Control Design For Mechanical Systems Research Articles

Designing Robust Control for Mechanical Systems: Constraint Following and Multivariable Optimization

This article proposes a novel robust control design for mechanical systems based on constraint following and multivariable optimization. The state of the concerned system is affected by (possibly fast) time-varying and bounded uncertainty. The objective is to drive the system to obey a set of prescribed constraints. A $\beta$ -measure is defined to gauge the constraint-following error; based on which, a feedback robust control scheme, which invokes design parameters, is proposed. For the seeking of optimal design parameters, a multivariable constrained optimization problem is formulated. The problem is successfully solved: with the existence, uniqueness , and analytical expression (i.e., closed form) of the optimal design parameters demonstrated. With the optimal parameters, the proposed robust control can render dual performance: guaranteed and optimal. As the guaranteed performance, the $\beta$ -measure is assured to be uniform boundedness and uniform ultimate boundedness. As the optimal performance, the performance index is globally minimized. This article is the first ever endeavour to cast both the constraint following and multivariable optimization into the control framework for uncertain mechanical systems.

運動方程式に基づく機械システムの解析と制御系設計 (モデリングと制御器設計の接点-システム表現を考える特集号)

運動方程式に基づく機械システムの解析と制御系設計 (モデリングと制御器設計の接点-システム表現を考える特集号)

Dynamic compensator‐based second‐order sliding mode controller design for mechanical systems

For mechanical systems using displacement measurements only, this study presents a dynamic compensator-based second-order sliding mode control algorithm without using any observer structure to estimate the velocity. Introducing the compensator into the sliding variable, a modified asymptotically stable second-order sliding mode control is developed. The proposed low-order dynamic controller inherently has low-pass filter property in which the effect of differentiators can be obtained. Using singular perturbation theory, the authors show that the system state is finally constrained in a small bound region when the gain is high enough. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.

Controller design for mechanical systems with underactuation degree one based on controlled Lagrangians method

This article extends controller design based on the controlled Lagrangians method from two to n degrees of freedom (DOF) mechanical systems with underactuation degree one. Importantly, a new kinetic energy equation (K-equation) is found from which the gyroscopic forces are separated due to the use of their property. Further, along with them chosen as an explicit solution, the other K-equations are satisfied for any regular controlled kinetic energy. As our main contribution, a sufficient matching condition is obtained which comprises the new K-equation and one P-equation (potential energy equation) cascaded, the regular condition and the explicit gyroscopic forces. Accordingly, the matching condition has an advantage for the fewest partial differential equations (PDEs) to be solved and the explicit gyroscopic forces. With all unknown functions of the controlled kinetic energy, the new K-equation can be simplified further under some choices on these functions and/or assumptions on specific original systems. Finally, taking the advantage, we obtain a nonlinear smooth state feedback control law that achieves local asymptotic stabilisation for a class of 3-DOF Pendubots in a vertical plane.

Constraint-following Servo Control Design for Mechanical Systems

A mechanical system is required to obey a set of constraints. The tools to accomplish this performance requirement are a set of servo controls1 that is, the servo controls are to generate the appropriate constraint force. In this article, the servo control design problem for constraint-following is thoroughly discussed. The problem is formulated as an algebraic setting in which a second order constraint is adopted. The control is a solution to the problem, whose projection to a subspace is used to ensure conformation to the constraint. The complete solution to this problem is provided in analytical form. It is shown that the environmentally constrained system simply adopts the minimum form of the complete solution. The setting presented here helps to broaden the scope of traditional Lagrangian mechanics.

Integrated Design of Structural and Control Systems Based on a Polynomial Matrix Approach: A Unified Framework for Structural and/or Control Design

A unified methodology of structural and/or control design for mechanical systems based on a polynomial matrix approach is proposed. A closed-loop D-stability specification is considered in this paper. By employing the polynomial matrix approach structural design parameters of mechanical systems, e.g., the mass, the damping and the stiffness and a feedback controller that is allowed to have a specified structure can be obtained simultaneously by solving LMIs. A simple iterative algorithm to obtain a better D-stable closed-loop system and a better central polynomial matrix is proposed. Design examples are provided to show the effectiveness of the present idea.

ADAPTIVE FRICTION COMPENSATION FOR MECHANISMS: A NEW PERSPECTIVE

Friction is an important aspect for control design of mechanical systems, including robotics, because it can lead to tracking errors, limit cycles, and undesired stick-slip motion. An adaptive friction compensator design is presented here as an option for control design of mechanisms with friction. Using the simplest friction model representation (the new perspective), consisting only of a constant value, which is assumed to be unknown, an adaptive friction compensator is developed. In numerical experiments, the system friction is modelled through a more representative function, previously used in performance evaluation of controlled systems with friction, and then using the well known LuGre friction model. Simulation results show an acceptable performance of our compensator compared with another adaptive friction compensator previously reported. The advantage of our controller is its simplicity.

Nonlinear Control of a Rodless Pneumatic Servoactuator, or Sliding Modes versus Coulomb Friction

Coulomb friction remains one of the major difficulties arising in control design for mechanical systems. Control of a translational pneumatic servoactuator is a typical example of such a problem. The aim of this paper is to demonstrate that sliding-mode control can be successfully used to compensate the friction of the piston in the cylinder, which is both viscous and Coulomb. A fourth-order nonlinear state-space model of a rodless pneumatic servoactuator will be developed with both numerical simulation and experimental validation. The comparison of sliding-mode control with classic PID control will be presented. © 1997 Elsevier Science Ltd.