Standard Control Design Research Articles

Unified Sufficient Conditions for Predefined-Time Stability of Non-Linear Systems and Its Standard Controller Design

This paper presents a unified Lyapunov-based predefined-time stability theorem that includes three sufficient conditions. The standard theoretical analysis method for achieving predefined-time stability of non-linear systems using this theorem is provided within the framework of Lyapunov theory. The developed Lyapunov-based theorem facilitates the establishment of equivalence between the existing Lyapunov theorems concerning predefined-time stability. Furthermore, when the presented sufficient conditions are relaxed, the predefined-time stability conclusion for non-linear systems degenerates into a finite-time one. Consequently, a standard non-singular sliding mode control framework based on the unified Lyapunov-based theorem is developed for a Lagrangian system to ensure its predefined-time stability. Exemplary numerical simulation results are subsequently given, in order to illustrate the convergence behavior of the system states and confirm that the controlled systems are predefined-time stable.

Nonlinear Tank-Level Control Using Dahlin Algorithm Design and PID Control

Liquid-level control in tanks is widely used in various industrial sectors. Due to problems arising from the case that the liquid level is above or below the recommended, the process of its control is of great significance. The proportional integral differential (PID) controller is one of the most widely used controllers in applications that require accuracy and optimal automatic control. In this paper, single and coupled ship fuel tank systems are discussed. In addition, mathematical models and their linearization using two different approaches are presented. The two control approaches are used to maintain the specified liquid level in tanks. The first is based on the design of standard PID controllers, with the application of the Ziegler–Nichols, Takahashi tuning, and Auto-tuning methods. The second approach, proposed by the authors, is based on the application of the Dahlin algorithm. The simple modification of the Dahlin controller, which can avoid the “ringing” of the control signal, is suggested in the paper. Moreover, the lower limit of the decrease in the desired time constant, which ensures the desired behavior of the system, is determined. The comparisons provided for different performance indexes show the advantages of the modified Dahlin algorithm approach compared to the standard PID controllers. Furthermore, the comparison with the literature-known approaches is realized.

Coordinated multi-robot trajectory tracking control over sampled communication

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is pre-computed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain k and sampling period T. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance.

Robust attitude control of a quadrotor unmanned aerial vehicles using optimized disturbance observer

AbstractThis article proposes a method of realizing robust attitude stabilization control of a quadrotor UAV using the disturbance observer (DOB), where Q–filter is optimally designed considering performances of attenuating disturbance and estimation noise, and robust stability against parameter variations and sampling duration delay due to discrete time control in microcontroller. Disturbance rejection performance mainly depends on the bandwidth determined by cut‐off frequency of DOB's Q–filter. However, extension of the Q–filter's bandwidth must be restricted due to the requirement of robust stability against parameter uncertainty and sampling duration delay in onboard microcontroller for flight control of quadrotor. In order to optimize the disturbance rejection performance under the restriction of bandwidth, an norm minimization problem is defined considering the frequency bands of disturbance and noise. The optimization problem is transformed into standard control design problem by pseudo loop factorization method so as to resolve the structural constraint of Q–filter. Then, stability of the discrete time system configured by digital controller is tested in relation with the time constant of the designed DOB's Q–filter under different inertia moment values. The comparisons between simulation results by different control methods validate that the robust control method using proposed DOB provides a better performance of disturbance attenuation than that using conventional DOB.

Machine Learning for Modeling and Control of Industrial Clarifier Process

In sugar production, model parameter estimation and controller tuning of the nonlinear clarification process are major concerns. Because the sugar industry’s clarification process is difficult and nonlinear, obtaining the exact model using identification methods is critical. For regulating the clarification process and identifying the model parameters, this work presents a state transition algorithm (STA). First, the model parameters for the clarifier are estimated using the normal system identification process. The STA is then utilized to improve the accuracy of the system parameters that have been identified. Metaheuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and State Transition Algorithm are used to evaluate the most accurate model generated by the algorithms. By capturing the principal dynamic features of the process, the clarifier model produced from State Transition Algorithm (STA) acts more like the actual clarifier process. According to the findings, the controllers provided in this paper may be used to achieve greater performance than the standard controller design during the control of any nonlinear procedure, and STA is extremely helpful in modeling a nonlinear process.

