The paper has developed, modeled a two-wheeledself-balancingbicyclemodel and designed a robust controller to control the balance of two-wheeled bicyle. The paper also introduces the stochastic balanced truncation algorithm based on Schur analysis and applies this algorithm to reduce the high order robust controller using to control the balance of two-wheeled bicyle. In particularly, the reduced 4 th and 5 th order controller can replace the original controller (30 th -order) while the performance of the control system is ensured. Using the reduced controller simplify the program, so the computational time is reduced. Therefore, the system respose is improved, and the requirements in real-time application are met. The simulation results show the correctness of the modelreduction algorithm and the robustcontrol algorithm of two-wheeledself-balancingtwo-wheeledbicycle.
The TWSR system is favoured by most researchers due to its highly nonlinear, strong coupling and unstable system  and is also studied in detail on the modelling and control strategy. Nguyen Gia Minh Thao et al.  used the Newton's Second Law of motion to identify the mathematical model of robot and PID control algorithm. Yufeng Zhuang et al.  derived the system dynamics by Lagrangian formulation. Mohammad Mahdi Azimi et al.  used Deterministic Autoregressive Moving Average model and robustcontrol. Some new configurations have expanded the applications of TWSR systems by adding more DOF to the system. K. Goher et al. [5, 6] designed a new configuration of two-wheeled vehicles based on multiple link inverted pendulum systems with multiple DOF. A. Almeshal et al.  designed a new configuration of a two-wheeled double inverted pendulum-like robotic vehicle with movable payload on an inclined plane. These new configurations consisted of TWSR and single pendulum (SP), but TWSR and SP were jointed through the motor. The authors have presented successful TWSVPS which have TWSR and SP, the novel point is that the TWSR body and SP were passively jointed through O1 axis.
Designing the self-balancingtwo-wheeled mobile robots and reducing undesired vibrations are of great importance. For this purpose, the majority of researches are focused on application of relatively complex control approaches without improving the robot structure. Therefore, in this paper we introduce a new two- wheeled mobile robot which, despite its relative simple structure, fulfills the required level of self-balancing without applying any certain complex controller. To reach this goal, the robot structure is designed in a way that its center of gravity is located below the wheels' axle level. The attention is more paid to obtaining a self-balancingmodel in which the robot’s arms and other equipment follow relatively low oscillations when the robot is subjected to a sudden change. After assembling the robot using the Sim-Mechanics toolbox of Matlab, several simulations are arranged to investigate the robot ability in fulfilling the required tasks. Further verifications are carried out by performing various experiments on the real model. Based on the obtained results, an acceptable level of balancing, oscillation reduction, and power supply is observed. To promote the self- balancingtwo-wheeled mobile manipulator, its platform is modified to climb high obstacles. In order to obtain this aim, some transformations are done in mechanical aspects like wheels, arms and main body without any increase in DOFs. The robot is supposed to follow proposed motion calculated according to stability criteria. The kinematic equations are utilized to find a possible motion. In a dynamic simulation, the robot ability in passing over an obstacle is verified. Keywords:
Twowheeledself-balancing vehicle based on the concept of an inverted pendulum is built by researchers at the industrial electronics laboratory. SEGWAY PT is such a one machine developed by Dean Kamen, now commercially obtainable as a battery-powered electric vehicle in the market. Researchers and engineers are working to develop techniques to make a dynamically stable system and to guarantee desired performance and robust solution. Many methods are applied and tested on this system platform. Dual-PID and LQR control techniques are designed and tested in Simulink and analysed for vertical balance and position control . There are many past studies about the stabilization and optimization of two-wheeled inverted pendulum robots. They are state feedback control with pole placement method , Proportional-Integral- Derivative (PID) and Proportional-Derivative(PD) controllers, LQR ,  , Model Predictive Control (MPC) . Kalman filtering and PID algorithm is used for a twowheeled car . PI control is not satisfactory for a twowheeledself-balancing robot to act in a real time application. Different new research works has found on inverted pendulum techniques in the implementation of bipedal locomotion , . This paper presents LQGand H-infinity mixed sensitivity design for a twowheeledself-balancing robot. Section two presents system modeling. Section three presents the control techniques. The simulation results are discussed in section four. Conclusions of the work are drawn in section five.
