Direct adaptive control for linear multivariable systems†

The aim of this paper is to survey direct adaptive control for linear multivariable systems. The discrete-time case is emphasized because of the increasing use of digital computers. Some adaptive control structures are given, as well as the different assumptions made on the process in order to achieve some specified objectives. Trends, new solutions and open problems are also discussed.     

Control of robotic manipulators—a neural network approach

A neural-network-based scheme is used for the control of a robotic manipulator. The main idea is that, by using a neural network to learn the characteristics of the robot system (or specifically its inverse dynamics), accurate trajectory following and good performance results are obtained. However, the traditional back-propagation algorithm commonly used for control and identification of nonlinear systems suffers from a slow rate of convergence. We investigate the effect of adusting the slope of the activation function (the node nonlinearity) on the performance of a back-propagation algorithm. It is shown that learning speed is increased significantly by making the slope of non-linearity adaptive. The results demonstrate that the proposed method gives better error minimization and faster convergence. The suggested method is applied to a two-link robotic manipulator. The resulting controller is sufficiently robust with respect to the changing conditions.     

Suboptimization techniques for improving transients in adaptive control†

Two possible optimization techniques for on-line adjustment of the design parameters involved in the adaptation algorithms of adaptive control schemes for minimum phase plants arc discussed. Sensitivity corrections adapled to this particular problem are introduced for correcting inaccuracies in an auxiliary model derived in order to be able to apply classical optimization techniques to the whole scheme. The main objective of such techniques is to improve the adaptation transient performances. The resulting strategies are discussed from the point of view of performance and possible implementation. Simulations illustrate the feasibility of the proposed optimizing procedures which are an extension, using a more general optimization theory and/or a sensitivity approach, of previous results and an alternative to the adaptive sampling approach of De la Sen (1984 c).     

Tracking control of non-linear systems using sliding surfaces,with application to robot manipulators†

A methodology of feedback control is developed to achieve accurate tracking in a. class of non-linear, time-varying systems in the presence of disturbances and para meter variations. The methodology uses in its idealized form piecewise continuous feedback control, resulting in the state trajectory sliding along a time-varying sliding surface in the state space. This idealized control law achieves perfect tracking; however, non-idealities in its implementation result in the generation of an undesirable high-frequency component in the state trajectory. To rectify this, it is shown how continuous control laws may be used to approximate the discontinuous control law to obtain robust tracking to within a prescribed accuracy without generating undesirable high-frequency signal. The method is applied to the control of a two-link manipulator handling variable loads in a flexible manufacturing system environment.     

Comments on ‘A new terminal sliding mode control for robotic manipulators’

In this article, we give some comments on the article ‘A new terminal sliding mode control for robotic manipulators’. The article presents a new terminal sliding mode control approach for global finite-time tracking of robotic manipulators. We point out a serious error occurred through the article, leading to the ineffectiveness of the proposed approach. A correction is proposed. Comparisons are presented.     

Linear control of saturating control systems†

The problem is considered of replacing optimum non-linear control of saturating, single-variable systems by sub-optimal linear control. Both the optimal and sub-optimal controllers are designed to minimize the integral-square-error of the systems in response to a step input, and a comparison is made of the values of this integral using the two forms of control. The values of the integral are obtained to high accuracy using numerical minimization techniques.

Consideration is also given to the stability of the systems under the linear controller.     

Decentralized adaptive neural network control of cascaded DC–DC converters with high voltage conversion ratio

Decentralized output voltage tracking of cascaded DC–DC converters is an interesting topic to obtain a high voltage conversion ratio. The control purpose is challenging due to the load resistance changes, renewable energy supply voltage variations and interaction of the individual converters. In this paper, four novel decentralized adaptive neural network controllers are designed on the cascaded DC–DC buck and boost converters under load and DC supply voltage uncertainties. In the beginning, individual buck and boost converter average models that can operate in both continuous and discontinuous conduction modes are derived. Then, the interconnected and decentralized state-space models of cascaded buck and boost converters are extracted. These models are highly nonlinear with unknown uncertainties which can be estimated by neural networks. Further, two decentralized adaptive backstepping neural network voltage controllers are proposed on cascaded buck converters to deal with uncertainties and interactions. However, these control strategies are not applicable to a boost converter due to its non-minimum phase nature. Then, two novel decentralized adaptive neural network with a conventional proportional–integral reference current generator are developed on the cascaded boost converters. Practical stability of the overall system is guaranteed for the proposed controllers using Lyapunov stability theorem. Finally, four control strategies provide good quality of output voltage in the presence of uncertainties and interactions. Comparative simulations are carried out on cascaded buck and boost converters to validate the effectiveness and performance of the designed methods.     

