Design and experimental evaluation of robust controllers for a two-wheeled robot

The paper presents the design and experimental evaluation of two alternative μ-controllers for robust vertical stabilisation of a two-wheeled self-balancing robot. The controllers design is based on models derived by identification from closed-loop experimental data. In the first design, a signal-based uncertainty representation obtained directly from the identification procedure is used, which leads to a controller of order 29. In the second design the signal uncertainty is approximated by an input multiplicative uncertainty, which leads to a controller of order 50, subsequently reduced to 30. The performance of the two μ-controllers is compared with the performance of a conventional linear quadratic controller with 17th-order Kalman filter. A proportional-integral controller of the rotational motion around the vertical axis is implemented as well. The control code is generated using Simulink® controller models and is embedded in a digital signal processor. Results from the simulation of the closed-loop system as well as experimental results obtained during the real-time implementation of the designed controllers are given. The theoretical investigation and experimental results confirm that the closed-loop system achieves robust performance in respect to the uncertainties related to the identified robot model.     

A fuzzy PID controller for nonlinear and uncertain systems

 In order to control systems that contain nonlinearities or uncertainties, control strategies must deal with the effects of these. Since most control methods based on mathematical models have been mainly focused on stability robustness against nonlinearities or uncertainties, they are limited in their ability to improve the transient responses. In this paper, a nonlinear fuzzy PID control method is suggested, which can stably improve the transient responses of systems disturbed by nonlinearities or unknown mathematical characteristics. Although the derivation of the control law is based on the design procedure for general fuzzy logic controllers, the resultant control algorithm has analytical form with time varying PID gains rather than linguistic form. This means the implementation of the proposed method can be easily and effectively applied to real-time control situations. Control simulations are carried out to evaluate the transient performance of the suggested method through example systems, by comparing its responses with those of the nonlinear fuzzy PI control method developed in [9].     

Model predictive control of VAV zone thermal systems concerning bi-linearity and gain nonlinearity

A new control strategy is proposed for zone thermal systems to deal with nonlinearities, uncertainties and constraints. The temperature control of VAV zone thermal systems is investigated. The system consists of two constrained processes: a zone temperature process with input-output bi-linearity and uncertainty, and a damper process with gain nonlinearity. Model predictive control is adopted for control design: a bilinear predictive controller is designed for the zone temperature process and a gain-scheduled robust predictive controller for the damper process. Both controllers deal with constraints directly and they operate in a cascaded manner. Case studies are given to show the effectiveness of the proposed strategy.     

Robust control of robot manipulators based on uncertainty and disturbance estimation

In this work, uncertainty and disturbance estimation (UDE) based robust trajectory tracking controller for rigid link manipulators was proposed. The UDE was employed to estimate the composite uncertainty that comprises the effects of system nonlinearities, external disturbances, and parametric uncertainties. A feedback linearization based controller was designed for trajectory tracking, and the same was augmented by the UDE‐estimated uncertainties to achieve robustness. The resulting controller however required measurement of joint velocities apart from the joint positions. To address the issue, an observer that employed the UDE‐estimated uncertainties for robustness was proposed, giving rise to the UDE‐based controller–observer structure. Closed‐loop stability of the overall system was established. The notable feature of the proposed design was that it neither required accurate plant model nor any information about the uncertainty. Also, the design needed only joint position measurements for its implementation. To demonstrate the effectiveness, simulation results of the proposed approach as applied to the trajectory tracking control of two‐link robotic manipulator and comparison of its performance with some of the well‐known existing controllers were presented. Lastly, hardware implementation of the proposed design for trajectory control of Quanser's single‐link flexible joint module was carried out, and it was shown that the proposed strategy offered a viable approach for designing implementable robust controllers for robots. Copyright © 2011 John Wiley & Sons, Ltd.     

A unified framework for the study of anti-windup designs

We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: ‘design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse effects of any control input nonlinearities on closed loop performance’. The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. This unification of existing schemes for AWBT compensation under a general framework is the main result of the paper.     

