Molong Duan

Energy-Efficient Controller Design for a Redundantly Actuated Hybrid Feed Drive With Application to Machining

This paper presents a method for designing a controller that achieves the best positioning performance while maximizing the energy efficiency of a redundantly actuated hybrid feed drive. A two-degree-of-freedom controller, consisting of a feedforward (FF) controller for tracking and a feedback (FB) controller for regulation, is assumed. It is shown that the ideal FF controller, which achieves perfect tracking with maximum efficiency, is not always stable. Therefore, a method for designing a stable FF controller that achieves perfect tracking with near optimal efficiency is proposed. Furthermore, the optimal relationship between FB control inputs, which guarantees maximum efficiency for any specified regulation performance, is derived. Two approaches for using the derived optimal relationship to synthesize a FB controller that achieves the best positioning performance while maximizing efficiency are proposed. Simulations and machining experiments are conducted to demonstrate the effectiveness of the proposed energy-efficient FF and FB controller design methods. Significant improvements in energy efficiency (without sacrificing positioning performance) are reported.

Tracking control of non-minimum phase systems using filtered basis functions: A nurbs-based approach

This paper proposes an approach for minimizing tracking errors in systems with non-minimum phase (NMP) zeros by using filtered basis functions. The output of the tracking controller is represented as a linear combination of basis functions having unknown coefficients. The basis functions are forward filtered using the dynamics of the NMP system and their coefficients selected to minimize the errors in tracking a given trajectory. The control designer is free to choose any suitable set of basis functions but, in this paper, a set of basis functions derived from the widely-used non uniform rational B-spline (NURBS) curve is employed. Analyses and illustrative examples are presented to demonstrate the effectiveness of the proposed approach in comparison to popular approximate model inversion methods like zero phase error tracking control.Copyright

Tracking Control of Linear Time- Invariant Nonminimum Phase Systems Using Filtered Basis Functions

An approach for minimizing tracking errors in linear time-invariant (LTI) single-input single-output (SISO) discrete-time systems with nonminimum phase (NMP) zeros using filtered basis functions (FBF) is studied. In the FBF method, the control input to the system is expressed as a linear combination of basis functions. The basis functions are forward filtered using the dynamics of the NMP system, and their coefficients are selected to minimize the error in tracking a given desired trajectory. Unlike comparable methods in the literature, the FBF method is shown to be effective in tracking any desired trajectory, irrespective of the location of NMP zeros in the z-plane. The stability of the method and boundedness of the control input and system output are discussed. The control designer is free to choose any suitable set of basis functions that satisfy the criteria discussed in this paper. However, two rudimentary basis functions, one in time domain and the other in frequency domain, are specifically highlighted. The effectiveness of the FBF method is illustrated and analyzed in comparison with the truncated series (TS) approximation method. [DOI: 10.1115/1.4034367]

Energy efficiency and performance optimized control of a hybrid feed drive

Linear motor drives (LMDs) are well known to provide significant advantages in terms of positioning speed and precision over traditional screw drives (SDs), making them better suited for high-speed, high-precision machine tools. However, their use in such machine tools is limited by their tendency to consume a lot of electrical energy and cause thermal issues that help drive up costs. A hybrid feed drive (HFD) has been proposed as a possible solution to this dilemma. The HFD combines LMD and SD actuation to achieve speeds and accuracies similar to LMDs while consuming much less energy. This paper explores control strategies to further improve the performance of the HFD without unduly sacrificing its efficiency. First, it highlights two performance limitations of the controller proposed for the HFD in prior work, namely, imperfect tracking and suboptimal feedback gains. Then it compares two approaches for achieving perfect tracking with regard to performance and energy efficiency. Finally, it presents an approach for optimizing the feedback gains of the HFD to achieve the best positioning performance. Simulations and experiments are used to demonstrate significant gains in precise positioning using the methods proposed in this paper, while maintaining superb energy efficiency relative to an equivalent LMD.Copyright

Corrections to “Energy-Efficient Controller Design for a Redundantly-Actuated Hybrid Feed Drive With Application to Machining” [Aug 16 1822-1834]

THIS note corrects an error in our paper [1], which presented energy-efficient feed-forward and feedback controller designs for a redundantly actuated hybrid feed drive using an optimal control input ratio. It shows that the optimal control input ratio derived in [1] is missing an adjoint operator. Furthermore, it shows that the correct optimal ratio (i.e., the ratio with the adjoint operator) is noncausal, hence difficult to implement in practice. Finally, it demonstrates that the ratio derived in [1] is a causal approximation of, and an appropriate substitute for, the correct ratio in the cases studied in [1]. Maintaining the same notations as in [1], the condition for energy optimality derived in [1, eq. (7)] is repeated as ∫ ( 2uff 1 Km1 2 δuff 1 + 2uff 2 Km2 2 δuff 2 ) dt = 0. (1)

Modeling and observer-based compensation of slip in a friction drive for servo positioning

This paper studies slip in friction drives in the context of a precision servo positioner equipped with a twist-roller friction drive. The servo positioner is modeled using a two-mass model that includes the experimentally-identified nonlinear slip dynamics of the friction drive. The model is then used to design an observer-based compensation scheme aimed at reducing the slip-induced performance degradation of the servo positioners linear time invariant controller. The compensation scheme is validated in simulations and experiments using state feedback controllers. Tracking performance with the proposed slip compensation scheme, compared with the original controller and an intuitive high pass filter approach, is shown to improve considerably.

Minimum-Time Cornering for Manufacturing Machines Using Optimal Control

When traversing sharp corners, manufacturing machines are forced to tradeoff speed and accuracy. The most common way of reducing this tradeoff is to smooth the sharp corner using a pre-specified curve (e.g., a circular arc or spline). However, pre-specified curves cannot guarantee optimal performance. This paper presents a preliminary investigation into the potential of using methods from optimal control to minimize this tradeoff. First, a useful simplification is made to the exact cornering problem to make it tractable. Dynamic programming is then used to determine the best free-form curve that minimizes corner traversal time while adhering to path tolerance and machine kinematic constraints. Significant improvements in cornering time are demonstrated compared to two methods that use pre-specified curves. However, dynamic programming is found to be too computationally costly, thus impractical. Less computationally intensive techniques in optimal control are considered for future work.© 2014 ASME