An improved integral backstepping sliding mode control (IIBSMC) strategy is proposed to address the problems of long regulation time and poor disturbance resistance of integral backstepping control (IBC) for quadrotor aircraft. The IIBSMC method first introduces the integral term into the virtual variable on the basis of IBC, which makes the system respond faster, overshoot smaller and anti-interference performance stronger. After that, combined with sliding mode control, the system is further processed to improve the control performance of the system. Finally, the quadrotor is controlled to achieve fixed-point hovering and trajectory tracking, and the rotation and translation performance of the aircraft and the stability under external interference are improved. When the quadrotor aircraft is subjected to instantaneous interference, constant interference, sinusoidal interference, white noise interference, and complex interference, the simulation experiments of IBC, improved integral backstepping control (IIBC), integral backstepping sliding mode control (IBSMC), and IIBSMC are compared. It can be obviously found that the IIBSMC method has smaller system overshoot, faster recovery of the original equilibrium position, shorter adjustment time, and smaller error. When using the IIBSMC method to design the controller, the stability of the controller is theoretically proved by backstepping recursion. Finally, the simulation results show that the designed controller can better achieve fixed-point hovering and trajectory tracking control well.
The dielectric elastomer actuator (DEA) is widely used in the field of soft robots due to its large deformation, light weight, fast response, and high-energy conversion efficiency. The high-precision control of the DEA is the precondition for soft robots to perform complicated tasks. In early studies, researchers usually employed integer order modeling and control methods to build the dynamic model of the DEA and to achieve its tracking control. However, these methods are not good at handling the complicated memory property of the DEA. In addition, the number of required parameters in integer order models and control methods is enormous, which hinders their practical applications. To solve these problems, the fractional order modeling method and fractional order internal model control method of the DEA are proposed in this paper. Firstly, a fractional order transfer function (FOTF) model of the DEA is built to depict its complicated memory property. Then, to achieve the computer control, an integer order approximation model (IOAM) of the FOTF model is built by using the Oustaloup filter. Considering that the order of the IOAM is too high, a reduced integer order approximation model is established by using the square root balance truncation algorithm to facilitate the system controller design. Next, a fractional order internal model controller is designed. Finally, tracking control experiments are exerted to demonstrate the effectiveness of the proposed method. Since the root-mean-square errors of all experimental results are less than 2%, the proposed modeling method and control method are superior from the perspective of the practical application.
The Fractional Complex Order Plant model, which has lately gained popularity in applied physics and control systems, is the main subject of this study. The major contribution of this study to the literature is the discussion of the physical phenomena of complex plant models and how they affect the stability and robustness of the systems. Because the Fractional Complex Order Plant model is the most general mathematical form, other plant models covering the Integer Order Plant and the Fractional Order Plant can be easily created with this benefit. The proposed approach using the classical Proportional Integral controller which is recalled as the Integer-Order PI controller in this paper gives the calculation equations of the physical alterations of plants having integer, fractional, and complex orders. Along with the visuals and with the aid of simulations, the consequences of the parameters on the system are described. Additionally, the advantages and disadvantages of the proposed controller designs for each of the three plant species are discussed.