Global robust output regulation of multivariable systems with nonlinear exosystem

It is well known that multi‐input, multi‐output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model‐based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non‐harmonic load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & Sons, Ltd.     

Global robust output regulation for a class of multivariable systems

In this paper, we study the global robust output regulation problem for a class of multivariable nonlinear systems. The problem is first converted into a stabilization problem of an augmented system composed of the original plant and an internal model. The augmented system is a multi‐input system containing both dynamic uncertainty and time‐varying static uncertainty. By decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by solving several single‐input control problems via a recursive approach utilizing the changing supply function technique. The theoretical result is applied to the speed tracking control and load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2011 John Wiley & Sons, Ltd.     

Non‐diagonal MIMO QFT controller design reformulation

This paper presents a reformulation of the full‐matrix quantitative feedback theory (QFT) robust control methodology for multiple‐input–multiple‐output (MIMO) plants with uncertainty. The new methodology includes a generalization of previous non‐diagonal MIMO QFT techniques; avoiding former hypotheses of diagonal dominance; simplifying the calculations for the off‐diagonal elements, and then the method itself; reformulating the classical matrix definition of MIMO specifications by designing a new set of loop‐by‐loop QFT bounds on the Nichols Chart, which establish necessary and sufficient conditions; giving explicit expressions to share the load among the loops of the MIMO system to achieve the matrix specifications; and all for stability, reference tracking, disturbance rejection at plant input and output, and noise attenuation problems. The new methodology is applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Copyright © 2008 John Wiley & Sons, Ltd.     

Generalized extended state observer–based repetitive control for systems with mismatched disturbances

A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.     

Optimal rejection of persistent bounded disturbances

In this paper, we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude, but is otherwise arbitrary. The objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance. Mathematically, this corresponds to requiring uniformly good disturbance rejection over all time. Since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used (see [7, sect. 5.6]), the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose L2-norm is small, as is the case with the currently popularH_{infty}theory. The present theory is a natural counterpart to the existing theory of optimal disturbance rejection (the so-calledH_{infty}theory) which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square-integrable and has unit energy. It is shown that the problem studied here has quite different features from its predecessor. Complete solutions to the problem are given in several important cases, including those where the plant is minimum phase or when it has only a single unstable zero. In other cases, procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers.     

Robust Trajectory‐Tracking Control of a PVTOL under Crosswind

This work proposes a robust controller to solve the trajectory‐tracking control problem of planar vertical take‐off and landing (PVTOL) aircraft under crosswind. The controller combines input–output feedback linearization and active disturbance rejection control techniques. The former linearizes the PVTOL dynamics and the latter actively estimates and compensates for the crosswind effects. Numerical simulations assess the effectiveness of the proposed approach.     

A quantitative feedback solution to the multivariable tracking error problem

This paper introduces a novel solution for the multi‐input multi‐output (MIMO) quantitative feedback theory control design problem with tracking error specifications. Looking for a minimum controller overdesign, the technique finds new controller quantitative feedback theory bounds based on necessary and sufficient conditions for the existence of suitable associated prefilter matrix elements. It improves previous approaches to the subject and includes (i) the possibility of a free selection of the nominal plant, (ii) a less conservative application of the Schwartz inequality to decisively reduce the potential controller overdesign, (iii) a methodology to design independently the elements of the prefilter matrix, and (iv) a scope of application to both sequential and nonsequential MIMO controller design methods. The benefits of the new control design technique are illustrated by means of two examples. The first one, a standard 2 × 2 MIMO problem, is provided for comparison purposes with previous approaches. The second example, included as a major control challenge, deals with a well‐known demanding distillation column benchmark problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

Decoupling Controller with Disturbance Observer for LTI MIMO Systems

In this paper, a decoupling multivariable control strategy for linear time‐invariant (LTI) multi‐input/multi‐output (MIMO) systems is proposed. The strategy includes a multivariable disturbance observer (MDOB) and a decoupling controller. This MDOB is introduced to improve the system performances when the system encounters severe external disturbances. H₂ optimal scheme is utilized to design the MDOB filter. The controller is developed based on an inverse control method, through which the design process can be simplified. Simulation results certify the effectiveness of the proposed control strategy.     

