This paper describes a system designed for linear servo cart systems that employs an integral-based Linear Active Disturbance Rejection Control (ILADRC) scheme to detect and respond to disturbances. The upgrade in this control technique provides extensive immunity to uncertainties, attenuation, internal disturbances, and external sources of noise. The fundamental technology base of LADRC is Extended State Observer (ESO). LADRC, when combined with Integral action, becomes a hybrid control technique, namely ILADRC. Setpoint tracking is based on Bode’s Ideal Transfer Function (BITF) in this proposed ILADRC technique. This proves to be a very robust and appropriate pole placement scheme. The proposed LSC system has experimented with the hybrid ILADRC technique plotted the results. From the results, it is evident that the proposed ILADRC scheme enhances the robustness of the LSC system with remarkable disturbance rejection. Furthermore, the results of a linear quadratic regulator (LQR) and ILADRC schemes are comparatively analyzed. This analysis deduced the improved performance of ILADRC over the LQR control scheme.

As industrial systems become more complex, their analysis and control become even more complex, thus increasing the complexity. Recent research focuses on designing control systems robust to uncertainties that are internal like dynamics or external like disturbances. Some advancements in the research mentioned above are discussed as follows. First is the scheme to control the external uncertainties of linear/nonlinear systems using sliding mode control [

It is concluded that when parametric uncertainties and system nonlinearities are present, linear control schemes such as linear quadratic regulators (LQRs) and proportional integral derivatives (PIDs) exhibit instability. [

LADRC control method solves both the setpoint tracking (SPT) and disturbance rejection (DR) problems more effectively than the standard method by accepting the disturbance as a variable [

In addition, it must be logical. Secondly, the specific polynomial that corresponds to the augmented model has a high order. Finally, this proposed work plays a significant role in the following:

Introduces the BITF model to control systems using integral-based controllers by imposing iso-dumping property in the CL response.

Proposes the LDARC control for necessary action with the SPT loop.

Contributes theoretically in designing a new control method for SPT controller using BITF.

Validates the theoretical contribution by simulation results, especially concerning SPT controller gain variations, to robustizing the control structure.

Implements the proposed ILADRC controller experimentally on a linear servo cart system. It is also more robust than the existing methods based on the results obtained.

Although there are many works on dynamic inversion-based controller algorithms, most of them integrated it with different other techniques and applied them to various applications. None of the investigations integrates with fractional-order control techniques as in our paper.

When designing a controller, the stability of the dynamical systems is the essential criterion. It is a well-known fact that model uncertainties and disturbances could cause instability to the system. For this reason, studies of new or improved controllers have continuously been an active research area. A linear servo cart system with a DC motor connected to a rack and cart is described in this article as an example of a dynamical system. The

There are many types of controllers introduced to overcome the mentioned issues. The RGDI controller has shown good setpoint tracking performance and robustness in dealing with system uncertainties in a similar application. However, there are still some tracking errors that we believe our proposed invention could improve, and there was also no proof if the RGDI can still perform well when disturbances are injected. Therefore, in this article, we will add a test where a disturbance is injected at a steady state and compare the performance of RGDI with our proposed invention.

The standard LADRC formulation for linear integer order systems does not require the control of the entire model. According to this method, the model’s gain and degree are the determining factors. For a second-order model, the controlled scheme is as follows:

Where

By using an ESO, the LADRC method estimates the unknown. In cases where

and

ESO is structured as follows

Asymptotically stable

As a standard solution to setpoint tracking, state feedback is used. Therefore, the control law

LADRC’s standard structure is shown in _{o} for the controller, and the

The main point to bear in mind is that derivatives of non-integer order have different meanings, and that these definitions are not always equivalent. In this paper, we propose a control system based on a LADRC and integer-ordered necessary actions. The present study has combined fractional integrals with another technique. Specifically, its main objective is to enhance the performance of the standard LADRC for fuzzy systems, specifically regarding the effect of external disturbances. It was shown in

According to the state feedback _{s}, the CL characteristic polynomial’s n poles may be placed at their discretion. _{i}. Then the LADRC structure may be strengthened in terms of the open-loop gain setpoint. In this case,

The following would be a progression of methods that can be used to determine the coefficient of state feedback _{s2}, the coefficient _{i} associated with the fractional integrator of

This corresponds to the open loop

The following is a simple way to write it

The transfer function in

kg - the ratio between the gears,

_{m}- constant of the back-emf,

As a result of its low value, motor inductance is ignored.

The driving force,

_{m} is the voltage applied to the actuator, and _{m} represents the gain of the actuator, obtained as

The steady-state gain and time constant are derived from the above transfer function as

The voltage and cart position transfer function can be computed through the cascading of an integrator (

An example of LADRC control scheme that validates the performance of the proposed Integral based LADRC control scheme consists of a linear servo cart system, which consists of two carts sliding on a track and driving one of them using a DC motor. This system has been found to be an interesting example of a LADRC control scheme that utilizes a linear servo motor to drive one of the carts. Due to the interaction between two systems, the modeling of this system is complex. During testing, determining the cart’s position was the objective, and the vibration was considered a permanent disturbance. As shown in

To demonstrate the LQR control scheme and compare ILADRC’s performance to the standard LQR structure, we use the linear servo cart system described above. A linear servo cart system is an interesting example since a DC motor drives a cart sliding on a track. Controlling the cart’s position is the goal, and the uncertainty is regarded as a permanent disturbance.

Computer simulations are performed on a linearized Linear Servo Cart (LSC) system to authenticate the controller’s performance to evaluate the real-time performance. In Simulink/Matlab, we create a simulation environment with a simulation time of 5 s in order to analyze numerically the controller performance. The square wave profile having an amplitude of 100 mm with a frequency of 0.66 Hz is commanded as a reference input command to the LSC system. The linear displacement and speed response and the controlled voltage to a reference square wave command are shown in simulation results.

The simulation is carried out by providing a square wave linear displacement profile with a magnitude of ±10 cm with a frequency of 0.1 Hz.

The simulation was performed by considering a sawtooth profile as a reference input to the LSC system to visualize the performance of ILARDC with traditional LQR for robustness and parametric uncertainties. The evolution of the linear position and speed responses and controlled voltages are illustrated in

Servo cart systems play a vital role in a number of automated systems because of their displacement and speed control. In this work, an ILADRC control technique is developed for displacement and speed control of linear servo carts. Several speed and position control technique-based related work was initially studied and analyzed. It is proposed to control a minimum phase-stable system using a LADRC structure with an integrated action (ILADRC). This contribution consists a novel design method is proposed for the ILADRC scheme based on the BITF. As elaborated in the previous section, a novel design method is proposed for the SPT controller. A critical contribution to the design of the LADRC control scheme is to use it from a practical point of view. Using results obtained from experiments on the linear servo cart system (LSC), the effectiveness of the proposed ILADRC scheme is illustrated. Results show improvements in robustness due to the rejection of disturbances in ILADRC scheme. In addition, results are compared between the integral-based LADRC and the traditional LQR schemes which are based on statistical methods.

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number (IFPRC-023-135-2020) and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.