A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk

In this paper, the problem of optimal feedrate planning along a curved tool path for 3-axis CNC machines with the acceleration and jerk limits for each axis and the tangential velocity bound is addressed. It is proved that the optimal feedrate planning must be “Bang–Bang” or “Bang–Bang-Singular” control, that is, at least one of the axes reaches its acceleration or jerk bound, or the tangential velocity reaches its bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of the curve parameter u. The explicit formula for the velocity function when a jerk reaches its bound is given by solving a second-order differential equation. Under a “greedy rule”, an algorithm for optimal jerk confined feedrate planning is presented. Experiment results show that the new algorithm can be used to reduce the machining vibration and improve the machining quality.     

Experimental study of contouring accuracy for CNC machines executing curved paths with constant and curvature-dependent feedrates

Experiments to measure and improve the contouring accuracy of CNC machines executing curved paths with strong curvature and variations of curvature at high feedrates are reported, using P and PI controllers with a wide range of gains. The experiments are based on test curves exhibiting (a) a steady increase of curvature; (b) a periodic curvature variation between fixed minima and maxima; and (c) a sudden “spike” in the curvature profile. For the P controller, the curvature-dependent feedrate yields a diminution of the contour error by up to an order of magnitude, compared to constant feedrate. The curvature-dependent feedrate appears to be most advantageous in situations exemplified by case (c), since it affords a dramatic suppression of local contour error with a modest increase in traversal time. Moreover, the improvement in contour accuracy is relatively insensitive to the P gain. The results are less predictable when the curvature-dependent feedrate is used in conjunction with PI control, because of its more “active” response to the excitation arising from the varying path geometry and feedrate.     

The Bang‐bang principle of time optimal controls for the Kuramoto–Sivashinsky–KdV equation with internal control

This paper is concerned with the time optimal control problem governed by the internal controlled Kuramoto–Sivashinsky–Korteweg‐de Vries equation, which describes many physical processes in motion of turbulence and other unstable process systems. We prove the existence of optimal controls with the help of the Carleman inequality, which has been widely used to obtain the local controllability or null controllability of parabolic differential systems. More precisely, with the help of the Carleman inequality, we obtain a relationship between the null controllability and time optimal control problem. Moreover, we give the bang‐bang principle for an optimal control of our original problem by using the one of approximate problems. This method is new for time optimal control problems. The bang‐bang principle established here seems also to be new for fourth‐order parabolic differential equations. Copyright © 2015 John Wiley & Sons, Ltd.     

State-local optimality of a bang–bang trajectory: a Hamiltonian approach

We give a sufficient condition for a bang–bang extremal to be a strong local optimizer for the minimum time problem with fixed endpoints. We underline that the conditions imply that the optimum is local with respect to the state and not necessarily to the final time. Moreover, it is given through a finite-dimensional minimization problem, hence is suited for numerical verification. A geometric interpretation through the projection of the Hamiltonian flow on the state space is also given.     

Nonlinear–nonquadratic optimal and inverse optimal control for stochastic dynamical systems

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for nonlinear stochastic dynamical systems. Specifically, we provide a simplified and tutorial framework for stochastic optimal control and focus on connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory. In particular, we show that asymptotic stability in probability of the closed‐loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady‐state form of the stochastic Hamilton–Jacobi–Bellman equation and, hence, guaranteeing both stochastic stability and optimality. In addition, we develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the stochastic stabilization problem. These results are then used to provide extensions of the nonlinear feedback controllers obtained in the literature that minimize general polynomial and multilinear performance criteria. Copyright © 2017 John Wiley & Sons, Ltd.     

The Boltzmann–Hamel equations for the optimal control of mechanical systems with nonholonomic constraints

In this paper, we generalize the Boltzmann–Hamel equations for nonholonomic mechanics to a form suited for the kinematic or dynamic optimal control of mechanical systems subject to nonholonomic constraints. In solving these equations one is able to eliminate the controls and compute the optimal trajectory from a set of coupled first‐order differential equations with boundary values. By using an appropriate choice of quasi‐velocities, one is able to reduce the required number of differential equations by m and 3m for the kinematic and dynamic optimal control problems, respectively, where m is the number of nonholonomic constraints. In particular we derive a set of differential equations that yields the optimal reorientation path of a free rigid body. In the special case of a sphere, we show that the optimal trajectory coincides with the cubic splines on SO(3). Copyright © 2010 John Wiley & Sons, Ltd.     

Constrained optimal control of Navier–Stokes flow by semismooth Newton methods

We propose and analyze a semismooth Newton-type method for the solution of a pointwise constrained optimal control problem governed by the time-dependent incompressible Navier–Stokes equations. The method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equation. We analyze the flow control problem and prove q-superlinear convergence of the method. In the numerical implementation, adjoint techniques are combined with a truncated conjugate gradient method. Numerical results are presented that support our theoretical results and confirm the viability of the approach.     

