Rotational/translational Actuator Research Articles

Linear Stabilization Control for Underactuated RTAC Based on Model Reconstruction

Rotational-translational actuator (RTAC) system has the underactuated characteristics, i.e., it has two states to be stabilized with only one control input. To overcome this problem, a new “actuated” state is constructed as an output by combining the unactuated and actuated states. The lumped disturbance for the reconstructed model, including nonlinear dynamics, external disturbances, and parametric uncertainty of the stiffness coefficient of the spring, is estimated by the linear extended state observer and can be compensated in real-time. The practical states of the controlled RTAC converge to the equilibrium in a steady manner. The corresponding convergence and stability can be backed up by Lyapunov-based analysis. The RTAC with the proposed controller is proved to be stable subject to the disturbances. Specifically, some tuning guidelines for the control gains are presented, and the closed-loop characteristics of the RTAC is illustrated in the frequency domain. The simulations and Monte Carlo test are provided to verify the effectiveness of the proposed controller. Finally, the hardware experiments are performed to further validate the proposed method. The comparisons with the existing methods show that the proposed controller can achieve superior performance.

A new hybrid PID-Immersion invariance stabilization control scheme for the RTAC benchmark control system

This paper presents results into a new regulation scheme using a PID and immersion invariance controller for robust stabilization and tracking in rotational-translational actuator (RTAC) system. The stabilization and tracking control of the RTAC system is first demonstrated by application of the immersion invariance control law acting alone before the utilization of the designed control law for robustification of an existing PID controller for the RTAC system. In the nonrobust PID stabilization experiment, settling times of about 15 s was recorded while the robust stabilization experiments with the immersion invariance controller in the loop had 10 s settling time. For the nonrobust PID tracking experiment a noticeable overshoot was recorded of about 36.27% and settling times of about 18 s. Robust tracking experiments with the immersion invariance controller in the loop saw zero overshoot and 8 s settling time.

Constraint-Based Control Design for Uncertain Underactuated Mechanical System: Leakage-Type Adaptation Mechanism

In this article, we are dedicated to coping with the control design for underactuated mechanical system (UMS) with system uncertainties, which is also subject to a set of servo constraints. For the nominal system without any initial condition deviations, this article provides a general model-based servo control with the idea of second-order constraints, which can be derived from both holonomic and nonholonomic ones. For the uncertain system, with the uncertainties being separated into matched portions and mismatched portions, this article provides an adaptive robust control scheme to guarantee the UMS to attain the deterministic performance on the basis of nominal control. The leakage-type adaptive law is to size up the unknown uncertainty bounds. The cart-pole system and the rotational-translational actuator system are used to verify the availability of the proposed adaptive robust control.

Nonlinear Stabilization Control of Multiple-RTAC Systems Subject to Amplitude-Restricted Actuating Torques Using Only Angular Position Feedback

Multiple rotational translational actuator (RTAC) systems are nonlinear complicated mechatronic systems introduced to investigate the self-synchronized phenomenon in mechanical engineering, which consist of a series of single-RTAC subsystems connected one by one through elastic springs. This paper studies the globally stabilizing control problem for multiple-RTAC systems by considering that the actuators are constrained in torque amplitudes and velocity signals are unavailable for feedback. More precisely, by carefully analyzing the system energy storage function and respecting the maximum allowable control torques, a novel amplitude-restricted control law is developed without requiring velocity feedback, which can stabilize multiple-RTAC systems from any initial condition theoretically. It is beneficial that the proposed control law does not involve any plant parameters, which consequently makes it insensitive to parameter uncertainties. The stability and convergence characteristics of the designed control system are rigorously supported with Lyapunov techniques. To the best of our knowledge, the proposed controller is the first one that can stabilize a multiple-RTAC system while simultaneously ensuring the practical control amplitude-restricted constraints, by using only output feedback. Both numerical simulation and hardware experiments are included to verify the effectiveness of the proposed control approach.

Nonlinear Continuous Global Stabilization Control for Underactuated RTAC Systems: Design, Analysis, and Experimentation

Rotational-translational actuator (RTAC) systems can capture the major working principle of dual-spin spacecrafts and can be used to study the despin maneuver. In this paper, we consider the problem of globally stabilizing RTAC systems, which work in the vertical plane and are affected by nonvanishing matched disturbances by employing continuous control inputs. To this end, a nonlinear continuous control approach is synthesized to effectively damp out the platform oscillations, while ensuring that the eccentric ball's rotation angle returns to zero without residual swing. To our knowledge, this paper yields the first continuous controller, which is designed and analyzed without linearizing/approximating the original nonlinear dynamical equations to globally stabilize both the rotation and translation of RTAC systems influenced by nonvanishing matched disturbances. We implement experiments to show that the proposed control approach can achieve superior performance vis-a-vis existing methods and it admits for good robustness.

