# Efficient Control of a Non-Linear System Using a Modified Sliding Mode Control
## 1 Introduction  
Decommissioning or dismantling nuclear power plants gained attention all over the world after the Fukushima nuclear power plant incident in Japan. Because of the dynamic or hazardous environment of a nuclear power plant it is better to use a robot, whether it is fully autonomous or semi-autonomous. For the dismantling of massive structures, hydraulic operated robot manipulators have been widely used as high-power actuator [1] and should be controlled by tele- operation because of high radioactive environment problem [2; 3; 4; 5; 6; 7; 8]. Hydraulic systems are highly non-linear in nature because they have a lot of uncertainties and non-linearity's. Due to the nature of a hydraulic system, it is complicated to control the system with conventional or linear control logic. To overcome this problem, a robust or non-linear control is needed. In the last few decades, using sliding mode control (SMC) as a kind of non-linear control has gained much attention among researchers because of its robust nature [9; 10; 11; 12; 13; 14]. The main idea is to design a desired sliding surface and force the system states to move towards it by using gain switching. It is used as a robust controller for a system with non-linearity. However, there is a problem with conventional SMC when the system reaches the sliding surface, because it is difficult to remain along the sliding surface due to a high gain switching control system output crossing back and forth around the sliding surface which causes chattering [15; 16; 17]. Chattering can be reduced by perturbation compensation where the perturbation consists of the uncertainties of a system, error of the dynamics, and external disturbances. Perturbation measurement or estimation is a challenging task for researchers because measuring external forces using a force sensor is not feasible in all instances, and by using a sensor we cannot estimate system uncertainties, etc. To overcome this problem [PERSON] et al. proposed using a sliding perturbation observer (SPO) [2]. SPO is the combination of a perturbation observer and a sliding observer (SO) [3]. SPO used partial state feedback from the non-linear system to estimate other variables in the high-performance state estimator. It can observe low-frequency perturbation accurately because of its mathematical design. SPO is similar to extended state observer (ESO) [18; 19]. Both algorithm estimates not only system states, but also perturbation, which can be further used for perturbation compensation or disturbance rejection. Sliding mode control with sliding perturbation estimation (SMCSPO) is a fusion of SMC and SPO, which utilizes only partial state feedback to estimate the system states and perturbation with reasonable accuracy. SMCSPO has good state estimation accuracy. This estimation of perturbation is useful in the reduction of chattering by using perturbation compensation techniques [2; 3]. SMCSPO is a highly accurate control scheme for the estimation of state and perturbation in control of surgical robots and hydraulic robot manipulators [20; 21; 22; 23]. The purpose of this estimation is used to reduce the chattering from system output by perturbation compensation. However, in conventional sliding mode control, during the sliding phase, the gain K should be greater than the upper bound of perturbation in order to satisfy the Lyapunov stability criteria. The greater the value of gain K, the larger the chattering at the system output, which is a highly undesirable phenomena in mechanical systems. Different techniques have been applied to reduce chattering from SMC, like the introduction of a boundary layer and perturbation compensation techniques [3]. The greater value of gain K increases the breaking frequency of the low pass filter between the sliding surface and perturbation because the system becomes sensitive to high-frequency perturbation.