Robust Performance Specifications Research Articles

Design and parameter tuning of active disturbance rejection control for uncertain multivariable systems via quantitative feedback theory

This paper proposes a new parameter tuning approach for active disturbance rejection control (ADRC) of multi-input multi-output (MIMO) uncertain systems. Firstly, decentralized ADRC (DADRC), dynamic decoupling ADRC (DD-ADRC), and inverted decoupling ADRC (ID-ADRC) are introduced. Three control schemes are uniformly transformed into a two-degree-of-freedom (2DOF) equivalent structure for analysis. Then, a parameter tuning approach based on multivariable quantitative feedback theory (QFT) is proposed to achieve the desired performance. Considering the coupling effects, the QFT performance specifications are reformulated to reduce the conservatism in design, and the closed-loop stability conditions are studied to establish the robust stability performance specification. Finally, the control schemes and the proposed tuning approach are applied to a heat integrated distillation column (HIDiC) process. The effectiveness of the parameter tuning approach is verified, and the respective advantages of the ADRC control schemes are analyzed in parameter tuning and simulations.

Robust control of a forward‐converter active battery cell balancing

AbstractControl of balancing current is important for the safety of battery cells and active cell balancing (ACB) power electronics. This paper presents a method, based on quantitative feedback theory (QFT), for robust control of balancing current despite uncertainties, which exist in the battery cells' and power electronics' dynamical models. A remarkable feature of QFT is its interactive graphical design environment, which gives useful insights for the selection of desired robust stability and performance specifications, controller structure, and parameters tuning. Without loss of generality, this paper describes the QFT‐based balancing current robust control system design for a forward‐converter‐based ACB. This paper also presents an average model of the forward‐converter‐based ACB circuit, operating in more than two modes; a case that has not been addressed in literatures. The effectiveness of the proposed QFT‐based balancing current robust control system is evaluated experimentally.

Robust networ ccontrol of an arm manipulator to time delays

Feedback control systems with network as information channels between sensors and between controllers and actuators, are called Network Control Systems (NCS). Network in the loop makes the analysis and design of a proper controller quite different from the traditional ones. Controllers for MIMO plants with wireless communication channels have different type of problems as to compete for the network resources, losses of data packages and presence of communication delays. This work deals with the problem of delays present in the feedback system. Various methodologies have been proposed to deal with the problem of network induced delays which depends on the nature of the delay as: constant, continuous discrete and random delays, and in MIMO systems independent channel delays This paper deals with design of a robust H∞ controller for a MIMO system with time delays limited to an interval, such as obtain a close loop system satisfy robust stability and robust performance specifications in ample ranges of time delays. The method is applied to a three degree of freedom arm manipulator.

Robust feedback feed-forward PD-type iterative learning control for uncertain discrete systems over finite frequency ranges

This paper proposes a robust feedback feed-forward proportional-derivative type (PD-type) iterative learning control (ILC) scheme for a class of linear discrete systems with polytopic uncertainty over finite frequency ranges. First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman–Yakubovich–Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. Compared with previously established works, the new algorithm is more effective in delivering higher performance and achieving better tracking effect.

First Order Plus Dead Time Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process

Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.

First Order Plus Dead Time (FOPDT) Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process

Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.

Nonlinear robust control of air handling units to improve the indoor air quality &[formula omitted] concentration: A comparison between [formula omitted] & decoupled sliding mode controls

Air-handling units (AHUs) are the installations responsible for the control of temperature and humidity inside a space using the heating, cooling, humidifier and drying air components. In this research, a multivariable nonlinear dynamic model of the AHU with one zone in the VAV (variable air volume) system for working in the summer is considered. The indoor temperature, relative humidity and carbon dioxide concentration are controlled via manipulation of the valve positions of the air flow rate, cold water flow rate and fresh air percent. Due to the complexity and nonlinearity of AHU model and also the existence of various operating points and uncertainty, model uncertainties are included. Then, two effective robust control strategies are designed to achieve the less energy consumption and providing the indoor comfort conditions. For this purpose, the indoor temperature, relative humidity and CO2 concentration are controlled in a desirable manner. In this study, linear optimal robust H∞ technique based on the μ̃-DKiteration algorithm is implemented on nonlinear model. Results are compared with the nonlinear decoupled sliding mode control approach. According to the results, for desired tracking objectives in terms of the robust performance specifications, the sliding-mode controller performs better than the linear optimal robust H∞ controller.

