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 .The typical structure of a slidingmode 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 slidingmodecontrol (PISMC) in their studies . 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).
In this study, the performance of SMC, P, PD and PIDcontrollers 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 PIDsliding surface instead of using conventional PID controller.
This paper presents a decoupling algorithm of slidingmodecontrol on invertedpendulum. The decoupled method provides a simple way to achieve asymptotic stability for a nth -order nonlinear systems. The system dynamics of SMC and invertedpendulum systems are encapsulated in the algorithm form and analysed by MATLAB Simulations. The convergence of the proposed slidingmodecontrol is verified by Lyapunov function to prove the stability of system. Numerical simulations of designed SMC control strategy for invertedpendulum demonstrate faster convergence, reduced disturbance in control input and overall robust performance.
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 invertedpendulum 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 invertedpendulum than the two fuzzy logic controller. The result is considered in term of maximum overshoot, settling time and steady state error.
Controlsystem design for wheeled inverted pendulums has been intensively studied in the literature. Many of early studies adopt linear controllers – based on a linear approximation of a nonlinear model around an equilibrium point. A limitation of linear controllers is that they are not necessarily effective in cases where the system state is far from the equilibrium point, such as in our transformation problem. More recent studies have proposed various nonlinearcontrol methods for wheeled inverted pendulums –. They can be classified by how to deal with the underactuation, which occurs mainly because both the velocity (or position) of the vehicle and the pitch angle of the body need to be controlled by a single actuator.
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-modecontrol (EFSMC) system, which does not need the plant model, is proposed for unknown nonlinear systems. The EFSMC system is applied to an invertedpendulum 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-modecontrol, the EFSMC system provides very high precision and finite-time controlperformance; (4) the system analysis is given in the sense of the gradient descent method.
The two-wheeled invertedpendulum, however, is well studied, and possesses similar dynamics to this platform. A number of review articles compare performancebetween 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 , . 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 . Nonlinear optimal control has been implemented on a TWIP , 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.
ABSTRACT: Double Rotary InvertedPendulum (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.
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.
Due to nonlinear characteristics of boost converter, some researches have employed nonlinear controller such as slidingmodecontrol. The robustness against parameter uncertainty and disturbance are the main reason why slidingmodecontrol is utilized to controlnonlinearsystem, including boost converter. Many slidingmodecontrol 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 slidingmodecontrol design, steady state error regulation needs to be considered. However, in , 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 systemperformance, adaptive slidingmodecontrol 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 slidingmode in finite time is employed reaching law dynamics and incorporates it to natural control signal. Therefore, nonlinear observer based adaptive slidingmodecontrol with PI sliding surface is proposed for boost converter. The main contribution of this paper is to improve the systemperformance of voltage regulation boost converter using the combination of nonlinear observer and adaptive slidingmodecontrol 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.
In this paper, a robust neural network global slidingmodePID-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 controlsystem with the fuzzy slidingmode 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. Slidingmodecontrol 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 slidingmode 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.
This work has presented an LQR based PID controller to control the invertedpendulumsystem. 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 invertedpendulum 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
The Matlab-Simulink models for the simulation of modeling ,analysis, and control of nonlinearinvertedpendulum cart dynamical system without and with disturbance input are developed. The typical parameters of invertedpendulum-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: 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
ABSTRACT: The invertedpendulumsystem findsit’s most widespread application in the study of control engineering. This paper focused on modelling and performance analysis of linear invertedpendulum and double invertedpendulumsystem. 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 invertedpendulumsystem. Simulation is done using Matlab software.
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. .
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.
Being an under-actuated, non-linear and unstable system, the invertedpendulum (IP) has been examined by many researchers to study the behavior and performance of different and new types of control algorithms , . The invertedpendulum 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 . Even though these types may have different shapes and sizes, their main objective is the same, namely, to balance the whole system. Since the invertedpendulum is a basic form of any advanced balancing systems -, its applications widely vary from simple robots like scooters and robot arms, to more sophisticated systems such as satellites and rocket launch , -.
ABSTRACT: Generally the invertedpendulum 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 controlsystem (FLC) was selected as the control technique due to its ability to deal with nonlinear systems such as invertedpendulum. Special feature of fuzzy logic control is that it controls the physical system.