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Grasser et al. [1] built a scaled-down prototype of a DSP-controlled two-**wheeled** vehicle based on the **inverted** **pendulum**, and Pathak et al. [2] studied the dynamic equations of the **wheeled** **inverted** **pendulum** by partial feedback linearization. Though the **control** system used to guarantee stability of the system in [1, 2], developing a highly accurate **model** of WIP system is complex. Ren et al. [3] proposed a self-tuning PID controller which the controller parameters are tuned automatically to overcome the disturbances and parameter variations. However, the system stability can not be guaranteed. A sliding-**mode** **control** method is proposed to be capable of handling both parameter uncertainties and external disturbances [4]. The algorithm of sliding-**mode** **control** required the system dynamics; however, it is difficult to be obtained in real-time application. Chiu [5] used an adaptive output recurrent cerebellar **model** articulation controller. The proposed scheme was implemented in a PC-based experimental system to verify its effectiveness but the design procedure is overly complex.

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A two-**wheeled** **inverted** **pendulum** (TWIP) mobile robot is a three-degree-of-freedom under- actuated mechanical system with highly nonlinear dynamics. It is quiet challenging to **control** such system due to its unstable and under-actuated nature. Numerous works on modeling and **control** of TWIP mobile robot have been presented in literature. Kim et al [1] investigated the exact dynamics of the TWIP mobile robot, and a Linear Quadratic Regulator (LQR) controller was developed for balancing the robot. Fiacchini et al [2] proposed linear and nonlinear controllers for stabilizing a personal **pendulum** vehicle. To compensate for the measurable disturbances, the work in [3] compared the performance of **Model** **Predictive** Controller and LQR. Multipoint pole placement **control** for velocity tracking of the TWIP is shown in [4]. In Jones and Stol [5], the performance of the two **wheeled** mobile robot in low-traction environment was investigated by designing a LQR controller based on linearized **model** of the robot which includes wheel slip effects. Pathak et al [6] proposed velocity and position controllers for the TWIP robot via partial feedback linearization. Dai et al [7] proposed sliding **mode** controllers for self-balancing and yaw motion and designed independently. While Kim et al [8] investigated a nonlinear motion **control** using the State-Dependent Riccati Equation (SDRE) **control** framework. Kharola et al [9] discussed a fuzzy logic **control** strategy for **control** and stabilization of TWIP.

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It is important to be noted that for the case of the tracking per- formance, where the controller effort should make y(t) ≈ r(t) as t → ∞, hence the DC gain of the transfer function should be approximately 1. Therefore, it is necessary to scale the reference input using pregain N ¯ . Simulation experiments were systematically conducted by varying the configuration of Q and R. Simulation results have been discussed in detail. The simulation results have shown that the larger Q and R the more you penalize the state and the **control** effort. Choosing a large value for R means that the controller stabilises the system with less (weighted) energy, it is called expensive **control** strategy. This **control** strategy is used when the **control** signal is constrained . On the contrary, choosing a small value for R means that the controller penalises the **control** signal (cheap **control** strategy), causing a large **control** signal. Large Q implies less concern about the changes in the states.

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A new kind of quadruped-imitating walking robot is designed, which is composed of a body bracket, leg brackets and walking legs. The walking leg of the robot is comprised of a first swiveling arm, a second swiveling arm and two striding leg rods. Each rod of the walking leg is connected by a rotary joint, and is directly controlled by the steering gear. The walking motion is realized by two striding leg rods alternately contacting the ground. Three assumptions are put forward according to the kinematic characteristics of the quadruped-imitating walking robot, and then the centroid equation of the robot is established. On this basis, this paper simplifies the striding process of the quadruped-imitating walking robot into an **inverted** **pendulum** **model** with a constant fulcrum and variable **pendulum** length. According to the **inverted** **pendulum** **model**, the stability of the robot is not only related to its centroid position, but also related to its centroid velocity. Takes two typical movement cases for example, such as walking on flat ground and climbing the vertical obstacle, the centroid position, velocity curves of the **inverted** **pendulum** **model** are obtained by MATLAB simulations. The results show that the quadruped-imitating walking robot is stable when walking on flat ground. In the process of climbing the vertical obstacle, the robot also can maintain certain stability through real-time **control** adjusted by the steering gears.

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In order to perform any research work on any system, the first and foremost thing is to know about the system dynamics. The dynamics of the double **inverted** **pendulum** can be explained using a series of differential equations called the equations of motion ruling over the double **inverted** **pendulum** response to the applied force. The double **inverted** **pendulum** is shown in the figure(4) below:

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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Keywords: FPGAs Architecture and Design Techniques, Xilinx PlanAhead Tool Based FPGA Design Flow and Steps, Synthesis Techniques and Simulations, Implementation.. Received: 18 July 201[r]

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• Objects and functions do not map to each other: the architecture of functionally decomposed system is significantly different from the architecture of an object-oriented system; from UML point of view, it is impossible to map directly from use case **model**, sequence diagram, system sequence diagram…etc. to domain **model** or object **model** and vice versa. Also using use cases within the context of object-oriented development - so called “differing localization strategies” - will result in the introduction of significant errors [9].

