New class of control laws for robotic manipulators Part 1. Non–adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has recently been recognized that the non-linear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third–order terms in the Lyapunov function derivatives, closed–loop exponential stability for both the set point and tracking control problem is demonstrated. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on–line computation of non–linear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing trade–offs between computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.     

Synthesis of adaptive sub-optimal feedback control laws†

In this paper a method for synthesizing a sub-optimal feedback controller which is sensitive to variations in plant parameters is presented. The structure of the sub-optimal control is a linear combination of suitably chosen basis functions multiplied by coefficients which are functions of the varying plant parameters. The coefficient multipliers are determined by the minimization of a mean-square error using data obtained from numerically computed optimal trajectories. The controller may be called adaptive since it uses identification of the varying plant parameters to modify the coefficient multipliers. Examples are included which show that with relative sensitivity as the criterion the method is superior to other methods of suboptimal control design.     

Suboptimal adaptive control of a class of non-linear systems†

The problem of controlling a class of nonlinear systems with uncertain parameters and imprecisely defined system and measurement noise terms is considered. A sub-optimal adaptive control algorithm is developed as a solution to coupled linear modelling and control optimization problems. Features of the algorithm are the forward-recursive generation of the modelling and control processes and necessity for past and present values of states and parameters alone in order to implement the algorithm (i.e. no precomputed nominal trajectory is required). These features make the algorithm ideally suited to real-time control applications

Real-time control of a non-trivial fifth-order system, (a model of a plasma torch furnace) is considered and the results of an experimental study are presented.     

On the speed of response of a model-reference adaptive control system†

An analytical evaluation of the adaptive loop response of a model-reference adaptive control system is presented using sinusoids as a test signal. A schematic diagram of the feedback system containing a primary control loop and an adaptive control loop are given.     

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.     

Comments on ‘An adaptive control scheme for robot manipulators’

Based on an extension of the classical linearization method, an adaptive control scheme has recently been proposed by Choi et al. (1986). This control scheme, however, implicitly involves taking the inverse of the matrix [I + G(x(t), u(x(t)))], which complicates the computation. Moreover, since the matrix inversion depend- ing on the system state x(t) does not necessarily exist for all time, the proposed control scheme may lose its effectiveness. In this paper, we present a modified control scheme in which the aforementioned weakness does not appear.     

Comments on ‘An adaptive control scheme for robot manipulators’

The structure of the adaptive regulator in a paper by Choi et al. (1986) is simplified by utilizing the positive definiteness of the inertia matrix.     

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.     

Convergence rate of least-squares identification and adaptive control for stochastic systems†

The strong consistency and the convergence rate of least-squares identification for the multidimensional ARMAX model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied. The parameter-identification results are applied to adaptive-control systems with a quadratic loss function. The rate of convergence of the loss function to its minimum is also obtained.     

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.     

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.     

Stability analysis of a model reference adaptive control system with sinusoidal inputs†

In this paper a rigorous method is presented for analysing an M.I.T. type model reference adaptive control system with sinusoidal inputs. The linearized equations for the adapting system, formed by using small perturbation analysis, are written in the matrix form [xdot] = A(t)x, where A(t) is periodic. This matrix equation is then integrated over one period using a Runge–Kutta technique. The transition matrix relating the value of x at the end of a period to its value at the beginning of the period is examined to see whether all its eigenvalues are within the unit circle, thus establishing stability.     

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.     

Chemical process control—A new technique for adaptive tuning of controllers†

This paper presents a new technique for determining the optimum settings of the conventional two-mode and three-mode controllers. The procedure which utilizes the practically available on-line closed loop data is an extension of the classical work of Ziegler and Nichols (1942). The advantages of the present method over that of Ziegler and Nichols are (i) that it does not require the process to undergo sustained oscillations, (ii) that the tuning constants are determined iteratively (and not by hit-and-miss technique) thereby making the tuning adaptive in nature and (iii) that it is possible to select a criterion of optimality other than the usual 1:4 decay ratio.     

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.     

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.     

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.     

A recursive least-squares approach to the on-line adaptive control problem†

A practical study of the application of recursive least squares methods to the adaptive control of a multivariable process is described. The process has a number of inputs and an equal number of state variables are required to be controlled. Investigations are carried out both off-line and in real-time using a hybrid computer. Results show the techniques to be ideally suited for on-line application.     

Respiratory control of heart rate†

A new model for the respiratory Control of the heart rate is suggested. The model includes the effect of pressoreceptor feedback in the production of the heart rate transient during respiration. The reflex is assumed to be initiated by a rate sensitive stretch receptor with varying compliances for inspiration and expiration. The effect of posture in altering the transient envelope is also considered.