SMC is a method in modern **control** theory that uses state- space approach to analyze such a **system**. Using state-space methods it is relatively simple to work with a multi-output **system** [8].The typical structure of a **sliding** **mode** controller (SMC) is composed of a nominal part and additional terms to deal with model uncertainty. The way SMC deals with uncertainty is to drive the plants state trajectory onto a **sliding** surface and maintain the error trajectory on this surface for all subsequent times. The advantage of SMC is that the controlled **system** becomes insensitive to **system** disturbances. The **sliding** surface is defined such that the state tracking error converges to zero with input reference. With the perspective to achieve zero steady state error, Cao and Xu (2001) and Sam et al. (2002) have proposed the proportional integral **sliding** **mode** **control** (PISMC) in their studies [9]. The proportional factor in this controller gives more freedom in selecting some parameters matrices that will make the output response faster and the stability condition to be more easily satisfied. The proportional integral **sliding** surface equation can be represented as (14).

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In this study, the **performance** of SMC, P, **PD** and **PID** **controllers** are evaluated for position tracking **control**. The Lyapunov approach is used in theoretical analysis in developing the SMC with **PID** scheme and to ensure that the **system** is under stable condition. The numerical simulation study shows that the proposed controller provides better **performance** in tracking accuracy and time response. The **control** effort produced from SMC without the chattering effect also is practical to be used in real application. In conclusion, a simple **control** method without much **control** effort and better **performance** can be made with the SMC design based on **PID** **sliding** surface instead of using conventional **PID** controller.

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This paper presents a decoupling algorithm of **sliding** **mode** **control** on **inverted** **pendulum**. The decoupled method provides a simple way to achieve asymptotic stability for a nth -order **nonlinear** systems. The **system** dynamics of SMC and **inverted** **pendulum** systems are encapsulated in the algorithm form and analysed by MATLAB Simulations. The convergence of the proposed **sliding** **mode** **control** is verified by Lyapunov function to prove the stability of **system**. Numerical simulations of designed SMC **control** strategy for **inverted** **pendulum** demonstrate faster convergence, reduced disturbance in **control** input and overall robust **performance**.

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The improvement of fuzzy logic controller **control** technique are continuously be studied by researchers. (Chun-e et al. 2011) also introduced fuzzy logic controller in the **system** as the second controller. In this paper research, the researchers implement fuzzy logic controller as a second controller since the **PID** controller are less effective toward the **performance** and robustness. The two fuzzy logic **controllers** give the angle and position of the **inverted** **pendulum** completed **control** in seconds. (Yadav et al. 2011) proposed a design of a fuzzy logic as another controller to make the **system** more stable and robust. The developing several combination of fuzzy logic **PD** and **PID** give the better result in **performance** and robust of **inverted** **pendulum** than the two fuzzy logic controller. The result is considered in term of maximum overshoot, settling time and steady state error.

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Abstract The brain emotional learning model can be implemented with a simple hardware and processor; how- ever, the learning model cannot model the qualitative aspects of human knowledge. To solve this problem, a fuzzy-based emotional learning model (FELM) with structure and parameter learning is proposed. The mem- bership functions and fuzzy rules can be learned through the derived learning scheme. Further, an emotional fuzzy **sliding**-**mode** **control** (EFSMC) **system**, which does not need the plant model, is proposed for unknown **nonlinear** systems. The EFSMC **system** is applied to an **inverted** **pendulum** and a chaotic synchronization. The simulation results with the use of EFSMC **system** demonstrate the feasibility of FELM learning procedure. The main contri- butions of this paper are (1) the FELM varies its structure dynamically with a simple computation; (2) the parameter learning imitates the role of emotions in mammalians brain; (3) by combining the advantage of nonsingular ter- minal **sliding**-**mode** **control**, the EFSMC **system** provides very high precision and finite-time **control** **performance**; (4) the **system** analysis is given in the sense of the gradient descent method.

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The two-wheeled **inverted** **pendulum**, however, is well studied, and possesses similar dynamics to this platform. A number of review articles compare **performance** **between** different classical **control** techniques applied to the TWIP such as **PID**, LQR, and pole placement techniques. These typi- cally find minimal **performance** difference **between** approaches given comparable parameter tuning, and consistently poor **performance** in the presence of constraints [3], [4]. Feedback linearisation can be used to negate some of the **nonlinear**- ities present in the **system**, achieved by a suitable change of variables and **control** input, transforming the **nonlinear** model into an equivalent linear one suitable for **control** by classical techniques. These methods have been applied to the TWIP for varying degrees of linearisation and **control** up to providing global position **control** for point to point manoeuvres [5]. **Nonlinear** optimal **control** has been implemented on a TWIP [6], using a **nonlinear** method similar to LQR to achieve full position **control**. However, none of these methods provide a systematic way of ensuring constraint satisfaction, and therefore must be provided with a suitable externally generated reference trajectory that results in the closed loop **system** observing the desired constraints. It must therefore be accepted that constraints may be violated during disturbance unless a suitable updated recovery trajectory can be provided sufficiently quickly as to prevent violation.