ADXL335 and angular velocity sensor ISZ-650 were used as sensors and Kalman filtering and PID algorithm were used as algorithms to implement the balance of the car with two wheels. This research provided some theories of algorithms for the two-wheel self-balanced technique. Some experimen- tal Data was provided for the two-wheel self-balanced robot from a paper named Two Wheel Self-Balanced Mobile Robot Identification based on Experimental Data. Also, in , two phases of system identification process were applied to implement dynamic equilibrium of the robot.  presented details on how to overcome the limitations of ‘Weiner-Hopf’ Filter in solving problems of statistical nature which seri- ously curtailed practical usefulness. The process is named as Kalman Filtering, which is powerful because it can estimate the past, present and future states. Several researchers have studied the application of Kalman Filtering in solving related robotic balancing problems, around the world. The authors in , and  provide research on how to use the Kalman Filtering to solve the problems of the self-balancingtwo-wheeled robot control.
restricted area during controlling vehicle on the road has been also utilized to evaluate PD-AFC algorithm. The proposed control system is implemented with and without disturbances conditions to show the robustness of the control system. In all discussed cases, the reference path is compared with PD, AFC and PD-AFC actual paths. Results shows the capability of PD-AFC to eliminate the effect of disturbances and maintain the track errors in zero level.
Accurate model of systems is required to design a controllers especially if the controllers are model based controllers . Many researchers have worked on modelling and control of the TWIP mobile robot. Euler Lagrange methods are implemented in [1, 2, 4, 5], Newton-Euler equations of motion method is used in [6, 7]. In [8, 9] the modelling of TWIP is carried out using Kane’s method of modelling. A Takagi–Sugeno (TS) fuzzy model was used in . All models developed using the various methods were able to emulate the dynamics characteristics of the TWIP to some extent, the Kane’s method gives best model presentation.
In order to obtain the tilt angle of the balancing robot; the Six Degree of Freedom Inertial Measurement Unit (IMU) is used as in Figure 3.3. The MPU 6050 is a 6 DOF which means that it gives six values as output. The value consists three values from the accelerometer and three from the gyroscope. This chip uses I2C (Inter Integrated Circuit) protocol for communication. The module has on board Digital Motion Processor (DMP) capable of processing complex 9-axis Motion-Fusion algorithms. The SDA and SCL pins are used to establish a connection with the Arduino pins A4 and A5 to receive the accelerometer and gyroscope data. The interrupt pint (INT) is to instruct the Arduino when to read the data from the module and this pin instruct the Arduino only when the values change.
Hybrid approach is the combination of two or more algorithms aimed to retain the advantages and eliminate the weaknesses of the original algorithms. This includes the synergization between different groups such as bio- inspired, nature-inspired, etc. Biswas et al. [10, 11] pro- posed hybrid BFA-PSO where a chemotactic strategy of bacteria was designed to represent exploitation part of the algorithm, while the exploration of optimum loca- tion was accomplished by PSO. The same approach using a constant step size was implemented by Korani , where the PSO operator was used to determine new direction of bacteria motion. Ghaffar et al.  adopted a modified PSO operator to determine new direction of bacteria to avoid local optima solution. Biswas et al.  proposed chemotactic differential evolution algorithm where adaptive chemotactic strategy of bacteria has been used to improve fitness accuracy of classical differential evolution (DE). Sinha et al.  implemented the same approach on an electric power system. Kim et al.  and Kim  used GA and BFA to tune a PID controller for automatic voltage regulation. Panigrahi and Ravikumar  and Hooshmand et al.  incorporated Nelder– Mead method into bacteria chemotaxis phase to enhance the search strategy and improve bacteria location. Other hybrid approaches involving BFA [41, 59] used bee col- ony algorithm and Tabu search.
