Flatness‑Based Control in Successive Loops of an H‑Type Gantry Crane with Dual PMLSM

Purpose In this article, the feedback control and stabilization problem of dual PMLSM-driven H-type gantry cranes is treated with the use of a fatness-based control method which is implemented in successive loops. Dual-drive gantry cranes can achieve high torque and high precision in the tasks’ execution. Such a type of crane can be used in several industrial applications. The solution to the associated nonlinear control problem is a particularly challenging research objective. Methods The integrated system that comprises the H-type gantry crane and two PMLSMs is shown to be diferentially fat. The control problem for this robotic system is solved with the use of a fatness-based control approach which is implemented in successive loops. To apply the multi-loop fatness-based control scheme, the state-space model of the H-type gantry crane with dual PMLSM is separated into subsystems, which are connected in cascading loops. Results For each subsystem, control can be performed with inversion of its dynamics as in the case of input–output linearized fat systems. The state variables of the preceding (ith) subsystem become virtual control inputs for the subsequent (i+1)th subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. Conclusion A novel nonlinear optimal control method has been developed for the dynamic model of a dual PMLSM-driven gantry crane. The proposed method achieves stabilization of the H-type gantry crane with dual PMLSM without the need for difeomorphisms and complicated state-space model transformations. Using the local diferential fatness properties of each one of the subsystems that constitute the gantry crane's model, the design of a stabilizing feedback controller is enabled.This research work has been partially supported by Grant Ref. 301022 ’Nonlinear optimal and fatness-based control methods for complex dynamical systems’ of the Unit of Industrial Automation of the Industrial Systems Institute. Besides, the authors, Pierluigi Siano and Mohammed Al-Numay acknowledge fnancial support from the Researchers Supporting Project Number (RSP2023R150), King Saud University, Riyadh, Saudi Arabia

Unified Approximate Tracking Control of Linear Systems with Unacceptable Zeros

This paper addresses the problem of modeling and control of linear continuous-time systems with unacceptable zeros in a sense that they are on the right-half plane of the S-domain (non-minimum phase) or cause the controller to have undesired behavior. The unified approximation of output tracking control using output redefinition will result in approximate output tracking, yet insuring stable internal dynamics of the system. Four different types of output redefinition are presented in a unified way and shown to satisfy different forms of control objectives through a simulation example of small-signal model of boost converter

Discrete-time modeling and tracking control of pulse-width modulated systems

Ph.D

APPROXIMATE OUTPUT TRACKING CONTROL FOR PWM SYSTEMS WITH UNACCEPTABLE ZEROS

Perfect output tracking, which requires inversion of the input-output dynamics, is not always a practical control objective. Difficulties are encountered for systems with zeros which are unstable, or stable but lightly damped. When the zeros are unacceptable in the above sense, perfect output tracking would require the control to be either unbounded, or bounded but highly oscillatory. In this paper, an approximate output tracking control design method is introduced for pulse width modulated (PWM) systems with unacceptable zeros. The design method is applied to the nonlinear sampled-data model of the PWM system, and is based on output redefinition.This work was supported in part by the National Science Foundation under grant ECS-9158037, by the Air Force Office of Scientific Research under grant F49620-9%1-0147,and by a graduate fellowship funded through King Saud University, Riyadh, Saudi Arabia