invaluable for developing robust risk information. Bayesian Networks (BN), a decision support tool, are being increasingly used in the broader risk assessment community and show promise for use in CCS. BNs explore the dependencies and uncertainties within a system and have the potential to provide a better understanding of risk than more traditional tools such as logic trees or other less integrated approaches. Working with experts from within the Cooperative Research Centre for Greenhouse Gas Technologies (CO2CRC), we have developed a generic BN structure for the storage sub-system of CCS which can be used to guide the development of BNs for other CCS applications and for use in both diagnostic and predictive analysis. This bi-directionality provides one of the more important benefits of BNs; it allows for (1) traditional bottom-up risk assessment where the likely consequences based on the expected state of the system can be calculated and also (2) top-down, or outcome oriented risk, where the state of the system leading to a particular outcome, such as the likelihood of 2% leakage in 1000 years, is determined. This allows for a comprehensive sensitivity analysis which highlights important contributors to the risk and also where additional knowledge may benefit the project and reduce uncertainty. A robust expert elicitation procedure, for both the development of the network structure and the determination of event probabilities, is an integral part of the use of any such BN tool in CCS. Finally, we show the direct application of a smaller CCS BN by the CO2CRC.

Synthesis of multiple model switching controllers using [formula omitted] theory for systems with large uncertainties

The switching based control is an effective way to handle systems with large and fast varying uncertainties. Many conventional methods, however, do not use robust controllers to stabilize each model, and thus need a large number of controllers to ensure the stability of systems with large uncertainties. Under the structure of supervisory control, this paper presents a robust multiple model switching control (RMMSC) method using H∞ control for MIMO linear systems with large parametric uncertainty. The proposed method uses H∞ controller to maximize the stability region of each model with uncertainties, and thus to significantly reduce the number of candidate controllers. The candidate controllers are designed by using linear matrix inequality (LMI), and an exponentially decaying switch index is proposed to select the proper controller by estimating the system norm of each model uncertainty. Using such switch index, the closed-loop control system is then equivalent to a switching system with smaller uncertainty whose system norm can be predefined by designers. The robust stability under arbitrary switching conditions is proven by the small gain theorem; and for slow switching conditions, the acceptable dwell time for stability is analyzed and presented. The effectiveness of this method is demonstrated with the second order inertial system with large model uncertainties.

Optimal design of a robust discrete parallel FP+FI+FD controller for the Automatic Voltage Regulator system

Abstract The purpose of this paper is to design a good tracking controller for the generator Automatic Voltage Regulator (AVR) system. A fuzzy logic-based controller that is called Fuzzy P + Fuzzy I + Fuzzy D (FP + FI + FD) controller has been designed optimally and applied to AVR system. In the proposed method, optimal tuning of controller parameters is very important to achieve the desired level of robust performance. Thus, a hybrid of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) (HGAPSO) technique has been used to find a better fuzzy system control. The motivation for using this hybrid method is to increase disturbance rejection effort, reduce fuzzy system efforts and take large parametric uncertainties into account. The developed FP + FI + FD control strategy leads to a flexible controller with simple structure that is easy to implement. The simulation results have been compared with the conventional Proportional–Integral–Derivative (PID) and fuzzy PID controllers. Three cases of simulation have been performed, case 1: comparing the tracking capability of the controllers, case 2: comparing the disturbance rejection capability of the controller and case 3: evaluating the performance of the controllers assuming that amplifier and exciter system parameters have 50% uncertainty. The simulation results shows that the proposed parallel FP + FI + FD controller has good performance from the perspective of overshoot/undershoot, settling time, and rise time in comparison with both conventional and fuzzy PID controllers.

Control system design for the mock ventricle with aortic and mitral valve resistance uncertainty

Reproducing the native left ventricle’s contractile behavior is the key ingredient for the mock cardiovascular circulatory system. It can be achieved by controlling either mock ventricle’s pressure or volume so that it could follow the reference signal calculated by the Elastance waveform. However, due to inherent uncertainties of the parameter values of the mock ventricle, such as check valve resistance, it is difficult to achieve high quality control performance. In this paper, we present an adaptive control scheme to overcome this parameter value uncertainty and to achieve high quality control performance. To the best knowledge of the author, it is the first report that reproduces the mock ventricle pumping dynamics precisely considering the resistance of the aortic/mitral check valves and overcoming the uncertainty of them. In the paper, along with the detailed design of the controller, rigorous proof of the stability and the convergence is presented as well. Computer simulation was performed using an electrical-analog cardiovascular circulatory system model and a piston pump mock ventricle model. Results confirmed that adaptive control achieved almost perfect tracking performance in spite of large parameter uncertainty and high bandwidth dynamic characteristics of the mock ventricle. Performance comparison verified the superiority of the adaptive controller over PID controllers.