Global maximum principle for the forward–backward stochastic optimal control problem with poisson jumps

This paper is concerned with the forward–backward stochastic optimal control problem with Poisson jumps. A necessary condition of optimality in the form of a global maximum principle as well as a sufficient condition of optimality are presented under the assumption that the diffusion and jump coefficients do not contain the control variable, and the control domain need not be convex. The case where there are some state constraints is also discussed. A financial example is discussed to illustrate the application of our result. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Razumikhin–Nussbaum‐lemma‐based adaptive neural control for uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays

This paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time‐varying delays. Based on a novel combination of the Razumikhin–Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed‐loop signals are shown to be 4‐Moment semi‐globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

A new discretized Lyapunov–Krasovskii functional for stability analysis and control design of time‐delayed TS fuzzy systems

This paper proposes a new Lyapunov–Krasovskii functional to cope with stability analysis and control design for time‐delay nonlinear systems modeled in the Takagi–Sugeno (TS) fuzzy form. The delay‐dependent conditions are formulated as linear matrix inequalities (LMIs), solvable through several numerical tools. By using the Gu's discretization technique and by employing an appropriated fuzzy functional, less conservative conditions are obtained. Numerical results illustrate the efficiency of the proposed methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability of current-mode control for DC–DC power converters

DC–DC power converters are switched devices whose averaged dynamics are described by a bilinear second-order system with saturated input. In some cases (e.g., boost and buck–boost converters), the input output dynamics can be of nonminimum-phase nature. Current-mode control is the standard strategy for output voltage regulation in high dynamic performance industrial DC–DC power converters. It is basically composed by a saturated linear state feedback (inductor current and output voltage) plus an output voltage integral feedback to remove steady-state offset. Despite its widespread usage, there is a lack of rigorous results to back up its stabilization capability and to systematize its design. In this paper, we prove that current-mode control yields semiglobal stability with asymptotic regulation of the output voltage.     

Discrete second‐order sliding mode control based on optimal sliding function vector for multivariable systems with input–output representation

The technique of linear matrix inequalities is a powerful method for solving optimization problems. In this paper, a sliding function vector was calculated using linear matrix inequalities approach. This technique provided optimal values of the coefficients of the sliding function vector, which led to the reduction of the reachability phase. Then, a discrete second‐order sliding mode control for multivariable systems was developed using this optimal sliding function vector. Two examples were used in order to illustrate the effectiveness of the proposed strategy. Simulation results prove good performances in terms of reduction of the reachability phase. Copyright © 2016 John Wiley & Sons, Ltd.     

Disturbance‐prediction–based control of input time delay systems for rejection of unknown frequency disturbances

In this paper, a novel disturbance rejection approach is presented for a class of input time‐delay systems subject to sinusoidal disturbances with unknown frequency. In particular, an auxiliary observer is proposed to represent the periodic disturbance in a parametric uncertainty form, where the unknown factor related to disturbance frequency can be estimated. Furthermore, the correlation between the future disturbance and the auxiliary observer output is analyzed, such that the future disturbances can be predicted and rejected through the input channel. Based on the aforementioned observer and predictor structure, the overall control architecture can be established as a framework of disturbance‐prediction–based control for systems with input time delays, where the conditions on the asymptotic stability of the closed‐loop systems are also derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed control approach.     

A robust adaptive dynamic surface control for a class of nonlinear systems with unknown Prandtl–Ishilinskii hysteresis

In this paper, a robust adaptive dynamic surface control for a class of uncertain perturbed strict‐feedback nonlinear systems preceded by unknown Prandtl–Ishlinskii hysteresis is proposed. The main advantages of our scheme are that the explosion of complexity problem can be eliminated when the hysteresis is fused with backstepping design and, by introducing an initialization technique, the ??_∞ performance of system tracking error can be achieved. It is proved that the new scheme can guarantee semi‐global uniform ultimate boundedness of all closed‐loop signals and make the convergence of the tracking error to an arbitrarily small residual set. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Neural network based switching control of AC–AC converter with DC–AC inverter for voltage sags, harmonics and EMI reduction using hybrid filter topology

A neural network based AC–AC voltage restorer is designed for voltage sags and PWM type active power filter with compound trap passive filter as a new hybrid filter are simultaneously used for voltage harmonics compensation and electromagnetic interference (EMI) reduction. First objective is to apply the neural network based switching control technique for the AC–AC voltage restorer to reduce time delays during the switching conditions and switching losses. The aim of the IGBTs used in the AC–AC voltage restorer is to test and to find the best switching frequency–power combination in the steps of the simulation. Thus, the proposed AC–AC voltage restorer has important advantages such as fast switching response, simplicity and more intelligent structure, better output waveform. The transient condition of the AC–AC voltage restorer is improved via the neural network based control technique. The second objective is the proposed strategy for elimination of voltage harmonics using PWM type DC–AC inverter part of the system as an active power filter. The last objective of the system is EMI reduction with using hybrid filter and voltage restorer together. Three problems which are voltage sags, harmonics and EMI are solved with the proposed system simultaneously.