This paper presents an enhanced internal model control (EIMC) scheme for a time-delayed second order unstable process, which is subjected to exogenous disturbance and model variations. Even though the conventional internal model control (IMC) can provide an asymptotic tracking response with desired stability margins, the major limitation of conventional IMC is that it cannot be applied for an unstable system because a small exogenous disturbance can trigger the control signal to grow unbounded. Hence, modify- ing the conventional IMC structure to guarantee the internal stability, we present an EIMC scheme which can offer better trade-off between setpoint tracking and disturbance rejec- tion characteristics. To improve the load disturbance rejection characteristics and attenuate the effect of sensor noise, we solve the selection of controller gains as an H¥ optimization problem. One of the key aspects of the EIMC scheme is that the robustness of the closed loop system can be tuned via a single tuning parameter. The performance of the EIMC scheme is experimentally assessed on a magnetic levitation plant for reference tracking application. Experimental results substantiate that the EIMC scheme can effectively coun- teract the inherent time delay in the model and offer precise tracking, even in the presence of exogenous disturbance. Moreover, by comparing the trajectory tracking performance of EIMC with that of the proportional integral velocity (PIV) controller through cumulative power spectral density (CPSD) of the tracking error, we show that the EIMC can offer better low frequency servo response with minimal vibrations.
In this paper, we propose a robust nonlinear control design concept based on a coefficient diagram method and backstepping control, combined with a nonlinear observer for the magnetic levitation system to achieve precise position control in the existence of external disturbance, parameters mismatch with considerable variations and sensor noise in the case, where the full system states are supposed to be unavailable. The observer converges exponentially and leads to good estimate as well as a good track of the steel ball position with the reference trajectory. A simulation results are provided to show the excellent performance of the designed controller.
This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.