Hierarchical Control Strategy for Maximising Power Conversion in Heaving Wave Energy Converters

This paper considers hierarchical control strategy (HCS) for maximising power conversion between mechanical and electrical powers in heaving wave energy converters. The maximisation conversion were obtained by designing the optimum reference for the buoy This reference were found by relating the mechanical and electrical models of the power-takeoff (PTO) device. A simple look-up table of the intrinsic resistance constant was obtained as function of wave’s significant height and peak frequency. A Robust PID controller was used to track this reference. The PID controller was tuned using complex polynomial stabilisation method to convert the robust performance specification into a set of linear programming problem. The interesting feature of the method is all (not only one) set of PID parameters, which satisfies the robust performance, were found. Finally, the simulation results were presented to verify the control objectives.

Maximising power conversion for heaving point absorbers using a reference‐based control technique

This study considers maximising conversion between the mechanical and electrical powers for heaving point absorbers (HPAs). The objective is implemented by generating the buoy's velocity reference by designing the intrinsic resistance. The authors designed the intrinsic resistance using a rapid procedure involving the mechanical and electrical models of HPAs. The electrical power conversion can be improved by tuning a weighting constant with the constraints on the maximum value of the control force and the power take-off utilisation index. The value of the intrinsic resistance is varied based on irregular sea states, which are characterised by their significant heights and peak angular frequencies. A simple robust proportional-integral-derivative (PID) controller is utilised in the servo feedback control system to follow the velocity reference. The PID controller is designed using the complex polynomial stabilisation to convert the robust performance into a set of linear programming problems. A set of admissible PID controller is obtained to satisfy the robust performance specifications. The authors tested the proposed method in various nominal and perturbation scenarios, and its performance was compared with existing reference and non-reference based HPA control strategies.

An interval-consistency-based hybrid optimization algorithm for automatic loop shaping in quantitative feedback theory design

A computationally efficient method for automatic synthesis of quantitative feedback theory (QFT)-based robust controllers is proposed. The synthesis problem consists of obtaining a fixed structure QFT controller that ensures stability and achieves the performance specifications in the presence of disturbances and parametric uncertainty. The proposed method uses an interval consistency technique (hull consistency HC4) and hybrid optimization. The HC4 method is used to remove inconsistent values, which are not part of the solution in the controller parameter regions. The hybrid part incorporates interval global optimization and nonlinear local optimization methods. The proposed algorithm is illustrated by means of two examples. The first one concerns the longitudinal motion control of an aircraft system (flexible), while the second one describes the experimental study of the position control of the industrial plant emulator setup. The robustness of the designed control system for emulator setup is validated by adding extra weights on the load disk in the presence of disturbances. The experimental results show that the designed controller satisfies the robust performance specifications.

Graphical tuning method for non-linear fractional-order PID-type controllers free of analytical model

The main focus of this paper is on a graphical tuning method of non-linear fractional-order PID (FOPID)-type controllers, i.e. a class of FOPID-type controllers that non-linearly depend on the control parameters, e.g. FO[PI], FO[PD] etc. Firstly, a method is proposed to determine the stabilizing region of non-linear FOPID-type controllers, namely the complete sets of FOPID-type controllers providing stability of the control system. Secondly, two different approaches are proposed to determine the H∞ region of these FOPID-type controllers, namely the complete sets achieving H∞ robust performance specifications. The first approach maps the H∞ constraints into the parameter space by solving a series of non-linear equations. The second approach transforms the original H∞ region problem into simultaneous stabilization of a family of characteristic polynomials. It turns out that these two approaches are both very flexible, and the second approach is more efficient than the former. The main advantage of our proposed graphical tuning method is that the exact mathematical model of the controlled plant is not needed. The stabilizing and H∞ regions can be computed only from the frequency response data of the plant. Finally, numerical and experimental results are presented to demonstrate the proposed graphical tuning method.