Robust control of flexible manipulators via μ-synthesis

An experimental flexible arm serves as testbed to investigate the efficacy of the μ-synthesis design technique in the control of flexible manipulators. A linearized model of the testbed is derived for control design. Discrepancies and errors between the linearized model and the physical system are accounted for in the control design via uncertainty models. These uncertainties include: unmodeled high-frequency dynamics, errors in natural frequencies and damping levels and actuator and sensor errors. Colocated and noncolocated controllers are designed using μ-synthesis. It is observed, theoretically and experimentally, that the μ-synthesis design technique is a viable control tool for tip tracking with flexible manipulators.     

Robust adaptive control of synchronous generators with SMES unit via Hamiltonian function method†

Superconducting Magnetic Energy Storage (SMES) units can be used to enhance the stability of power systems. Using Hamiltonian function method, this article investigates robust adaptive control design for synchronous generators with such a unit, and proposes an energy-based robust adaptive controller for the systems with disturbances and unknown parameters. The generator used in this article is a 4th order model with both excitation and steam valve controls. It is shown that the generator with one SMES unit can be changed as a dissipative Hamiltonian system, with which the energy-based robust adaptive control law can be designed for the system by using the structural properties of dissipative Hamiltonian systems. Study on simulations shows that the controller proposed in this article works very well.     

State-feedback control of non-linear systems†

A design method for state-feedback controllers for single-input non-linear systems is proposed. The method makes use of the transformations of the non-linear system into ‘controllable-like’ canonical forms. The resulting non-linear state feedback is designed in such a way that the eigenvalues of the linearized closed-loop model are invariant with respect to any constant operating point. The method constitutes an alternative approach to the design methodology recently proposed by Baumann and Rugh. Also a review of different transformation methods for non-linear systems is presented. An example and simulation results of different control strategies are provided to illustrate the design technique.     

Fuzzy control of steam turbines†

A feasibility study of a fuzzy logic speed control of a steam turbine is reported. The efficiency of the fuzzy control is compared with conventional PID control. As a basis for this comparison, we use a mathematical model of the turbine which has been well validated at a real turbine in connection with the design of the PID control. For this model, a simple fuzzy controller is designed. To assess the resulting fuzzy control, we study by simulation the step response of the speed at a full load reduction, as well as the robustness with respect to parameter variations of the turbine.     

Adaptive control of parallel manipulators via fuzzy-neural network algorithm

This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms （FNNA）. With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric uncertainties are eliminated. FNNA is used to handle model uncertainties and external disturbances. In the proposed control scheme, we consider modifying the weight of fuzzy rules and present these rules to a MIMO system of parallel manipulators with more than three degrees-of-freedom （DoF）. The algorithm has the advantage of not requiring the inverse of the Jacobian matrix especially for the low DoF parallel manipulators. The validity of the control scheme is shown through numerical simulations of a 6-RPS parallel manipulator with three DoF.     

Performance characteristics of an adaptive hydraulic servo-mechanism†

This paper presents the results of an extensive set of experiments which were carried out on an adaptive hydraulic servo-mechanism: this system embodied adaptive controllers designed on the basis of Liapunov's direct method.     

Closed-loop control of a class of non-linear systems†

A technique is described for the closed-loop control of a class of non-linear systems iii a potentially large neighbourhood of a nominal trajectory. By the introduction of extra states it is shown how to reduce non-linear differential equations to a related canonical linear form. Since the linear form is not readily amenable to standard design techniques a new synthesis procedure is proposed for the construction of a closed-loop control. The proposed technique relies heavily on computer computation. The computation for the closed-loop control of a lifting body, a system not completely controllable, is given in detail to illustrate the applicability of the method.     