Output-feedback control of linear time-varying and nonlinear systems using the forward propagating Riccati equation

For output-feedback control of linear time-varying (LTV) and nonlinear systems, this paper focuses on control based on the forward propagating Riccati equation (FPRE). FPRE control uses dual difference (or differential) Riccati equations that are solved forward in time. Unlike the standard regulator Riccati equation, which propagates backward in time, forward propagation facilitates output-feedback control of both LTV and nonlinear systems expressed in terms of a state-dependent coefficient (SDC). To investigate the strengths and weaknesses of this approach, this paper considers several nonlinear systems under full-state-feedback and output-feedback control. The internal model principle is used to follow and reject step, ramp, and harmonic commands and disturbances. The Mathieu equation, Van der Pol oscillator, rotational-translational actuator, and ball and beam are considered. All examples are considered in discrete time in order to remove the effect of integration accuracy. The performance of FPRE is investigated numerically by considering the effect of state and control weightings, the initial conditions of the difference Riccati equations, the domain of attraction, and the choice of SDC.

Dynamical Analysis and Stabilizing Control of Inclined Rotational Translational Actuator Systems

Rotational translational actuator (RTAC) system, whose motions occur in horizontal planes, is a benchmark for studying of control techniques. This paper presents dynamical analysis and stabilizing control design for the RTAC system on a slope. Based on Lagrange equations, dynamics of the inclined RTAC system is achieved by selecting cart position and rotor angle as the general coordinates and torque acting on the rotor as general force. The analysis of equilibriums and their controllability yields that controllability of equilibriums depends on inclining direction of the inclined RTAC system. To stabilize the system to its controllable equilibriums, a proper control Lyapunov function including system energy, which is used to show the passivity property of the system, is designed. Consequently, a stabilizing controller is achieved directly based on the second Lyapunov stability theorem. Finally, numerical simulations are performed to verify the correctness and feasibility of our dynamical analysis and control design.

A MATLAB toolkit for composite nonlinear feedback control — 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.

Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems

In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in L2-gain optimal control, suboptimal Hinfin control, of nonlinear systems affine in input with the control policy having saturation constraints. The result is a closed-form representation, on a prescribed compact set chosen a priori, of the feedback strategies and the value function that solves the associated Hamilton-Jacobi-Isaacs (HJI) equation. The closed-loop stability, L2-gain disturbance attenuation of the neural network saturated control feedback strategy, and uniform convergence results are proven. Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation.

Explicit construction of [formula omitted] control law for a class of nonminimum phase nonlinear systems

This paper addresses a nonlinear H ∞ control problem for a class of nonminimum phase nonlinear systems. The given system is first transformed into a special coordinate basis, in which the system zero dynamics is divided into a stable part and an unstable part. A sufficient solvability condition is then established for solving the nonlinear H ∞ control problem. Moreover, based on the sufficient solvability condition, an upper bound of the best achievable L 2 gain from the system disturbance to the system controlled output is estimated for the nonlinear H ∞ control problem. The proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear H ∞ control problem. In particular, the solution to the nonlinear H ∞ control problem does not require solving any Hamilton–Jacobi equations. Finally, the obtained results are utilized to solve a benchmark problem on a rotational/translational actuator (RTAC) system.

Robust control of a class of non-linear cascade systems: a novel sliding mode approach

A novel robust control scheme based on a sliding mode approach is proposed for a general class of non-linear uncertain systems with saturation-bounded inputs. By introducing a new sliding variable as a complement to the conventional sliding variable, a useful error measure is defined from which a new sliding mode controller is developed. This controller can give a closed-loop system with better error responses during the reaching phase and a smaller ultimate error bound when in the boundary layer. Without raising the stability issue, an antiwindup compensator is incorporated into the proposed control scheme to help counteract the input-saturated effect. The non-linear benchmark problem, RTAC (Rotational/Translational Actuator)s was used as a simulated example to demonstrate the effectiveness of the design.

Global output-feedback tracking for a benchmark nonlinear system

The output-feedback global tracking problem is solved for the well-known nonlinear benchmark RTAC (rotational-translational actuator) system, in which one of the unmeasured states appears quadratically in the state equations. Our observer/controller backstepping design yields a nonlinear output-feedback controller that forces the translational displacement to globally asymptotically track an appropriate time-varying signal. The proposed solution is new even for the case of global output-feedback stabilization, namely when the reference signal is zero.