MPC-based dual control with online experiment design

We present two dual control approaches to the model maintenance problem based on adaptive model predictive control (mpc). The controllers employ systematic self-excitation and design experiments that are performed under normal operation, resulting in improved control performance with smaller output variance and less control effort. Our control formulations offer a novel approach to the question of how to excite the plant input to generate informative data within the context of mpc and adaptive control. One controller actively tries to reduce the parameter-estimate error covariances; the other controller maximizes the information in the signals for enhanced learning. Our approach differs from existing ones in that we let our controllers converge to standard certainty equivalence (ce) mpc when the parameter uncertainty decreases or more information is generated, and as a result we avoid plant excitation when the uncertainty is low or enough information has been generated. We demonstrate that the controllers work well with a large number of tuning configurations and also address the issue of models that are not admissible for control design.     

Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction

This paper aims at investigating the fuzzy adaptive control design for uncertain multivariable systems with unknown actuator nonlinearities and unknown control direction that possibly exhibit time-delay. The actuator nonlinearities involve dead-zone or backlash-like hysteresis, while the control direction is closely related to the sign of the control gain matrix. Two fuzzy adaptive controllers are proposed to deal with such an issue. The design of the first controller is mainly carried out in the free time-delay case, while the second control design is performed assuming that the system exhibits time-varying delays. Of practical interest, the adaptive compensation of the effects of the actuator nonlinearities requires neither the knowledge of their parameters nor the construction of their inverse. Furthermore, the lack of knowledge of the control direction is handled by incorporating in the control law a Nussbaum-type function. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.     

Making Complex Articulated Agents Dance

We discuss the tradeoffs involved in control of complex articulated agents, and present three implemented controllers for a complex task: a physically-based humanoid torso dancing the Macarena. The three controllers are drawn from animation, biological models, and robotics, and illustrate the issues of joint-space vs. Cartesian space task specification and implementation. We evaluate the controllers along several qualitative and quantitative dimensions, considering naturalness of movement and controller flexibility. Finally, we propose a general combination approach to control, aimed at utilizing the strengths of each alternative within a general framework for addressing complex motor control of articulated agents.     

Contril of rigid-link,flexible-joint robots:a survey of backstepping approaches

The purpose of this article is to show how the design procedure commonly referred to as integrator backstepping can be used to design globally stable trajectory tracking controllers for Rigid-Link Flexible-Joint (RLFJ) robot manipulators. Three different types of controllers are developed: (1) an exact model knowledge-based controller, (2) an adaptive controller that compensates for parametric uncertainty, and (3) a robust controller that compensates for parametric uncertainty and unknown bounded disturbances. All three controllers are based on previously published work but are presented here in a unifying framework. © 1995 John Wiley & Sons, Inc.     

Guaranteed cost control of stochastic uncertain systems with slope bounded nonlinearities via the use of dynamic multipliers

This paper presents a new approach to constructive output feedback robust nonlinear guaranteed cost controller design. The approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant. Dynamic multipliers are introduced to exploit these repeated nonlinearities. The linear part of the controller is synthesized using minimax LQG control theory.     

Stabilization of Time‐Varying and Disturbed Complex Dynamical Networks with Different‐Dimensional Nodes and Uncertain Nonlinearities

This paper investigates the stabilization problem for time‐varying and disturbed complex dynamical networks (CDNs) with different‐dimensional nodes and uncertain nonlinearities. To be consistent with the properties of real‐world networks, both the disturbances of our networks and the nonlinear structures of the nodes permit are completely unknown but bounded. Furthermore, the norm bounds of the uncertain nonlinearities and disturbances (NBUND) are applied to design the stabilization controllers. When the NBUND are known in advance, some decentralized state feedback controllers are proposed to stabilize our networks. And when they are unknown, adaptive decentralized stabilization schemes are brought forward for our network models. The effectiveness and feasibility of our theoretical results are verified by two simulation examples.     

