Balancing control of sliding inverted-wedge system: Classical-method-based compensation

Root-locus-based PID controller and LQR-based controller always fail as system nonlinearity increases. We here propose the optimization-compensated block/diagram to reinforce the stabilization ability of these two classical control methods for nonlinear system, and besides, to achieve other performance requirements such as constrained overshoot and fast response. The controller design of a nonlinear sliding weights balancing mechanism is based on optimization-compensated root locus and LQR method. First, according to root-locus of the linearized dynamic system, we propose extra poles and zeros addition to roughly draw the locus shifting to left to achieve stabilization requirement. The poles and zeros are realized by P/PD/PID controllers. For LQR approach, we choose performance parameters to meet stabilization and minimum energy requirement. The controller is realized as feedback controller. Further, to compensate the model-error from nonlinearity and to meet other performance such as overshoot and setting time, some P/PID parameters for root-locus method and the feedback gain for LQR method are optimized via optimal parameter searching in NCD/Matlab toolbox. The simulation results demonstrate the stability and the constrained performances of the entire closed-loop system can be ensured by the proposed compensated control block diagrams.