# Enhanced Trajectory Tracking via Disturbance-Observer-Based Modified Sliding Mode Control
## 1 Introduction
Due to disturbance rejection, the performance of the system was improved. [PERSON] et al. [32] designed a DO-based non-singular terminal sliding mode control for an n-degree-of-freedom robot manipulator. Disturbance rejection reduced the system chattering. [PERSON] et al. [34] proposed an intermediate observer (IO)-based control scheme for the electromagnetic docking of spacecraft in elliptical orbit. The proposed IO estimated the relative motion and the total disturbance. The extended-state observer (ESO) estimates system states and perturbation. In the ESO, the idea is to define the system uncertainty, modeling error, and known and unknown dynamics as perturbations. This defined perturbation is then assumed to be an extended state of the system. The observer (ESO)'s task is to estimate the defined perturbation and the system states. This estimated-perturbation information is useful for perturbation rejection. The design of the ESO requires a minimal amount of information about the system, and it does not require the nominal model of the system. It is easy to implement. The researchers designed and implemented an ESO-based SMC for real-life applications [35; 36; 37]. The idea is to estimate the perturbation and use the estimated information in feedback (along the control input) to cancel the actual perturbation. [PERSON] et al. [35] designed an ESO-based SMC for friction compensation in a three-wheeled omnidirectional mobile robot. The frictional modeling was a tedious task, but this information was necessary for the desired control performance. They defined the friction model as part of the perturbation. By utilizing the known dynamics of the mobile robot, they proposed a reduced-order ESO to estimate system states and perturbation. This estimated perturbation helped to achieve the desired performance. [PERSON] et al. [37] proposed a cascade-ESO-based SMC for the accurate control of underactuated flexible-joint robots. The ESO was utilized to estimate the unmeasurable states and lumped disturbance. The chattering was reduced due to disturbance rejection. Although that work used DOs (ESO and others) to estimate the system uncertainty and external disturbance, its design required the nominal model of the system. The estimation techniques are necessary to estimate the nominal system's model. Implementing such techniques requires experiments, which in turn increases the computational cost. Additionally, it should be noted that system parameters vary with time and the position of the system (e.g., gravity changes with the position). [PERSON] et al. [38] proposed a model-free control algorithm (ESO-based SMC) for the accurate trajectory tracking of a multi-DOF virtual robot manipulator. The algorithm was implemented on a virtual simulator developed in MATLAB (Simulink), and the desired trajectory was assigned through an external joystick. Although the controller's performance was satisfactory, there was a need to further reduce the error. The objective of the current research is to further reduce the trajectory-tracking error and design a model-free control for the nonlinear system. To address this issue, a new algorithm is discussed below. In this research, an SMC with a proportional integral derivative (PID) sliding surface was designed and integrated with a saturation function-based ESO. The ESO estimates system states and perturbation, and the estimated state information was used in the design of the control algorithm. The estimated perturbation was combined with the PID-SMC input and utilized as a feedback term to cancel the effect of the actual perturbation. The utilization of a PID-type sliding surface enhanced the system's performance, leading to the following benefits:  
1. Reduced tracking error compared to the existing method;
2. Effectiveness in mitigating low-frequency perturbations when compared to the existing method;
3. The design requires minimal information about the system, making it a model-free control approach.