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ABSTRACT: Double Rotary **Inverted** **Pendulum** (DRIP) is a member of the mechanical under-actuated **system** which is unstable and **nonlinear**. The DRIP has been widely used for testing diﬀerent **control** algorithms in both simulation and experiments. The DRIP **control** objectives include Stabilization **control**, Swing-up **control** and trajectory tracking **control**. In this research, we present the design of an intelligent controller called “hybrid Fuzzy-LQR controller” for the DRIP **system**. Fuzzy logic controller (FLC) is combined with a Linear Quadratic Regulator (LQR). The LQR is included to improve the rules. The proposed controller was compared with the Hybrid **PID**-LQR controller. Simulation results indicate that the proposed hybrid Fuzzy-LQR **controllers** demonstrate a better **performance** compared with the hybrid **PID**-LQR controller especially in the presense of disturbances.

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II. PLC (programmable logic controller): - It is used in electrical **system** to improve the reliability and efficiency of electrical equipment (electrical motor) in automation processes. To obtain accurate result PLC is interfaced with converter, PC (Personal computer) and other electrical equipment. In this application PLC of Allen Bradley is used to communicate with VFD and in turn it **control** 3 phase induction motor. A **control** program is developed to get required operation of motor and VFD.

Electricity which is an increasing demand leads to the persistent demand to operation of the power **system**. So power **system** stability and the quality power to the consumers have equal importance that as the electric power demands. The size and structural components of electric power **system** vary even though they have some basic characteristics. For the generation of electricity synchronous machines are used. Prime mo vers convert the primary source of energy to mechanical energy which in turn converts to electrical energy by synchronous generators. Electric power generated at generating stations, through a complex network of individual components is transmitted to consumers. The individual components include transmission lines, transformers and switching devices. With a high degree of efficiency and reliability form of electrical energy can be transported and controlled. A wide variety of disturbances occurs frequently and electric **system** must withstand and remain intact for these disturbances.

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Due to **nonlinear** characteristics of boost converter, some researches have employed **nonlinear** controller such as **sliding** **mode** **control**. The robustness against parameter uncertainty and disturbance are the main reason why **sliding** **mode** **control** is utilized to **control** **nonlinear** **system**, including boost converter. Many **sliding** **mode** **control** methods [9-13] had been applied to boost converter. However, in practical, this **control** method requires to be fully known some variables, such as input voltage, inductor current, output voltage, and resistance load. As consequences, many sensors are needed to be installed to acquire those variables as input **control**. Implementing those methods causes increasing cost production and adding more space and weight in real **system**. Therefore, to reduce the number of sensors, **nonlinear** disturbance observer [13-15] is designed to estimate some variables, such as inductor current, output voltage, resistance load, and input voltage generated from solar array. The **nonlinear** disturbance observer accurately generates the estimated value of resistance load and input voltage such that when the variations of those variables exist, the proposed controller is still able to overcome those disturbances. In **sliding** **mode** **control** design, steady state error regulation needs to be considered. However, in [13], it is employed standard **sliding** surface and only use equivalent **control** signal to regulate boost converter. This can cause the output voltage response cannot track the varying desired output voltage and leads to steady state error. To enhance **system** **performance**, adaptive **sliding** **mode** **control** is applied to the boost converter for overcoming parameter uncertainty and disturbance [16-17]. Steady state error can be eliminated by constructing PI **sliding** surface, while ensuring **sliding** **mode** in finite time is employed reaching law dynamics and incorporates it to natural **control** signal. Therefore, **nonlinear** observer based adaptive **sliding** **mode** **control** with PI **sliding** surface is proposed for boost converter. The main contribution of this paper is to improve the **system** **performance** of voltage regulation boost converter using the combination of **nonlinear** observer and adaptive **sliding** **mode** **control** by modifying the conventional **sliding** surface into PI structure **sliding** surface. In addition, the stability of proposed method is proven by using direct Lyapunov method.

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In this paper, a robust neural network global **sliding** **mode** **PID**-controller is proposed to **control** a robot manipulator with parameter variations and external disturbances. The chattering phenomenon is eliminated by substituting a single-input radial-basis-function (RBF) neural network. The weights of hidden layers of the neural network are on-line updated to compensate the **system** uncertainties. Moreover, a theoretical proof of the stability and the convergence of the proposed scheme are provided.