Optimal design of robust quantitative feedback controllers using random optimization techniques

Quantitative design of robust control systems proposes a transparent and practical controller design methodology for uncertain single-input single-output and multivariable plants. There are several steps involved in the design of such controllers. The main steps involved in the design are template generation, loop shaping and pre-filter design. In the case of multivariable uncertain plants, manipulation of tolerance bounds within the available freedom, for both sequential and non-sequential designs, consideration of template size of next step in sequential design, and the appropriate selection of the nominal transfer function matrices in the equivalent disturbance attenuation design are also crucial steps. In all the quantitative designs, a time-consuming trial-and-error procedure is adapted and a successful compromise between various design requirements is very much dependent on the designer experience and expertise. In this paper, these steps are reformulated in terms of different cost functions, and it is shown that the optimization of these cost functions leads to an optimal design of quantitative controllers, for both single input single output and multivariable plants. This proposes a nonlinear constrained optimization problem that can be easily solved using any of the random optimization techniques. Simulation results are used to show the effectiveness of the proposed method.     

H∞ tracking of linear continuous‐time systems with stochastic uncertainties and preview

The problem of finite‐horizon H_∞ tracking for linear continuous time‐invariant systems with stochastic parameter uncertainties is investigated for both, the state‐feedback and the output‐feedback control problems. We consider three tracking patterns depending on the nature of the reference signal i.e. whether it is perfectly known in advance, measured on line or previewed in a fixed time‐interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. In the state‐feedback case, for each of the above three cases a game theory approach is applied where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy‐bounded disturbance. The problems are solved using the expected value of the standard performance index over the stochastic parameters, where, in the state‐feedback case, necessary and sufficient conditions are found for the existence of a saddle‐point equilibrium. The corresponding infinite‐horizon time‐invariant tracking problem is also solved for the latter case, where a dissipativity approach is considered. The output‐feedback control problem is solved as a max–min problem for the three tracking patterns, where necessary and sufficient condition are obtained for the solution. The theory developed is demonstrated by a simple example where we compare our solution with an alternative solution which models the tracking signal as a disturbance. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust stabilization of linear multivariable systems: relations to approximation

A simple feedback controller methodology is presented that allows for exact tracking of the sinusoidal input signals and rejection of the sinusoidal disturbances in a closed loop control system. The control method is motivated by a mathematical inequality that expresses the tracking and disturbance rejection requirements for a closed loop system. The exact tracking of the input command at a particular frequency requires an infinite loop gain for the system at the frequency of the in put command. A second order undamped transfer function is cascaded to each input channel to increase the loop transfer function gain at the frequency of the input command. A feedback controller is then designed via the LQG/LTR method to stabilize the system while the loop gain remains large at the frequency of the input. The method is experimentally verified on a single axis servo system and extended to multivariable systems.     

Output Regulation and Active Disturbance Rejection Control: Unified Formulation and Comparison

Output regulation theory aims to design a controller for achieving reference tracking and disturbance rejection while maintaining system stability. Different from the stabilization problem about an equilibrium point, the output regulation problem is capable of characterizing more complicated steady‐state trajectories induced by reference and/or disturbance. Many efforts have been made to reveal how a steady‐state trajectory can be characterized, estimated, and hence compensated by a controller such that output regulation can be asymptotically achieved. When the steady‐state trajectory is approximately treated as a constant “quantity”, the standard output regulation implies an approximate version within which output regulation is practically achieved. It is revealed in this paper that such an approximate version of output regulation includes the later developed active disturbance rejection control (ADRC) method as a special case.     

