**1. Introduction**

Unknown plant parameters or, more generally, plant uncertainty and the preferences in which the system dynamics are purposely represented by simplifications, such as the use of linearized friction model, lead to model imprecision [1]. Control engineering classifies the model inaccuracies, which were used here as synonym of imprecision, into two main categories as structured and unstructured uncertainties. The first one implies inaccuracies within the model and the second one corresponds to inaccuracies on the system order (i.e., underestimated system order). Modeling inaccuracies can have adverse effect on nonlinear control systems [1].

Robotic manipulators represent the best examples for strongly coupled, highly nonlinear, time-varying dynamical systems [2]. These qualities alongside structured uncertainties caused by model imprecision of link parameters and payload variation, and unstructured uncertainties produced by unmodeled dynamics such as

nonlinear friction, compliance in gearing, sensor noise, external disturbances, and the high-frequency part of the dynamics turn the motion control of rigid-link manipulators into a complex problem [2]. Particularly, robotic manipulators suffer so much from these structured and unstructured uncertainties. The consequence of having to deal with various uncertainties in their dynamics and the necessity to manage the various tools and, hence, the variation of dynamic parameters during operation make it difficult for robots to introduce a mathematical model suitable for employing model-based control strategies.

The theory of conventional sliding mode control (SMC) as a simple robust nonlinear control scheme has been applied to robotic manipulators successfully since the 1980s. In those studies, the advantages of the SMC properties such as its robustness against disturbances and variation of parameters, and its fast dynamic response have been utilized greatly. Two important approaches, such as robust control and adaptive control, can deal with modeling uncertainty [1]. Particularly, adaptive control is effective in solving the structured and unstructured uncertainties and is capable of maintaining a uniformly good performance over a limited range.

SMC as a special class of the variable structure systems (VSS) has been preferred in practical applications for over 50 years due to its simplicity and robustness against parameter variations and disturbances [3]. VSS concept was first evolved from the pioneering work of Emel'yanov and Barbashin in the early 1960s in Russia [4]. Especially, VSS and SMC have received a great attention by the control research community worldwide since the published 1977 article [4]. SMC methodology is used to design a control law that imposes all system trajectories to converge on a surface in the state space, the so-called sliding surface *S t*ð Þ. The designer chooses the dynamics of this surface so that all trajectories will asymptotically converge to the set point. When the trajectory lies inside the sliding surface, the system operates in so-called sliding mode and is sensitive to parametric variations and external disturbances [5]. Control action in sliding mode is discontinuous by nature and can stimulate high-frequency dynamics [6]. Discontinuous nature of the control action serves to maintain a resulting superior system performance of VSS and SMC by switching between two incomparably different system structures such that sliding mode with this feature is also referred to as a new type of system motion in a manifold, or in another substantial terms, in the vicinity of a prescribed switching manifold, the velocity vector of the controlled state trajectories is always directed toward the switching manifold by such motion induced by imposing discontinuous control actions [3, 6]. This system performance is expected to exhibit insensitivity to parameter variations as well as demonstrate complete disturbance rejection [6].

Despite its advantages such as simplicity and robustness, SMC suffers from a rather widespread and well-known chattering problem, which is generally perceived as motion oscillating about the predefined switching manifold(s) [3, 6]. There are two reasons behind the chattering phenomenon: first, under the absence of switching nonidealities such as delays, that is, in a situation where the switching device ideally switches at an infinite frequency, the presence of parasitic dynamics in series with the plant causes a small amplitude high-frequency oscillation to occur around the sliding manifold. If the closed loop pole locations are well defined or the closed loop poles are well assigned with the aid of the pole placement design technique, these parasitic dynamics which represent the fast actuator and sensor dynamics are often neglected in the open loop model used for control design in control applications. In general, the motion of the real system is closer to an ideal system where the parasitic dynamics are neglected, and the difference between the ideal and the real motion, which is at negligible time constants, shows a rapid decline. However, the parasitic dynamics interacted with variable structure control