Abstract —In this paper, a robust **control** **system** with the fuzzy **sliding** **mode** controller and the additional compensator is presented. The additional compensator relaying on the **sliding**- **mode** theory is used to improve the dynamical characteristics of the drive **system**. **Sliding** **mode** **control** method is studied for controlling DC motor because of its robustness against model uncertainties and external disturbances, and also its ability in controlling **nonlinear** and MIMO systems. In this method, using high **control** gain to overcome uncertainties lead to occur chattering phenomena in **control** law which can excite unmodeled dynamics and maybe harm the plant. Different approaches, such as intelligent methods, are used to abate these drawbacks.. In order to enhancement the **sliding** **mode** controller **performance**, we have used fuzzy logic. For this purpose, we have used a **PID** outer loop in the **control** law then the gains of the **sliding** term and **PID** term are tuned on-line by a fuzzy **system**, so the chattering is avoided and response of the **system** is improved against external load torque here. Presented simulation results confirm the above claims and demonstrate the **performance** improvement in this case.

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This work has presented an LQR based **PID** controller to **control** the **inverted** **pendulum** **system**. To facilitate an integration with a PLC, the **control** design uses a **control** zon- ing approach where the entire **pendulum** is divided into two regions: a normal **pendulum** regions where the nonlinearities are inherent, and the **inverted** **pendulum** region where the **system** is approximately linear close to the upright position. The errors in position and angle are denoted **control** states to enable the use of the LQR architecture to obtain the optimal gains for the **PID** controller. An algebraic approach was also presented to allow a systematic method for selection of the Q and R matrices, which in turn yielded an optimal set of **control** gains K design . Experimental implementations with

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The Matlab-Simulink models for the simulation of modeling ,analysis, and **control** of **nonlinear** **inverted** **pendulum** cart dynamical **system** without and with disturbance input are developed. The typical parameters of **inverted** **pendulum**-cart **system** setup are selected as mass of the cart (M): 1 kg; mass of the **pendulum** (m):0.1 kg; length of the **pendulum** (l): 0.3m; length of the cart track (L): ± 0.5m; the friction coefficient of the cart and pole rotation is assumed negligible. The disturbance input parameters taken in the simulation are[3]: band limited white noise power = 0.001, sampling time = 0.01, seed = 23341.After linearization, the **system** matrices used to design LQR are computed as

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ABSTRACT: The **inverted** **pendulum** **system** findsit’s most widespread application in the study of **control** engineering. This paper focused on modelling and **performance** analysis of linear **inverted** **pendulum** and double **inverted** **pendulum** **system**. A comparative study of the time specification **performance** of both the systems are shown using Linear Quadratic Regulator (LQR) controller. Two **control** methods are used in this paper, Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) controller for linear **inverted** **pendulum** **system**. Simulation is done using Matlab software.

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Active suspension **system** shows better **performance** than passive and semi-active suspension systems. Active suspension systems can provide more handling capability and ride quality than passive or semi-active suspension systems. But the main problem facing by the active suspension systems are actuator faults and parameter variations. Due to these factors, its effectiveness decreases. However, suitable solutions are needed to optimize their **performance** and provide closed-loop stability in a full- scale car model to mitigate road disturbances such as bumps and grade changes on the passenger’s ride comfort. [7].

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Figure 1.3: Classification of modern automotive suspension in Xue et al. (2011) In addition, researches over the past five decades have shown that a linear optimal **control** scheme offers an effective method in designing active suspension **control** strategies that can improve both vehicle ride and handling **performance** simultaneously, Hrovat (1997). In fact, most researchers focused on active suspension **system** with a linear model without uncertainties. However, a modern active suspension **system** is characteristically **nonlinear** and uncertain especially for the MacPherson active suspension **system**.

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Being an under-actuated, non-linear and unstable **system**, the **inverted** **pendulum** (IP) has been examined by many researchers to study the behavior and **performance** of different and new types of **control** algorithms [1], [2]. The **inverted** **pendulum** has several forms and types where each type has its own characteristics and degree of freedom. The most common types are the single IP, double IP, single rotary IP, and double rotary IP [3]. Even though these types may have different shapes and sizes, their main objective is the same, namely, to balance the whole **system**. Since the **inverted** **pendulum** is a basic form of any advanced balancing systems [4]-[6], its applications widely vary from simple robots like scooters and robot arms, to more sophisticated systems such as satellites and rocket launch [2], [7]-[9].

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ABSTRACT: Generally the **inverted** **pendulum** is unstable, because the **pendulum** will fall downward due to the gravitational force acting on mass of the **pendulum**. Keeping the **pendulum** at vertically **inverted** position, the position of DC motor shaft needs to be controlled using closed loop analysis. For closed loop analysis, feedback or input device such as encoder is used. To **control** and set the **pendulum** at desired **inverted** position in LABVIEW, fuzzy **control** logic was selected. Fuzzy **control** logic provides the stabilization of **pendulum** at vertical position without using mathematical approach such as conventional approach. Fuzzy logic **control** **system** (FLC) was selected as the **control** technique due to its ability to deal with **nonlinear** systems such as **inverted** **pendulum**. Special feature of fuzzy logic **control** is that it controls the physical **system**.

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