Convergence of coprime factor perturbations for robust stabilization of Oseen systems

<p style='text-indent:20px;'>Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard robust controller designs can compensate small uncertainties if they can be qualified as a coprime factor perturbation of the plant. We show that for the linearized Navier-Stokes equations, a linearization error can be expressed as a coprime factor perturbation and that this perturbation smoothly depends on the size of the linearization error. In particular, improving the linearization makes the perturbation smaller so that, eventually, standard robust controller will stabilize the system.</p>

Velocity-sensorless proportional–derivative trajectory tracking control with active damping for quadcopters

The proposed observer-based control mechanism solves the trajectory tracking problem in the presence of external disturbances with the reduction in sensor numbers. This systematically considers the quadcopter nonlinear dynamics and parameter and load variations by adopting the standard controller design approach based on a disturbance observer (DOB). The first feature is designing first-order observers for estimating the velocity and angular velocity error, with their parameter independence obtained from the DOB design technique. As the second feature, the resultant velocity observer-based control action including active damping and DOBs secures first-order tracking behavior for the position and attitude (angle) loops through pole zero cancellation, thereby forming a proportional–derivative control structure. Closed-loop analysis results reveal the performance recovery and steady-state error removal properties in the absence of tracking error integrators. The numerical verification confirms the effectiveness of the proposed mechanism using MATLAB/Simulink.

Offset-free IMC with generalized disturbance models

Integral action is an essential component for offset-free response in many feedback control systems. Standard internal model control design rules ensure an offset-free response for open-loop stable plants. In this paper a linear feedback control structure is proposed that comprises an observer using an augmented plant model, state estimate feedback and disturbance estimate feedback. This allows internal model control design principles to be applied to unstable and marginally stable plants. Conditions are given for both nominal internal stability and offset-free action even in the case of plant-model mismatch. The Youla parameterization is recovered as a limiting case with reduced-order observers. The design is illustrated on a large scale non-square model with marginally stable dynamics.

A sliding-mode based controller for trajectory tracking of perturbed Unicycle Mobile Robots

In this work a tracking robust algorithm for the perturbed kinematic model of an Unicycle Mobile Robot (UMR) is proposed. The control design is based on the well-known first order sliding mode control approach, with a modification that helps to reduce the chattering effect. This strategy takes into account perturbations and consider any admissible (with respect to the nonholonomic constraints) smooth reference trajectory, ensuring the convergence of the tracking error dynamics to the origin asymptotically. The resulting control input is a discontinuous switched function. Its implementability is validated through experiments using a QBot2 and compared with standard well-established control design methods for this problem.

Finite-time H∞ control for a chaotic finance system via delayed feedback

ABSTRACTThis paper is concerned with the finite-time control problem for a chaotic finance system subject to energy-bounded external disturbance via delayed feedback controller. Based on an augmented Lyapunov-like functional, the Wirtinger-based inequality and the novel finite-time boundedness analysis approach, a delay-dependent sufficient condition is proposed in terms of linear matrix inequalities such that the closed-loop error system is finite-time bounded with a prescribed performance level. By simple modification, the sufficient condition based on the standard control design is also obtained. Finally, simulation results are given to demonstrate the effectiveness and advantages of our proposed results.

Stabilization and analytical tuning rule of double-loop control scheme for unstable dead-time process

The presence of unstable dead-time systems in process plants often leads to a daunting challenge in the design of standard PID controllers, which are not only intended to provide close-loop stability but also to give good performance-robustness overall. In this paper, we conduct stability analysis on a double-loop control scheme based on the Routh-Hurwitz stability criteria. We propose to use this unstable double-loop control scheme which employs two P/PID controllers to control first-order or second-order unstable dead-time processes typically found in process industries. Based on the Routh-Hurwitz stability necessary and sufficient criteria, we establish several stability regions which enclose within them the P/PID parameter values that guarantee close-loop stability of the double-loop control scheme. A systematic tuning rule is developed for the purpose of obtaining the optimal P/PID parameter values within the established regions. The effectiveness of the proposed tuning rule is demonstrated using several numerical examples and the result are compared with some well-established tuning methods reported in the literature.