ENHANCED IMC-PID CONTROLLER DESIGN WITH LEAD-LAG FILTER FOR UNSTABLE AND INTEGRATING PROCESSES WITH TIME DELAY

In this article, a design method for a PID controller is proposed based on IMC principles for control of open loop integrating and unstable first-order processes with time delay. The design is based on H2 optimal closed-loop transfer function for set point changes and step input disturbances. The method has one tuning parameter, and systematic guidelines are provided for the selection of this tuning parameter based on peak value of the sensitivity function. The performance of the designed controller is verified on various integrating and unstable processes, and it is observed that nominal and robust control performance is achieved with the proposed design method. Improved closed-loop performance was obtained when compared to other methods recently reported in the literature. Further, the proposed method provides good closed-loop performance even when there are large uncertainties in the process parameters.

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

In this article, a new methodology based on fuzzy proportional‐integral‐derivative (PID) controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm (GA) and particle swarm optimization (PSO) techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions (MF) are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78–93, 2015

RFID-Based Mobile Robot Trajectory Tracking and Point Stabilization Through On-line Neighboring Optimal Control

In this manuscript, we propose an on-line trajectory-tracking algorithm for nonholonomic Differential-Drive Mobile Robots (DDMRs) in the presence of possibly large parametric and measurement uncertainties. Most mobile robot tracking techniques that depend on reference RF beacons rely on approximating line-of-sight (LOS) distances between these beacons and the robot. The approximation of LOS is mostly performed using Received Signal Strength (RSS) measurements of signals propagating between the robot and RF beacons. However, an accurate mapping between RSS measurements and LOS distance remains a significant challenge and is almost impossible to achieve in an indoor reverberant environment. This paper contributes to the development of a neighboring optimal control strategy where the two major control tasks, trajectory tracking and point stabilization, are solved and treated as a unified manner using RSS measurements emitted from Radio Frequency IDentification (RFID) tags. The proposed control scheme is divided into two cascaded phases. The first phase provides the robot's nominal control inputs (speeds) and its trajectory using full-state feedback. In the second phase, we design the neighboring optimal controller, where RSS measurements are used to better estimate the robot's pose by employing an optimal filter. Simulation and experimental results are presented to demonstrate the performance of the proposed optimal feedback controller for solving the stabilization and trajectory tracking problems using a DDMR.

Guided Rocket Control System Design Based on Discrete-Time Adaptive Sliding Mode

The discrete-time adaptive sliding mode controller for spinning rockets in presence of parameter error is proposed. Considering the nonlinear characteristics for the system, input-output feedback linearization is utilized to transform the system model into two standard form subsystems. Then a discrete-time controller for guided rockets is designed based on discrete-time sliding mode control principle. In order to diminish the switch width of the discrete-time sliding mode system corresponding to parameter error, a dead-zone parameter adaptive law is designed. The stability of the uncertain closed-loop system is proved by Lyapunov theory, which make the controller have high robustness. Simulation result indicates that the proposed controller is robust with respect to large aerodynamic parametric uncertainty, and has excellent dynamic tracking performance.

Direct adaptive actuator failure compensation control: a tutorial

A resilient control system is expected to have the capacity to restore the desired system stability and tracking performance in the presence of uncertain system faults such as actuator failures. While redundant actuators are used for actuator failure accommodation, uncertain actuator failures, whose failure time, pattern, and values may be unknown, can bring new challenges to feedback control design as such uncertain failures can introduce large structural, parametric, and actuation uncertainties. Two technical issues are associated with using redundant actuators: how redundant actuators should be coordinated for effective failure compensation control, and how a feedback control law should be adaptively designed to compensate uncertain actuator failures. In this paper, we present a tutorial on direct adaptive failure compensation-based solutions to these issues for different types of control systems: state tracking using state feedback, output tracking using state feedback or output feedback, for linear, non-linear, and multi-input multi-output systems. We give an overview on such adaptive actuator failure compensation designs which have special capacities to effectively use actuation redundancy to handle uncertain actuator failures, using either direct or indirect adaptive control approaches for direct adaptive actuator failure compensation without explicit failure detection, for fast and effective failure accommodation.

