Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems

The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly reduced compared to classical CLFs, which makes \emph{flexible CLFs} more suitable for stabilization of constrained discrete-time nonlinear systems and real-time control. The purpose of this overview is to highlight the potential of flexible CLFs for real-time control of fast mechatronic systems, with sampling periods below one millisecond, which are widely employed in aerospace and automotive applications.Comment: 2 figure

Mechatronics of systems with undetermined configurations

This work is submitted for the award of a PhD by published works. It deals with some of the efforts of the author over the last ten years in the field of Mechatronics. Mechatronics is a new area invented by the Japanese in the late 1970's, it consists of a synthesis of computers and electronics to improve mechanical systems. To control any mechanical event three fundamental features must be brought together: the sensors used to observe the process, the control software, including the control algorithm used and thirdly the actuator that provides the stimulus to achieve the end result. Simulation, which plays such an important part in the Mechatronics process, is used in both in continuous and discrete forms. The author has spent some considerable time developing skills in all these areas. The author was certainly the first at Middlesex to appreciate the new developments in Mechatronics and their significance for manufacturing. The author was one of the first mechanical engineers to recognise the significance of the new transputer chip. This was applied to the LQG optimal control of a cinefilm copying process. A 300% improvement in operating speed was achieved, together with tension control. To make more efficient use of robots they have to be made both faster and cheaper. The author found extremely low natural frequencies of vibration, ranging from 3 to 25 Hz. This limits the speed of response of existing robots. The vibration data was some of the earliest available in this field, certainly in the UK. Several schemes have been devised to control the flexible robot and maintain the required precision. Actuator technology is one area where mechatronic systems have been the subject of intense development. At Middlesex we have improved on the Aexator pneumatic muscle actuator, enabling it to be used with a precision of about 2 mm. New control challenges have been undertaken now in the field of machine tool chatter and the prevention of slip. A variety of novel and traditional control algorithms have been investigated in order to find out the best approach to solve this problem

Hybrid modeling and control of mechatronic systems using a piecewise affine dynamics approach

This thesis investigates the topic of modeling and control of PWA systems based on two experimental cases of an electrical and hydraulic nature with varying complexity that were also built, instrumented and evaluated. A full-order model has been created for both systems, including all dominant system dynamics and non-linearities. The unknown parameters and characteristics have been identi ed via an extensive parameter identi cation. In the following, the non-linear characteristics are linearized at several points, resulting in PWA models for each respective setup. Regarding the closed loop control of the generated models and corresponding experimental setups, a linear control structure comprised of integral error, feed-forward and state-feedback control has been used. Additionally, the hydraulic setup has been controlled in an autonomous hybrid position/force control mode, resulting in a switched system with each mode's dynamics being de ned by the previously derived PWA-based model in combination with the control structure and respective mode-dependent controller gains. The autonomous switch between control modes has been de ned by a switching event capable of consistently switching between modes in a deterministic manner despite the noise-a icted measurements. Several methods were used to obtain suitable controller gains, including optimization routines and pole placement. Validation of the system's fast and accurate response was obtained through simulations and experimental evaluation. The controlled system's local stability was proven for regions in state-space associated with operational points by using pole-zero analysis. The stability of the hybrid control approach was proven by using multiple Lyapunov functions for the investigated test scenarios.publishedVersio

A Robust Controller Design for Simple Robotic Human Arm

Nowadays, the manipulator of two degrees of freedom (2DOF) has many applications. One is a human arm that may be utilized in robotic rehabilitation. The 2DOF controlled robot manipulator usually acts like human arms. This paper aims to design a robust, stable controller for the upper limb robotic model. A sliding mode control (SMC) approach is proposed to realize stability, tracing accuracy, and robustness for 2DOF robotic manipulator. Based on the general manipulator equation of motion, two SMCs are designed. The first is designed according to the input–output stability constraints. The second is designed according to the adaptive law. Not only the trajectory tracking is guaranteed but also stability is ensured. The stability of the controllers is examined based on Lyapunov stability criteria. The controllers and the robotic arm are formulated analytically. The MATLAB platform is adopted to examine and validate the proposed controller’s performance. The addition of adaptation law in the SMC scheme improves the results for the two designed controllers and shows remarkable trajectory tracking and system stability as well. The improvement rate shows an enhancement of 40.5% and 36.7% for manipulator joints 1 and 2, respectively

New Trends in the Control of Robots and Mechatronic Systems

In recent years, research into the control of robotic and mechatronic systems has led to a wide variety of advanced paradigms and techniques, which have been extensively analysed and discussed in the scientific literature [...

Integrated structure and control design for mechatronic systems with configuration-dependent dynamics

This paper considers the optimal design of mechatronic systems with configuration-dependent dynamics. An optimal mechatronic design requires that, among the structural and control parameters, an optimal choice has to be made with respect to design specifications in the different domains. Two main challenges are treated in this paper: the non-convex nature of the optimization problem and the difficulty in modeling serial machines with flexible components and their embedded controllers. The optimization problem is treated using the direct design strategy which considers simultaneously structural and control parameters as variables and adopts non-convex optimization algorithms. Linear time-invariant and gain-scheduling PID controllers are addressed. This methodology is exploited for the multi-objective optimization of a pick-and-place assembly robot with a gripper carried by a variable-length flexible beam. The resulting design tradeoffs between system accuracy and control efforts demonstrate the advantage of an integrated design approach for mechatronic systems with configuration-dependent dynamics. 2009 Elsevier Ltd. All rights reserved