Methodology for robust multi-parametric control in linear continuous-time systems

This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92 (2016) 64–77] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-off based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade.     

Feedback linearization based control of a rotational hydraulic drive

The technique of feedback linearization is used to design controllers for displacement, velocity and differential pressure control of a rotational hydraulic drive. The controllers, which take into account the square-root nonlinearity in the system's dynamics, are implemented on an experimental test bench and results of performance evaluation tests are presented. The objective of this research is twofold: firstly, to present a unified method for tracking control of displacement, velocity and differential pressure; and secondly, to experimentally address the issue of whether the system can be modeled with sufficient accuracy to effectively cancel out the nonlinearities in a real-world system.     

A MATLAB toolkit for composite nonlinear feedback -- improving transient response in tracking control

We present in this article a MATLAB toolkit with a user-friendly graphical interface for composite nonlinear feedback control system design. The toolkit can be utilized to design a fast and smooth tracking controller for a class of linear systems and nonlinear systems with actuator and other nonlinearities as well as with external disturbances. The parameters of the controller can be tuned easily on the user panel or autotuned by the toolkit. The toolkit is capable of displaying both time-domain and frequency-domain responses on its main panel and generating three different types of control laws, namely, the state feedback, the full-order measurement feedback and the reduced-order measurement feedback controllers. The usage and design procedure of the toolkit are illustrated by practical examples on a rotational/translational actuator (RTAC) system and a hard disk drive servo system. The toolkit can be utilized to design servo systems that deal with point-and-shoot fast targeting.     

Cooperative Adaptive Fuzzy Output Feedback Control for Synchronization of Nonlinear Multi‐Agent Systems in the Presence of Input Saturation

This paper considers the leader‐following synchronization problem of nonlinear multi‐agent systems with unmeasurable states in the presence of input saturation. Each follower is governed by a class of strict‐feedback systems with unknown nonlinearities and the information of the leader can be accessed by only a small fraction of followers. An auxiliary system is introduced and its states are used to design the cooperative controllers for counteracting the effect of input saturation. By using fuzzy logic systems to approximate the unknown nonlinearities, local adaptive fuzzy observers are designed to estimate the unmeasurable states. Dynamic surface control (DSC) is employed to design distributed adaptive fuzzy output feedback controllers. The developed controllers guarantee that the outputs of all followers synchronize to that of the leader under directed communication graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are semiglobally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. An example is provided to show the effectiveness of the proposed control approach.     

Real-time implementation of multi-linear model-based control strategies––an application to a bench-scale pH neutralization reactor

The real-time implementation of a set of multi-linear model-based control design methodologies is studied using a bench-scale pH neutralization system that exhibits nonlinear dynamics. It is envisaged that advanced model-based control strategy based on the multi-linear models presents a promising paradigm to design controllers for complex nonlinear plants. The multi-linear modeling philosophy is based on the selection of a set of linear models, complemented with an adaptation mechanism to explain the nonlinear plant behavior in the whole operating range. Practical implications of each control strategy are evaluated and discussed.     

A methodology for designing controllers for industrial systems based on nonlinear separation model and control

A feasible method of controller design for industrial nonlinear dynamic systems is proposed, by separating the nonlinear dynamic system into nonlinear static parts and a linear dynamic part. The proposed method of industrial controller design reduces the existing gaps between the control theory and the actual field. In the controller construction procedure of a system, the nonlinearities are eliminated by using the inversion functions of the nonlinear static parts. Any conventional control theory is ideally applicable to a linear dynamic part of the system. Based on the proposed method of nonlinear separation, controllers were constructed for three different systems: a chemical reactor, a temperature level-controlled tanked water system, and the contour-following control of an articulated robot arm. Some encouraging control performances, superior to those of other existing controllers, showed its significant potential for application to industrial systems with nonlinearities.