[Paper Review] Robust Tracking and Model Following Controller Based on Higher Order Sliding Mode Control and Observation: With an Application to MagLev System

Siddhartha Ganguly, Manas Kumar Bera+1 more|arXiv (Cornell University)|Jul 11, 2020

Magnetic Bearings and Levitation Dynamics40 references4 citations

TL;DR

This paper proposes a robust tracking and model following (RTMF) controller for uncertain linear time-invariant (LTI) systems using second-order sliding mode control (super-twisting algorithm, STA) combined with a higher-order sliding mode observer (HOSMO) to estimate unmeasurable states. The method achieves asymptotic stability of tracking error and eliminates chattering, with experimental validation on a MagLev system showing smoother control and improved precision compared to standard super-twisting observers.

ABSTRACT

This paper deals with the design of robust tracking and model following (RTMF) controller for linear time-invariant (LTI) systems with uncertainties. The controller is based on the second order sliding mode (SOSM) algorithm (super twisting) which is the most effective and popular in the family of higher order sliding modes (HOSM). The use of super twisting algorithm (STA) eliminates the chattering problem encountered in traditional sliding mode control while retaining its robustness properties. The proposed robust tracking controller can guarantee the asymptotic stability of tracking error in the presence of time varying uncertain parameter and exogenous disturbances. Finally, this strategy is implemented on a magnetic levitation system (MagLev) which is inherently unstable and nonlinear. While implementing this proposed RTMF controller for MagLev system, a super twisting observer (STO) is used to estimate the unknown state i.e the velocity of the ball which is not directly available for measurement. It has been observed that the RTMF controller based on STA-STO pair, is not good enough to achieve SOSM for a chosen sliding surface using continuous control. As a remedy, continuous RTMF controller based on STA is implemented with a higher order sliding mode observer (HOSMO). The simulated as well as the experimental results are provided to illustrate the effectiveness of the proposed controller-observers pair.

Motivation & Objective

• To design a robust tracking and model following (RTMF) controller for LTI systems under time-varying uncertainties and disturbances.
• To eliminate the chattering effect inherent in traditional sliding mode control while preserving robustness.
• To address the challenge of unmeasurable state estimation—specifically velocity—in the magnetic levitation (MagLev) system.
• To implement and validate the RTMF controller in real-time on a physical MagLev platform.
• To compare the performance of STA-based controllers with super-twisting observer (STO) versus higher-order sliding mode observer (HOSMO).

Proposed method

• The RTMF controller is designed using the super-twisting algorithm (STA), a second-order sliding mode (SOSM) control technique that ensures finite-time convergence of the sliding variable and its derivative.
• A higher-order sliding mode observer (HOSMO) is employed to estimate the unmeasurable velocity of the MagLev ball, improving estimation accuracy over standard STO.
• The controller-observer pair is implemented in real-time on a Feedback Instruments Ltd. MagLev system (Model No. 33-210), with position as the only measurable state.
• Theoretical analysis proves asymptotic convergence of the tracking error to zero under bounded uncertainties and disturbances.
• Control gains are tuned via simulation and experiment, with λ₁=λ₂=10 or 15 and HOSMO gains L₁=35, L₂=100, L₃=600.
• Performance is evaluated under external disturbances (e.g., w(t)=5sin(t)) and for sinusoidal/trapezoidal reference signals.

Experimental results

Research questions

• RQ1 Can a continuous, chattering-free RTMF controller be designed for uncertain LTI systems using the super-twisting algorithm?
• RQ2 Does the use of a higher-order sliding mode observer (HOSMO) improve state estimation and control performance compared to a standard super-twisting observer (STO) in real-time MagLev control?
• RQ3 Can the STA-based RTMF controller achieve asymptotic tracking of time-varying references despite parametric uncertainties and external disturbances?
• RQ4 How does the control effort and sliding surface precision compare between STA-STO and STA-HOSMO configurations in experimental MagLev implementation?
• RQ5 Is the proposed controller-observer pair robust and effective in practical hardware implementation, not just simulation?

Key findings

• The RTMF controller based on STA with HOSMO achieved smoother control signals compared to the STA-STO configuration, as evident in experimental control effort plots (Fig. 7, 13).
• The sliding surface in the HOSMO-based system showed improved precision, with clearer convergence and reduced ripple in zoomed plots, indicating better second-order sliding mode performance.
• Experimental results confirmed asymptotic convergence of the tracking error to zero under both sinusoidal and trapezoidal reference inputs, even with external disturbance w(t)=5sin(t).
• The HOSMO-based observer provided estimation accuracy comparable to STO, but enabled the continuous control signal to achieve true second-order sliding mode motion on the chosen sliding surface.
• The controller-observer pair based on STA and HOSMO successfully achieved robust, chattering-free, and high-precision tracking in real-time hardware implementation on a MagLev system.
• The study demonstrated that the STA-HOSMO pair is superior to STA-STO for achieving second-order sliding mode behavior with continuous control in practical applications.