Design of an embedded inverse-feedforward biomolecular tracking controller for enzymatic reaction processes.

Feedback control is widely used in chemical engineering to improve the performance and robustness of chemical processes. Feedback controllers require a 'subtractor' that is able to compute the error between the process output and the reference signal. In the case of embedded biomolecular control circuits, subtractors designed using standard chemical reaction network theory can only realise one-sided subtraction, rendering standard controller design approaches inadequate. Here, we show how a biomolecular controller that allows tracking of required changes in the outputs of enzymatic reaction processes can be designed and implemented within the framework of chemical reaction network theory. The controller architecture employs an inversion-based feedforward controller that compensates for the limitations of the one-sided subtractor that generates the error signals for a feedback controller. The proposed approach requires significantly fewer chemical reactions to implement than alternative designs, and should have wide applicability throughout the fields of synthetic biology and biological engineering.

Robust Stability for Multiple Model Adaptive Control: Part I—The Framework

An axiomatic framework providing robust stability and performance bounds for a wide class of Estimation based Multiple Model Switched Adaptive Control (EMMSAC) algorithms is developed. The approach decouples development of both the atomic control designs and the estimation processes thus permitting the usage of standard controller design and optimization approaches for these components. The framework is shown to give tractable algorithms for MIMO LTI plants, and also for some classes of nonlinear systems (for example, an integrator with input saturation). The gain bounds obtained have the key feature that they are functions of the complexity of the underlying uncertainty as described by metric entropy measures. For certain important geometries, such as a compact parametric uncertainties, the gain bounds are independent of the number of plant models (above a certain threshold) which are utilized in the implementation. Design processes are described for achieving a suitable sampling of the plant uncertainty set to create a finite candidate plant model set (whose size is also determined by a metric entropy measure) which achieves a guaranteed robustness/performance.

Control with Constraints for Multivariable Objects with Time Delay

Methods for parametric design of standard controllers for multivariable dynamic objects with time delay are presented. This methods enable approximate control quality optimization with various criteria in the case of interconnected and multivariable plant with control constraints. Adaptive tuning algorithm for standard controller adjustment is presented. The study presents a software prototype for automated controller design.

Creativity and heuristics in process control engineering

We study the relationship between heuristics and standard tool application in the design of process control systems. This relationship is illustrated by classical control history examples. Features of modern engineering objects are highlighted that challenge classical control approach and leave substantial space for creative solutions. We focus on inevitable heuristics in control design for modern complex process systems. The study suggests new systematic approach to heuristic control design. The approach is based on simplification technique and follow three steps. First, certain assumptions (e.g. negligible nonlinearity or dynamic behavior) help to develop the simplified model and problem setup. Second, standard control design is performed on this reduced model. Third, the perturbation theory methods help to find corrections to the obtained control to cope with the real plant. Special attention is given to the paradigm of concurrent (or integrated) plant and control design. The study suggests finding a proper compromise between investments in the process and its control. Several cement manufacturing process examples demonstrate that this method can generate better effect comparing to autonomous approach.

A Novel Instructional Approach to the Design of Standard Controllers: Using Inversion Formulae

This paper describes a range of design techniques for standard compensators (Lead-Lag networks and PID controllers) that have been applied to the teaching of many undergraduate control courses throughout Italy over the last twenty years, but that have received little attention elsewhere. These techniques hinge upon a set of simple formulas—herein referred to as Inversion Formulae —for the computation of the parameters of the controller as functions of the typical specifications of steady-state performance, stability margins, and crossover frequency.