#### *An In-Depth Analysis of Sliding Mode Control and Its Application to Robotics DOI: http://dx.doi.org/10.5772/intechopen.93027*

(VSC) in particular produce a nondecreasing oscillatory component with a finite amplitude and a frequency, referred previously to as chattering phenomenon already. Second, the switching nonidealities alone can cause such high-frequency oscillations around the sliding surface *S t*ð Þ [3, 6]. These may include small time delays due to sampling (e.g., zero-order hold), execution time required to calculate the control, and transmission delays in networked control systems [3]. As time delays cause the resulting chattering phenomenon, and the delay type of switching nonidealities is the most relevant to any electronic implementation of the switching device whether it includes analogue or digital circuits, delay type nonidealities are considered in general for the design approaches, and discrete-time control design techniques are the most commonly used design approaches by control engineers to mitigate the chattering caused by the switching delays [6]. Many design methodologies have been applied so far to mitigate or reduce the chattering. To eliminate the chattering, a boundary layer around the sliding surface *S t*ð Þ has been introduced [1]. Inside the boundary layer, the switching function is replaced by a high-gain proportional control [5]. In order to reduce the chattering level, several switching functions such as saturation functions, relay functions, hyperbolic functions, and hysteresis saturation functions have been used in literature. The use of these functions can minimize or, if desired, completely eliminate the chattering, but it turns perfect tracking into a tracking with a guaranteed precision problem, meaning that a steady-state error is always maintained.

SMC design procedure is split into two major steps corresponding to the two main phases [3]: reaching phase is defined to derive the system state from initial state to reach the switching manifolds in finite time; and sliding-mode phase is defined to induce the system into the sliding motion on the switching manifolds like an attractor.

No matter how active the research on SMC has been during the last 50 years, the key technical challenges such as chattering, the elimination of the effects caused by unmodeled dynamics, disturbances and uncertainties, adaptive learning, and improved robustness can still remain to be addressed to reach a perfect solution [3]. An ideal sliding mode can only be achieved when the dynamic equation governing the sliding mode is satisfied by the system state for all time. This implies an infinite switching to assure the sliding motion [3]. Although the switching rate of the switching control device of the SMC system (design) is infinite ideally, it is much lower than that in practice due to the physical limitations of switching [6]. Physical limitations of switching have been tried to be explained in the previous paragraphs.

Usually, intelligent control approaches can mitigate the effects of structured parametric uncertainty and unstructured disturbance with their effective learning ability without requiring a detailed knowledge of the controlled plant within the design process. SMC research has recently been integrated with intelligent control approaches such as neural networks, fuzzy logic, genetic algorithms, and probabilistic reasoning, just a few of them, to make it more intelligent [3, 7–11]. Another goal behind the combination of the intelligent control with the attractive features of this traditional control is to create more powerful control algorithms. Nevertheless, it appears that many intelligent control algorithms do not take into account actuator dynamics in robot control systems, which play a critical role in overall robot dynamics and their negligence can cause adverse effects, especially in the case of high-speed torque, respectable load variations, friction, and actuator saturations [2]. Electrical actuators are very much controllable than others and are more suitable for driving robot manipulators [2, 12].

Sliding mode control strategy is the simple approach to robust control. By intuition, controlling first-order systems is much easier than controlling general *nth*order systems, even if they are nonlinear or uncertain. Therefore, an introduction of

#### *Automation and Control*

a notational simplification allows *nth-*order problems to be replaced by equivalent first-order problems. Thus, it is then easy to demonstrate in principle the achievement of perfect performance under the presence of arbitrary parameter inaccuracies for the transformed problems. However, such performance is only achieved at the expense of extremely high control activity. This is typically disputed by the other source of modeling uncertainty, such as the presence of neglected dynamics, which the high control activity can stimulate. This leads to a change in control laws aimed at achieving an effective trade-off between tracking performance and parametric uncertainty, given the acceptable control activity [1].

The concepts will first be presented for systems that have a single control input that allows us to develop an intuition about the fundamental aspects of nonlinear controller design.