Adaptive Consensus Control of Multi-Agent Systems with Large Uncertainty and Time Delays

A weighted multi-model adaptive control (WMMAC) method is proposed to achieve consensus of multi-agent system with large parameter uncertainty and communication delays, in which control is adopted as local control strategy to deal with smaller parameter uncertainty. Moreover a simple and effective weighting algorithm is adopted to assign weights for each local controller, based on which the global control law is obtained as a weighted sum of all the local control at each time instant. The simulation results demonstrate the effectiveness of the proposed method.

Optimal fuzzy load frequency controller with simultaneous auto-tuned membership functions and fuzzy control rules

In this paper, an auto-tuned fuzzy load frequency controller (FLFC)-based articial bee colony (ABC) algorithm is developed to quench the deviations in the frequency and tie-line power due to load disturbances in an interconnected power system. Optimal tuning of membership functions (MFs) and fuzzy control rules is very important to improve the design performance and achieve a satisfactory level of robustness for a particular operation. In this work, to reduce the fuzzy system design eort and take large parametric uncertainties into account, a new systematic and simultaneous tuning method is developed for designing MFs and fuzzy rules. For this, the designing problem is restructured as an optimization problem and the ABC algorithm is employed to solve it. This newly developed method provides some advantages such as a exible controller with a simple structure and easy algorithm. For the purpose of the proposed method's evaluation, the designed controller is applied to a 2-area power system with considerations regarding governor saturation and the results are compared to the one obtained by a classic proportional-integral controller. Simulation results show better operation and improved system parameters, such as the settling time and step response rise time, using the proposed approach, in the presence of system parameter variations.

Path Following of Autonomous Vehicle in 2D Space Using Multivariable Sliding Mode Control

A solution to the path following problem for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty is proposed. For a general class of vehicles moving in 2D space, we demonstrated a path following control law based on multiple variable sliding mode that yields global boundedness and convergence of the position tracking error to a small neighborhood and robustness to parametric modeling uncertainty. An error integration element is added into the “tanh” function of the traditional sliding mode control. We illustrated our results in the context of the vehicle control applications that an underwater vehicle moves along with the desired paths in 2D space. Simulations show that the control objectives were accomplished.

Non-certainty equivalence adaptive tracking control for hypersonic vehicles

The design of a novel non-certainty equivalence adaptive control system for hypersonic vehicles is presented, based on the immersion and invariance (I&I) theory. The interest here is to achieve a robust trajectory tracking of the reference commands in spite of large parameter uncertainties. The architecture of the whole control system is constructed by decomposing the vehicle model into the velocity subsystem and the flight path angle (FPA) subsystem. A backstepping design procedure is applied to the cascaded FPA subsystem. Three non-certainty equivalence controllers, each consisting of a control module and an I&I based parameter estimator, are designed respectively for the velocity subsystem and the two steps of the FPA subsystem, which suffer from parameter uncertainties. First-order filters are implemented in all the design of the three controllers to avoid solving certain partial differential inequality in I&I adaptive control. Stability analysis is presented using Lyapunov theory and asymptotical convergence of the tracking errors to zero is accomplished. Simulation results with rapid and accurate command tracking show the effectiveness and robustness of the proposed control system.

Robust estimation of linear switched systems with dwell time

A covariance analysis is introduced for linear switched systems with dwell time constraints. This analysis reduces the conservatism that is encountered in the analysis of switched systems without dwell. An upper-bound on the covariance of the states of the switched system is obtained that depends on the switching signal. The obtained results are then applied to filtering problems in switched systems with driving and measurement with noise signals, where general type filters are considered. These filters assume that the switching signal is not given a priori but it is available in real time. In order to overcome the deficiencies of the standard approaches to robust filtering of systems with large parameter uncertainties, we also present a new method of estimation for non-switched, exponentially stable, uncertain systems. We divide the uncertainty region into several overlapping sub-regions where, for each of these sub-regions, a separate filter should be assigned. The resulting system is then treated as a switched system that switches between the sub-regions. The theory developed is demonstrated by two simple examples. In the first, a filtering solution is obtained for a switched system with error variance that is very close to the best achievable result for a single subsystem. The second example demonstrates the benefit, from the estimation error point of view, of dividing the uncertainty polytope of an uncertain non-switched system into two overlapping subpolytopes.