Decentralized linear–quadratic–Gaussian control of networked control systems with asymmetric information

The decentralized linear–quadratic–Gaussian (LQG) control problem for networked control systems (NCSs) with asymmetric information is investigated, where controller 1 shares its historical information with controller 2, and not vice versa. The asymmetry of the information structure leads to the coupling between controller 2 and estimator 1, and hence the classical separation principle fails. Through the assumption of linear control strategy, the coupling between controller 2 and estimator 1 (CCE) is decoupled, but the estimation gain is still coupled with the control gain. It is noted that the control gain conforms to the backward Riccati equation while estimation gain abides by the forward equation, which is computationally challenging. Applying the stochastic maximum principle, the solvability of the decentralized LQG control problem is reduced to that of corresponding forward and backward stochastic difference equations (FBSDEs). Further, necessary and sufficient conditions for the solvability of optimal control problem are presented by two Riccati equations, one of which is nonsymmetric. Moreover, a novel iterative forward method is proposed to calculate the coupled backward control gain and forward estimation gain.     

Self-adapting control parameters modified differential evolution for trajectory planning of manipulators

Control parameters of original differential evolution （DE） are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed.     

Supervisory control for co-ordination of multiple robots†

This paper deals with a solution of supervisory control problem for co-ordination of multiple robots. The application of two or more robots employed in a co-operating mode can increase the level of flexibility and productivity in an automated manufacturing environment. However, as the number of robots or the intricacy of task to be performed increases, the control requirements also increase substantially. Co-operating robots can be used in typically complex assembly operations where the payload may be too heavy for a single arm to handle; the object to be manipulated may be irregularly shaped and provide only limited access for physical handling, or the two parts to be assembled together may require simultaneous orientation and unique positioning.

The co-ordination control strategies developed were applied to two IBM 7540 SCARA robots. Several control schemes were devised to achieve concurrent robot co-ordination and trajectory tracking. A digital computer program operable on an IBM PS/2 System 80 provided multiple concurrent programming of the two robots. Interactive control strategy and master-slave control strategy were designed, implemented, optimized, and tested. The results showed excellent trajectory adherence and repeatability for both control schemes     

Robust adaptive control of a class of nonlinear uncertain systems

A smooth robust dynamic feedback controller is constructed, and the problem of robust H∞ almost disturbance attenuation with internal stability is solved for high-order nonlinear systems with parameter uncertainties. Finally, illustrative example and simulation results demonstrate the effectiveness of the proposed method.     

Error-based adaptive optimal tracking control of nonlinear discrete-time systems

In this paper,for the output tracking problem of nonlinear discrete-time systems,a performance index is newly defined using the adaptive dynamic programming(ADP) technique to completely eliminate tracking errors in theory.In contrast to traditional definitions of performance indices in other ADP-based methods,the proposed performance index is not only designed from the perspective of output tracking errors but also introduced errors of system states and control inputs at adjacent stages,which is...     

Infinity-norm acceleration minimization of robotic redundant manipulators using the LVI-based primal–dual neural network

Kinematically redundant manipulators admit an infinite number of inverse kinematic solutions and hence the optimization of different performance measures corresponding to various task requirements must be considered. Joint accelerations of these mechanisms are usually computed by optimizing various criteria defined using the two-norm of acceleration vectors in the joint space. However, in formulating the optimization measures for computing the inverse kinematics of redundant arms, this paper investigates the use of the infinity norm of joint acceleration (INAM) (also known as the minimum-effort solution). The infinity norm of a vector is its maximum absolute value component and hence its minimization implies the determination of a minimum-effort solution as opposed to the minimum-energy criterion associated with the two-norm. Moreover, the new scheme reformulates the task as the online solution to a quadratic programming problem and incorporates three levels of joint physical limits, thus keeping the acceleration within a given range and avoiding the torque-instability problem. In addition, since the new scheme adopts the LVI-based primal–dual neural network, it does not entail any matrix inversion or matrix–matrix multiplication, which was embodied in other's researches with expensive O(n³)$O(n^3)$ operations. This new proposed QP-based dynamic system scheme is simulated based on the PUMA560 robot arm.