Control design pattern based on safety logical constraints for manufacturing systems: application to a palletizer

This paper presents an original approach for safe controller design for manufacturing systems controlled by PLC (Programmable Logic Controller). In this work, manufacturing systems are considered as Discrete Event Systems (DES) with logical Inputs (sensors) and logical Outputs (actuators). The proposed approach, which separates the functional control part from the safety control part, is easy to implement and ensures that the designed controller is safe. The methodology is based on the use of safety constraints in order to get a permissive safe controller which can be validated off line by model-checking. This controller is then constrained by functional constraints. The approach is illustrated with a palletizer simulated process using the ITS PLC software from the Real Games Company (www.realgames.pt). The control algorithm is presented and allows resulting in a safe control using a standard control design pattern, may be simpler than a conventional approach based on a complete specification in GRAFCET (IEC 60848) that does not distinguish the functional aspect from the safety aspect. This approach presents interesting perspectives like the management of several operating modes linked to a Manufacturing Execution System (MES) or the manual modes through Human-Machine Interfaces (HMI) or Supervisory Control and Data Acquisition (SCADA) systems.

Robust nonlinear HVAC systems control with evolutionary optimisation

Purpose – The purpose of this research is to design a robust high-performance nonlinear multi-input multi-output heating, ventilation and air conditioning (HVAC) system controller for temperature and relative humidity regulation. Buildings are complex systems which are subjected to many unknown disturbances. Further complicating the control problem is the fact that, in practice, buildings and their systems have static nonlinearities such as power saturation that make stability difficult to guarantee. Therefore, in order to overcome these issues, a control system must be designed to be robust (performance insensitive) against uncertainties, static nonlinearities and effectively respond to unknown heat load and moisture disturbances. Design/methodology/approach – A state of the art nonlinear inverse dynamics (NID) technique is combined with a genetic algorithm (GA) optimisation scheme in order to improve robustness against uncertainty in the system's modelling assumptions. The parameter uncertainty problem is addressed by optimising the control system parameters over a specified range of uncertainty. The NID control structure provides further robustness with effective disturbance handling and a stability criteria that holds in the presence of actuator saturation. Findings – The proposed method delivers significantly more energy efficient performance whilst achieving improved thermal comfort when compared with a current industry standard HVAC controller design such as proportional-integral-derivative. The expected excellent response to disturbances is also demonstrated. Research limitations/implications – This method can easily be extended to account for other parameters with a specified uncertainty range. Practical implications – This research presents a method of optimised NID controller design which can be easily implemented in real HVAC controllers of building energy management systems with a high degree of confidence to provide high levels of thermal comfort whilst significantly reducing energy usage. Originality/value – A novel HVAC optimised NID control strategy using the robust inverse dynamics estimation feedback control topology with GA optimisation for improved robustness and tuning over a range of parameter uncertainty is described, designed and its performance benefits shown through simulation studies.

Control of differential linear repetitive processes using strong practical stability and ℋ∞ disturbance attenuation

Repetitive processes have a 2D systems structure and therefore standard control theory and design algorithms are not applicable. This article develops new algorithms for differential processes to achieve stabilisation together with a prescribed level of disturbance attenuation as measured by an H ∞-norm. There are several physically motivated definitions of stability for repetitive processes and in this article the interest is in strong practical stability.

Fuzzy Adaptive Hysteresis Band Current Controller for Solar Photovoltaic Inverter

Photovoltaic inverters are important solar energy application. This paper presents a novel Fuzzy Adaptive Hysteresis Current Controller to control the inverter, used in the non-linear time-variant solar photovoltaic cell. The proposed controller has the advantages of both fuzzy as well as adaptive controller. It is capable of reducing the total harmonic distortion and to provide acceptable switching frequency. The mathematical model of Photovoltaic array is developed using the Newton’s method using the parameter obtained from a commercial photovoltaic data sheet under variable weather conditions, in which the effect of irradiance and temperature are considered. The modeled Photovoltaic array is interfaced with DC-DC boost converter, AC-DC inverter and load. A DC-DC boost converter is used to step up the input DC voltage of the Photovoltaic array while the DC-AC single-phase inverter converts the input DC comes from boost converter into AC. The performance of the proposed controller of inverter is evaluated through MATLAB-Simulation. Unlike standard adaptive controller designs, this adaptive fuzzy controller does not require an explicit mathematical model of the system. The results obtained with the proposed algorithm are compared with those obtained when using conventional fixed hysteresis current controller for single-phase photovoltaic inverter in terms of THD and switching frequency.