Load Frequency Control in Deregulated Power System using Fuzzy C-Means

this paper, a fuzzy C-means controller proposed to the generation of optimal fuzzy rule base by Fuzzy C - Means clustering technique (FCM) for load frequency control in deregulated environment. The phase-plane plot of the inputs of the fuzzy controller is utilized to obtain the rule-base in the linguistic form. The proposed method is tested on a two-area power system with different contracted scenarios under various operating conditions. The results of the proposed controller are compared with the fuzzy PID controller and conventional PID controller to illustrate its robust performance. These comparisons demonstrate the superiority and robustness of the proposed controller. and/or similarity functions. These groups can later be used directly in selecting appropriate fuzzy set boundaries. Also the algorithms can automatically combine similar objects (data entries) in order to reduce the global size of the data. Finally the clustering algorithms let us easily detect potential outliers (clusters containing one or very few data entries). This feature is taken into consideration to design a decentralized fuzzy controller. The phase plane plot of the input space is formed into clusters with the cluster centers is formed to obtain the required rule-base of the proposed fuzzy controller(22).The proposed control has simple structure and does not require an accurate model of the plant. Thus, its construction and implementation are fairly easy and can be useful for the real world complex power system. The proposed method is applied to a two-area restructured power system as a test system. The results of the proposed Fuzzy-C-means controller are compared with the Fuzzy PID (FPID) controller (18) and conventional PID controller (9) through some performance indices in the presence of large parametric uncertainties and system nonlinearities under various area load changes

Adaptive predictive control of periodic non‐linear auto‐regressive moving average systems using nearest‐neighbour compensation

Many practical non-linear systems can be described by non-linear auto-regressive moving average (NARMA) system models, whose stabilisation problem is challenging in the presence of large parametric uncertainties and non-parametric uncertainties. In this work, to address this challenging problem for a wide class of discrete-time NARMA systems, in which there are uncertain periodic parameters as well as uncertain non-linear part with unknown periodic time delays, we develop adaptive predictive control laws using the key ideas of `future outputs prediction' and `nearest-neighbour compensation', among which the former is carried out to overcome the non-causalness problem and the latter novel idea is proposed to completely compensate for the effect of non-linear uncertainties as well as unknown time delays. To achieve the desired asymptotic tracking performance in the presence of semi-parametric uncertainties with time delays, an ` n -step parameter update law' is first designed, based on which an `one-step update law' is then elaborately constructed to obtain smoother closed-loop signals. This study in general develops a systematic adaptive control framework for periodic NARMA systems with guaranteed boundedness stability and asymptotic tracking performance, which are established by rigorous theoretic proof and verified by simulation studies.

Robust control design for automatic regulation of blood pressure

The problem of automatic administration of vasoactive drugs to a patient can be treated as a regulation problem of a system, which is characterised by large parametric uncertainty, non-Gaussian disturbances and unmodelled dynamics, yet carries strict requirements in terms of robustness and performance. A number of approaches have been proposed in the past to tackle this problem, particularly for the postoperative management of blood pressure in cardiac surgery patients. We describe the design of a robust multiple-model adaptive control (RMMAC) architecture and investigate whether this can overcome some issues observed with earlier methods. Key features of RMMAC are robust optimal controller design using an iterative μ synthesis algorithm and improved system estimation. Simulation results indicate that RMMAC is capable of avoiding transient instability and delivering performance in the face of significant parameter changes over time and large disturbances including non-zero-mean signals. The findings support further research into RMMAC as a potentially viable approach to the design of safer automatic closed-loop drug administration technologies capable of operating under challenging clinical conditions such as may arise in an intraoperative setting.

Robust Control of Linear Systems via Switching

The standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty. In the case where the latter polytope is large, the design may become very conservative. We present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem. Assuming that there is online information on which of the regions the parameters of the system move to, a recently developed method for H∞ design of switched system with dwell time is applied. A Lyapunov Function (LF) in a quadratic form, which is non-increasing at the switching instants, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the L2 -gain of the switched system. The obtained results are used to solve the corresponding robust H∞ state-feedback and static output-feedback control problems.