In this paper, a study of the GBOT1001 twowheeled mobile robot manufactured by Googol Technology Ltd 1 , is presented. The control objective of the Two-wheeled mobile robots is to perform motion and speed control of the wheels while stabilizing the pendulum around the upright position (unstable equilibrium point). This type of systems that have less numbers of actuators than the degrees of freedom to be controlled, are called “under-actuated systems . In studies carried out by Wu, Zhang and Wang on this robot [7,8,9]. a linear model for the robot is derived and a variety of controllers such as Pole Placement and the LQR controller , fuzzy controller  and Fuzzy-PD controller  are designed for the linearized model. The present paper intends to introduce a modified fuzzy controller that serves as a variation on the previously introduced fuzzy controller [8,9] for the GBOT1001 two-wheeled mobile robot. The proposed fuzzy controller is then combined with a linear quadratic regulator, the parameters of which are tuned with the aid of a Genetic Algorithm. The designed fuzzy controller is also combined with the LQR of previous papers [7,8]. so that the effectiveness of the tuning can be observed in computer simulations.
2. 1. Calculation of Odometry Error Odometry is a measuring method of wheel rotation as a function of time. If the two wheels of the robot are joined to a common axle, orientation of the centre of the axle relative to the previous orientation can be determined from odometry measurements on both wheels. In actual practice, optical encoders mounted on both wheels feed discretised wheel increment information to the controller, which in turn used to calculate the robot’s state using geometric equations. The wheel base (W) of the robot is the space between the contact points of two rear wheels. The center of the robot with respect to odometry is the midpoint between these two contacts. To calculate the variation in position and orientation of the robot with respect to starting point (P) across a given span of time, linear distance D R and D L of each wheel
One of the most widely applied methods for balancing robot is the PID method –. However, how to tune the PID parameter is still a major problem for researchers. That is because usually the system has a nonlinear system and there are unknown disturbances, such as friction, slip, and external force. The performance of the motor also has a lot of effects on the PID tuning value due to the nonlinearity of the motor itself . One of the Artificial Intelligence tuning methods is Particle Swarm Optimization (PSO).
Wheeled robots are the robots that can transport themselves form one place to another with the help of their wheels. A robot with wheeled motion can achieve mechanical term easily and with low cost compared to legged mobile robot. In addition, the control of wheeled moving is generally simpler. Due to these reasons, wheeled robots are becoming one of the most frequently seen robots. The types of wheeled mobile robot that have been developed by other researchers will be introduced at the following section.
In psychology, operant is a class of behavior that pro- duces consequences by operating (i.e., acting) upon the environment. Operant conditioning (OC) is a technique of behavior modification through reinforcement and punishment. The research about operant conditioning theory  was started in 1938 by Skinner, a psychology professor. Its consequence influences the occurrence and form of behavior. Operant conditioning and classical conditioning  are two main learning ways of associa- tive learning, and all animals, including human, have these two learning way. Operant conditioning is distin- guished from classical conditioning in that operant con- ditioning deals with the modification of operant behavior. Operant conditioning reflects the relation between be- havior and its outcome, and the learning with OC theory is called operant learning (i.e. instrument learning). Re- cently, researchers apply OC theory in the robot learning and control and have done plenty of experimental studies. For example, Björn Brembs et al.  from Germany applies himself to the research of the operant condition- ing in flies (Drosophila) and snails. 'Pure' operant condi- tioning and parallel operant conditioning at the flight simulator were studied. Chengwei, Yao et al.  ap- plied OC theory into emotion development and presented an emotion development agent model based on OCC
Another twowheeled robot called ‘SEGWAY HT’ is available commercially (Dean Kamen ,2001) . It is invented by Dean Kamen who has design more than 150 systems which includes climate control systems and helicopter design. An extra feature this robot has is that it is able to balance while a user is standing on top of and navigate the terrain with it. However, this uses five gyroscopes and a few other tilt sensors to keep it balanced.