Design and Evaluation of a Robust PID Controller for a Fully Implantable Artificial Pancreas

Treatment of type 1 diabetes mellitus could be greatly improved by applying a closed-loop control strategy to insulin delivery, also known as an artificial pancreas (AP). In this work, we outline the design of a fully implantable AP using intraperitoneal (IP) insulin delivery and glucose sensing. The design process utilizes the rapid glucose sensing and insulin action offered by the IP space to tune a PID controller with insulin feedback to provide safe and effective insulin delivery. The controller was tuned to meet robust performance and stability specifications. An anti-reset windup strategy was introduced to prevent dangerous undershoot toward hypoglycemia after a large meal disturbance. The final controller design achieved 78% of time within the tight glycemic range of 80–140 mg/dL, with no time spent in hypoglycemia. The next step is to test this controller design in an animal model to evaluate the in vivo performance.

Flight Control of a Quadrotor under Model Uncertainties

Quadrotor type helicopters continue to grow in popularity for academic research and unmanned aerial vehicle applications. However, the model uncertainties caused by battery voltage drop, payload variation and flight condition change, have rarely been considered in control design. This work proposes a quantitative feedback theory based robust design approach to deal with these uncertainties. By analyzing the rigid body dynamics and aerodynamic forces/moments under different voltages, payloads and flight conditions, we model quadrotor dynamics as a set of linear models with parameter uncertainties, which represent a larger flight envelop than models linearized from hover condition. These model uncertainties, as well as the robust stability requirements and performance specifications of flight control system are then used for designing and tuning the controllers, to perform tradeoff between controller complexity, robust requirements, and performance specifications. We also implemented a prototype system, and conducted a serial of experiments in realtime outdoor flights to evaluate its performance. The results show good, robust, and reliable performances of the designed system in autonomous hovering, takeoff, waypoint navigation and landing flights.

LPV Control for Active Vibration Mitigation in High Stability Space Missions: A Comparative Study

The research work considered in this paper draws expertise from the European Space Agency, Airbus Defence & Space and the IMS laboratory, on mixed active-passive control strategy for mitigating the micro-vibrations induced by the reaction wheels in a flexible spacecraft structure. High frequency disturbances are handled using passive isolation, based on elastomer devices, while an active control strategy is used to mitigate the micro-vibrations, in the low frequency range. The control strategy proposed in this paper, is based on H∞ LPV synthesis and handles robust stability and performance specifications. Different LPV synthesis approaches are also investigated. The results are compared by means of different H∞-oriented criteria and simulation results demonstrate the potential of the proposed methods.

Robust PID controller design using particle swarm optimization-enabled automated quantitative feedback theory approach for a first-order lag system with minimal dead time

This paper presents the design of a robust proportional integral and derivative (PID) controller for a first-order lag with pure delay (FOLPD) model using particle swarm optimization (PSO)-enabled automated quantitative feedback theory (QFT). The plant model considered here can be approximated as a first-order system with a non-minimum phase (NMP) zero. Synthesis of controller for the FOLPD model via manual graphical technique involved in the QFT method is always a challenging and cumbersome task, because an NMP system stabilizes by a small gain. In this paper, a proposal is being presented to automate the loop-shaping phase in the QFT design method to synthesize a robust controller that can undertake the exact amount of plant uncertainty even in the presence of larger uncertainties than those assumed initially and can ensure a proper trade-off between robust stability and tracking performance specifications over the entire range of design frequencies. In this paper,s the PSO technique has been employed to tune the controller automatically,which can significantly reduce the computational effort compared with manual graphical techniques. It has also been demonstrated that this methodology not only automates loop shaping but also improves design quality and, most usefully, improves performance with optimally tuned PID controller in quantitative manner.