The effect of quantization factor and scale factor on the **control** effect of fuzzy controller is further analyzed. Because the fuzzy controller is obtained by the linear state feedback controller, in order to maintain the approx- imate linear relationship between the **control** variables and the state variables, the value of the quantization fac- tor and scale factor can be changed under the following conditions:

It is seen from the above end products and analysis that all the planned models work to stabilize the **Inverted** **Pendulum**. The implemented PID’s **control** design has the slowest response due to Integral term, while the PD’s controlling proposal improves this transient response. Furthermore, outcomes also reveal that, experimented SMC scheme depicts the best results, when compared to PID’s and PD’s. This methodology has less settling time as well as the best response, when it reaches to the unstable point. However, due to applied discontinuous **control** signal, fast and finite amplitude oscillations (known as chattering) are generated, which travel to the plant in a controlled manner. In addition, the future scope belongs to the cutback of produced chattering phenomenon, exclusive of upsetting the basic nature of the controller itself.

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Routing is fundamental such a network because there is no infrastructure that manages the information exchanged between network nodes.Two major classes of routing algorithms are defined,[r]

ABSTRACT: For at least fifty years, the **inverted** **pendulum** has been the most popular benchmark, among others, for teaching and researches in **control** theory and robotics. This paper presents the key motivations for the use of that system and explains, in details, the main reflections on how the **inverted** **pendulum** benchmark gives an effective and efficient application. Several real experiences, virtual models and web-based remote **control** laboratories will be presented with emphasis on the practical design implementation of this system. A bibliographical survey of different design **control** approaches and trendy robotic problems will be presented through applications to the **inverted** **pendulum** system. In total, 150 references in the open literature, dating back to 1960, are compiled to provide an overall picture of historical, current and challenging develop- ments based on the stabilization principle of the **inverted** **pendulum**

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Next problem in this project is faced by hardware part, where the selection of the appropriate tools and equipment to ensure the system is always running smoothly. The device selection is involved in this project including microcontroller circuit and also the device to allow the **pendulum** to know differ angles depending on the situation. In terms of equipment, the selection of designing a cart, the materials used for the **pendulum** and also the selection motor to drives a cart from dropping the **pendulum**. Lastly, the problem is faced from installation software into the hardware part which is to ensure the **pendulum** always maintain in upward position by using controlling the speed of wheel. Then to strength the result for performance this system, data from simulation will be compared where all the equipment and tools will combine together to get the **Inverted** **Pendulum** (IP) systems with movement a cart in full functioning.

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A robust MPC algorithm is developed in Chapter 3 for continuous-time uncertain non- linear systems. This R-MPC (Robust and re-solvable MPC) algorithm generates online a nominal feedforward **control** policy based on a modified FHC. An additional offline-designed feedback policy is added in R-MPC to generate an invariant tube that ensures the actual states remain in the proximity of the nominal feedforward trajectory. The tube provides an explicit characterization of the R-MPC robustness, which can accommodate uncertainties and disturbances in the actual dynamics up to the level considered in the feedback policy design. An important contribution of the R-MPC algorithm is the modified FHC, which puts a relaxation on the initial nominal state for re-solves. The initial nominal state is allowed to be within the invariant tube rather than fixed to the actual state, as in the base- line MPC; this relaxation guarantees continued FHC feasibility during re-solves and leads to robust asymptotic stability of the R-MPC algorithm. The R-MPC algorithm places no requirements on the re-solve rate, which is useful in online applications with computational limitations. Additionally, specific design methods are provided for a class of continuous-time systems with uncertain nonlinear terms that have norm-bounded derivatives. The R-MPC algorithm development was joint work performed with Beh¸ cet A¸cıkme¸se [1].

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probability Sample Rule Table Meaningful rule table First attempt at defining zero Definition of zero excluding values not in the domain Useful definition of zero Definition of the lingu[r]

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Fig. 11 and Fig. 12 show two sets of results comparing the application of fuzzy **control** and conventional **control** (PID controller) techniques to the **inverted** **pendulum** problem simulation. For the same system parameters here, the PID controller proportional gain, Kp, derivative gain, Kd and integral gain, Ki are found to be 9, 14, and 0.06 respectively. The first two graph show that the fuzzy logic controller gives a smaller overshoot and shorter settling time. In the second set, the mass of the cart is changed without modifying the controllers. Fig. 14 shows that the conventional controller totally failed to balance the **pendulum** as it was designed for the nominal value of cart mass. On the other hand, the fuzzy logic controller exhibited small performance degradation due to this parameter change as shown in Fig. 13. This proves that fuzzy logic is not based on the mathematical **model** of the **inverted** **pendulum** and more robust to mass variations.

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Abstract : Here modeling and simulation study of basically two **control** strategies of an **inverted** **pendulum** system are presented. The **inverted** **pendulum** represents a challenging **control** problem, which continually moves toward an uncontrolled state. Certain modern techniques are now available because of the development of artificial intelligence and soft computing methods. Fuzzy **control** based learning makes the system more reliable and taking the advantage of precise **control** at different levels of existence as fuzzy is applicable to non value zero to full value as one, rest of the interim values are also considered [3]. ANFIS is one of an example of fused neuro fuzzy system in which the fuzzy system is incorporated in such a framework which is adaptive in nature [7]. The fuzzy controllers are used to sort out the problem of learning and when the ANFIS is used the adaptability of the system get improves which is based on that learning feature for non-linear system of **inverted** **pendulum** **model** [5]. D. K. Somwanshi ,Department of EIC & Electrical Engineering ,Jagannath gupta institute of engineering & technology sitapura, jaipur,

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