Positional control of rotary servo cart system using generalized dynamic inversion

Abstract

This paper presents the design approach of Generalized Dynamic Inversion (GDI) for angular position control of SRV02 rotary servo base system. In GDI, linear first order constraint differential equations are formulated based on the deviation function of angular position and its rate, and its inverse is calculated using Moore-Penrose Generalized Inverse to realize the control law. The singularity problem related to generalized inversion is solved by the inclusion of dynamic scaling factor that will guarantee the boundedness of the elements of the inverted matrix and stable tracking performance. Numerical simulations and real-time experiment are performed to evaluate the tracking performance and robustness capabilities of the proposed control law considering nominal and perturbed model dynamics. For comparative analysis, the results of GDI is compared with conventional PID control. Simulation and experimental results demonstrate better angular position tracking for the square-wave and sinusoidal waveforms, which reveals the superiority, and agility of GDI control over conventional PID.

Survey on Robust Control Applications in Inverted Pendulum Systems

“…A general Lyapunov function based Uncertain Furuta Pendulum [17] and mixed 𝐻 ∞ Controller based rotary double inverted pendulum [15] are two major works which utilize the novel robust control strategies. The linear and non-linear switched controls along with its stability analysis and implementation with IP system is a noteworthy work based on its novelty and innovativeness [16].…”

“…The linear and non-linear switched controls along with its stability analysis and implementation with IP system is a noteworthy work based on its novelty and innovativeness [16]. The robust generalized dynamic inversion control technique can be added to this category where in [17], a rotary inverted pendulum is subjected with this control technique.…”

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

“…The description and numerical values of the variables required to compute the motor torque are given by equation ( 9) and can be found in the work by Mehedi et al (2018).…”

“…On the contrary, a nonlinear technique called generalized dynamic inversion (GDI) is emerging as a novel inversion-based control law, where control objectives are defined in the form of constraint differential equations (Mehedi et al, 2018). The virtual constraint dynamics are formulated as the function of controlled state variable deviation functions, which are evaluated along the solution trajectories of the dynamical system.…”