shows the corresponding raw sensor data and the body tilt angle plot against time. Height data plots the height calculated from the ground to the sonar sensor. The height data has an offset of 5 cm above ground when the robot is balancing still. AccZ graph plots the accel- eration in the robot frame z axis (pointing up) with grav- ity subtracted. At time t = 1.86 s, sudden increased in height measurement indicates that the robot is currently airborne. The controller switches into airborne control mode and applies balancing torque generated through the rotating wheels. We have set the reference body tilt angle for airborne controller to a small positive value (+6 degrees), to tilt the robot backwards during airborne. The reason for this is to compensate the forward momentum during landing and reduce the torque needed to balance upon landing. This is analogous to landing with feet in front and uses momentum to bring the body to a neutral position. At time t = 2.02 s, the wheel hits the ground and causes large fluctuation in the accelerometer read- ings. Phase changed is detected and the robot switches into ground mode to keep its balance. From the figure, the fluctuation in accelerometer reading does not affect the body angle estimation due to robustness of the Kalman filter. At the moment of impact upon landing, we observe the upper body mass moves downward. This motion acts as an absorber to absorb the impact force from the ground and mitigate any recoil effect which is observed in the previous rigid prototype. From the height vs time plot, there is a false positive indication of increase
The two-wheel mobile robots can be divided into two parts. The first is the lower parts which consist of two wheels connected to the axis and driven independently. The second part is the body of the robot which is placed at the centre of mass above the axis. The controller drives the wheel to maintain the body on the up-right position. Twowheeled mobile robots are well suited for traversing narrow spaces and slopes. Its characteristic includes compact size, light weight and lower energy consumption .
Harrison (2003) implemented a near optimal, non-linear controller based on linear quadratic (LQ) optimal control theory on a single IP on a cart. The resulting regulator could be implemented in real-time. However, the need to solve an algebraic Riccati equation at every time-point is burdensome. Lin et al. (1996) proposed a linear state feedback controller to balance an IP based on combining a low gain and high gain state feedback. Bugeja (2003) developed a state feedback pole-placement controller to swing-up and stabilize an IP system using a cascade control loop. Fiacchini et al. (2006) presented various controller types for both linear and non-linear control mechanisms including: partial linearization, energy shaping, velocity stabilization and non-linear controller tuning on a personal IP vehicle. Bogdanov (2004) applied different optimal controllers on a double IP system. Linear Quadratic Regulator (LQR), state-dependent riccati equation (SDRE) and optimal neural network controllers have been compared. Xiong et al, (2010) presented a new method to find the parameters of an optimal LQR controller for a double IP system. Optimal selection of the LQR controller parameters was superior and tended to equilibrium point faster than heuristic selection of the parameters. Wongsathan and Sirima (2009) applied genetic algorithm (GA) to design an LQR controller for the IP system. Nasir et al, (2010) presented a comparison between LQR and PID- controller for a two-wheeled robot in terms of input tracking and the capability of disturbances rejection. Nawawi et al (2006) proposed a robust controller based on sliding mode control for stabilization and disturbance rejection. 2.1 Paper Contribution
As managing the temperature of processors is a major concern in server cluster, we focus on the thermal and power properties of processors. Extending our work to thermal con- trol for the other system components is part of our future work. The processor of each server has estimated active power P a (e.g., the active power in the specification of the processor) when it is executing tasks. It is important to note that the actual active power of a processor may deviate from the estimated at run time and different tasks may incur different power consumption , . For example, an earlier study showed that the active power consumption of different applications may differ by as much as 35% . In earlier literature some researchers  referred to such significant power variation dur- ing run time as power phase behavior. At the instruction level, different instruction types, inter-instruction overhead, memory system state and pipeline related effects cause fluctuation of task powers . When the processor is idle, the processor switches to a low power mode and consumes power of P idle . We employ a widely adopted thermal model – for the processor P r i as follows.