Observer‐based adaptive control using multiple‐models switching and tuning

Despite the remarkable theoretical accomplishments and successful applications of adaptive control, this field is not mature enough to solve challenging problems where strict performance and robustness guarantees are required. The needs of an approach that explicitly accounts for robust performance and stability specifications is a critical to the design of practical adaptive control systems. Towards this goal, this study extends the robust adaptive controller using multiple models, switching and tuning to multiple input multiple output and non-linear systems. The use of ‘extended superstability’, instead of superstability, allows us to establish overall performance guarantees and reduce the conservativeness of the resulting closed-loop system. The authors show that under the proposed framework, the output and states remain bounded for bounded disturbances, as a direct consequence of the passivation properties of superstability. The effectiveness of the proposed algorithm is demonstrated in numerical simulations of a non-linear continuous stirred tank reactor.

Robust control of depth of anesthesia based on H∞ design

Abstract This paper presents a case study on the design of a robust controller for the depth of anesthesia (DoA) induced by the drug propofol. This process is represented by a linear model together with a non-parametric uncertainty description that is evaluated using a patient model bank with 20 patients undergoing sedation. By using H∞ methods, the controller is aimed to comply with robust stability and performance specifications for the class of patient models considered. A minimization problem of sensitivity and complementary sensitivity is made to design the controller. The controller that results from this procedure is approximated by a controller with a lower order, that in turn is redesigned in discrete time for computer control application. The resulting controller is evaluated in simulations using a realistic nonlinear model of DoA.

Fractional calculus in 13C separation column control

Controller design for an isotope separation column is recognized as a difficult and challenging problem. The dynamics of the isotope separation process is difficult to model precisely using integer order transfer functions; thus, a fractional order approach is preferred. The objective of this work is to design two different PI controllers—a classical one and a fractional order one—and test their closed loop performance under nominal conditions as well as gain uncertainties. Since the process is represented by a fractional order mathematical model, the simplest approach to design both controllers is based on a frequency specification. For the fractional order of the PI controller and its parameters, the authors solve a system of equations that includes a robust performance specification to gain uncertainties. For the classical PI controller, a traditional tuning algorithm based on phase margin specification is implemented. The simulation results show that both controllers meet the design specifications, with the fractional order PI controller behaving more robustly to plant gain variations.

Automated design of fractional PI QFT controller using interval constraint satisfaction technique (ICST)

In this paper, a fractional-order proportional-integral (FOPI) controller is proposed and designed for a class of nonlinear integer-order (IO) systems. For fair comparison, the proposed FOPI and the traditional integer-order PID (IOPID) controllers are designed following the same set of imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of controller design for the nonlinear IO plant. We also propose a new and efficient method for automated synthesis of a fixed structure Quantitative Feedback Theory (QFT) FO controller. This is achieved by solving QFT quadratic inequalities of robust stability and performance specifications. The controller synthesis problem is posed as interval constraint satisfying problem (ICSP) and solved with interval constraint solver. The main feature of this method is that it guarantees to find all feasible controllers of given structure in the specified search domain. The designed FOPI and the traditional IOPID controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that the designed FO controllers work more efficiently, with improved performance compared with the designed stabilizing IOPID controller.

Classical controller design techniques for fractional order case

This paper presents some classical controller design techniques for the fractional order case. New robust lag, lag-lead, PI controller design methods for control systems with a fractional order interval transfer function (FOITF) are proposed using classical design methods with the Bode envelopes of the FOITF. These controllers satisfy the robust performance specifications of the fractional order interval plant. In order to design a classical PID controller, an optimization technique based on fractional order reference model is used. PID controller parameters are obtained using the least squares optimization method. Different PID controller parameters that satisfy stability have been obtained for the same plant.