Robust MIMO disturbance observer analysis and design with application to active car steering

A multi‐input–multi‐output extension of the well‐known two control degrees‐of‐freedom disturbance observer architecture that decouples the problem into single‐input–single‐output disturbance observer loops is presented in this paper. Robust design based on mapping D‐stability and the frequency domain specifications of weighted sensitivity minimization and phase margin bound to a chosen controller parameter space is presented as a part of the proposed design approach. The effect of the choice of disturbance observer Q filter on performance is explained with a numerical example. This is followed by the use of structured singular values in the robustness analysis of disturbance observer controlled systems subject to structured, real parametric and mixed uncertainty in the plant. A design and simulation study based on a four wheel active car steering control example is used to illustrate the methods presented in the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Global stabilization with almost disturbance decoupling of a class of uncertain non-linear systems

In this paper we study the global stabilization of a class of non-linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The class of non-linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order. Although the plants considered are non-linear, the compensator developed here is linear. Our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback. Model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so-called ‘matching conditions’ and/or by treating a family of plants  for which a single controller simultaneously globally exponentially stabilizes all the plants in  while achieving almost disturbance decoupling of the output.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

Multivariable gain-scheduled fuzzy logic control of an exothermic reactor

Fuzzy logic control frequently exhibits superior performance to classical linear controllers even for ‘hard’, mathematically well defined plants, as described in this paper. The case-study of a highly nonlinear exothermic continuous stirred tank reactor, which poses a multivariable control problem with two interacting loops and open-loop instability, is used. The behaviour of the fuzzy logic controller is compared with that of a PID controller. A smooth, easily tuneable gain-schedule is designed to handle offset-like problems with a fuzzy controller. It is analytically shown that such a gain-schedule is the simpler, intuitive equivalent of a manipulation of the corresponding fuzzy membership functions. The fuzzy controller structure chosen is a parsimonious one, with the choice of Gaussian bell-shaped membership functions generating a smooth input/output surface with nontrivial inferencing spanning the entire input space. This provides a clear, non-heuristic reason to select Gaussian over triangular shapes for membership functions. The gain-scheduled fuzzy controller shows excellent control performance, significantly outperforming the PID controllers in both servo and regulatory modes. The disturbance rejection behaviour of the modified fuzzy controller is observed to be particularly good.     

Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

We study in this paper the problem of iterative feedback gains auto‐tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization‐based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model‐free multi‐parametric extremum seeking control to iteratively auto‐tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi‐parametric extremum seeking model‐free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.     

Feedback passivity approach to output feedback disturbance attenuation for uncertain nonlinear systems

The problem of output feedback disturbance attenuation for a class of uncertain nonlinear systems is studied based on output feedback passification. Previous work on output feedback disturbance attenuation is extended to the case where (1) the nominal system is not transformable into the normal form and (2) the uncertainty is parameterized nonlinearly. An adaptive output feedback controller is also provided that makes a nonlinear system passive. The paper then considers the output feedback disturbance attenuation problem for a class of uncertain nonlinear systems in the normal form and of relative degree one. The difference is that the result is applicable to nonlinear systems that include the uncertainty in the input matrix and do not satisfy the matching condition.     

Adaptive tracking and asymptotic rejection of unknown but bounded disturbances in nonlinear MIMO systems

The goal of this paper is global disturbance rejection in nonlinear systems. An output feedback controller with disturbance rejection is developed for a class of nonlinear multi input-multi output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance and reference tracking will is guaranteed. By the aid of designing an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. For tracking problem, an adaptive pre-compensator is used. The control methodology is robust against both constant and time varying bounded disturbances, maintaining effective performance. The adaptive laws are derived based on the Lyapunov synthesis method, therefore closed-loop asymptotic stability is also guaranteed. Moreover, for chattering reduction we use a low-pass filter. Consequently, small gain theorem is adopted to prove the stability of the closed-loop system. Simulation results are employed to illustrate the effectiveness of the proposed controller.