Abstract: An inter-area mode oriented pole-shifting method (named: IAMO-PS) with coordination of control efforts is proposed in this paper to tune power oscillation damping controllers under multiple operating conditions. Firstly, to provide incentives for developing IAMO-PS, a pole-shifting method (named: SCCS-PS), which tunes the controllers by moving all closed loop poles to a sequentially compressed conic section in the complex plane, is proposed to investigate impact of other modes on the control of inter-area modes. Thus, compared to SCCS-PS, a specific pole placement suitable for damping control of inter-area modes is implemented in IAMO-PS. Moreover, since a novel index is proposed to effectively measure control effort of the controller, IAMO-PS is capable of reasonably allocating the control burden among different controllers, which will be attractive for applications in practice. Optimization of both methods is solved by the efficient method of sequential quadratic programming, and a two-stage optimization procedure is proposed for IAMO-PS so that a feasible solution can be easily obtained in practical applications. Both methods are applied for control coordination in the New England and New York interconnected systems. Simulation results verify the effectiveness of IAMO-PS in robustly mitigating inter-area oscillations and coordinating control efforts, and some beneficial conclusions are also confirmed by comparing control results of the two methods.

Abstract: As a standard form for the characteristic polynomial, the K-polynomial has been defined in terms of two specific parameters: a characteristic ratio and generalized time constant [1]. It allows us to synthesize all pole transfer function with such a K-polynomial denominator so that the model satisfies the prescribed overshoot and settling time. This note presents the damping property of the K-polynomial with respect to the characteristic ratio. The analysis was performed for a case where its degree is less than or equal to 5.

Abstract: Based on the pole placement design technique, a full state feed back controller using separation factor is proposed to stabilize a real single inverted pendulum. The strategy is to start with selection two dominant poles that achieve a certain desired performance, using a separation factor between the selected dominant poles and the other poles to eliminate their effect on the system performance, and finally Ackermann’s formula can be used to calculate the feed back gain matrix to place the system poles at the desired locations. Simulation and experimental results demonstrate the effectiveness of the proposed controller, which offers an excellent stabilizing and also ability to overcome the external resistance acting on the pendulum system. Key words-Inverted pendulum, separation factor, state feedback controller I. INTODUCTION The single inverted pendulum is a classical problem in the field of non-linear control theory; it also offers a good example for control engineers to verify a modern control theory. The inverted pendulum is a highly nonlinear and open-loop unstable system. The characteristics of the inverted pendulum make identification and control more challenging. Inverted pendulum can be considered as a popular system that is used to approximate highly complex models such as rockets during liftoff, bipedal walking, cranes, robots, and etc. Several control strategies based on the conventional control theory, modern control theory, and intelligent control have been used to control the inverted pendulum, such as PID controller [1, 2], linear quadratic regulator (LQR) [3-5], fuzzy logic controller (FLC) [6-8]. In [9] JiaJan Wang introduced a simple scheme to design a conventional PID controller to stabilize and track three types of inverted pendulum. Although PID controller is a good controller for controlling the single-input-single-output (SISO) systems, only one PID controller can not be able to control both the cart position and the pendulum angle. On the other side, modern control theory is based on the description of system equations in terms of n first-order differential equations, and the system can be described by state space equation form. This means that only one controller can successfully stabilize the inverted pendulum system. The main design approach for systems described in state-space form is the use of state feedback, or pole placement. The first step in the pole placement design approach is to choose the locations of the desired closed loop poles. The most frequently used approach is to choose such poles based on experience in the root locus design, placing a dominant pair of closed poles and choosing other poles so that they are far to the left of the dominant closed loop poles. Another approach is based on the quadratic optimal control approach. This approach will determine the desired closed-loop poles such that it balances between the acceptable response and the amount of control energy required. In [10] Yan Lan presented a controller design based on state space pole placement method for a non-linear dynamic system described by an inverted pendulum. In [11], Huan made a comparison between several types of controller such as PID, FLC, and state feedback. In [12] Prasad used the inverted pendulum as a benchmark for implementing the control methods. PID controller and two types of fuzzy inference systems are implemented to justify the comparative advantages of fuzzy control methods. In this paper, the design of the state feed back controller based on pole placement approach using separation factor is given in details. This scheme makes the inverted pendulum control design very easy based on pole placement approach. The real single inverted pendulum experiment is used to verify the effectiveness and the robustness of the proposed control method. Proceedings of 2012 International Conference on Mechanical Engineering and Material Science (MEMS 2012) © 2012. The authors Published by Atlantis Press 711 The remaining part of this paper is organized in the following manner. In section II, the mathematical modeling of the real inverted pendulum is introduced. The design steps of the proposed controller are presented in section III. Simulations and experimental results are presented in section V and section IV respectively. Finally the conclusions are presented in section VI. II. MATHEMATICAL MODELING After ignoring the air resistance and a variety of friction, the linear inverted pendulum can be abstracted into a cart and a homogeneous rod, shown in Figure 1. Figure 1 Pendulum system force analysis. From the sum of force in both horizontal and vertical directions and the sum of moments around the centroid of the pendulum, the system can be described by the following two nonlinear differential equations [13]: u ml x b x ) m M (           (1) x ml mgl ) ml I ( 2          (2) Where: M Cart mass. m Rod mass. b Friction coefficient of the cart. l Distance from the rod axis rotation center to the rod mass center. I Rod inertia. F Force acting on the cart. x Cart position. Φ The angle of the pendulum with the vertical upward direction. θ The angle of the pendulum and the vertical downward direction (taking into account the initial position of the pendulum for vertical down). A set of state variables sufficient to describe this system are chosen as the position and velocity of the cart, the angular position and change of angular position of the pendulum. Therefore, the equations that describe the behavior of the inverted pendulum are as the following: u Mml ) m M ( I ml Mml ) m M ( I ) m M ( mgl x Mml ) m M ( I mlb u Mml ) m M ( I ) ml I ( Mml ) m M ( I gl m x Mml ) m M ( I b ) ml I ( x x x

Abstract: In this paper we propose a method to find a low order controller for a single input single output linear continuous time system which guarantees that the closed loop poles are placed within some pre-specified region in the complex plane. Additionally, the method can also ensure that any subset of the closed loop poles are placed at specific pre-designed locations. Further, it is possible to ensure that the resulting controller is proper. The problem is solved by formulating it as an LMI constrained optimization problem. The proposed method is demonstrated on a power system example.

Abstract: Recently several robust control designs have been proposed to the Load- Frequency Control (LFC) problem. However, the importance and difficulties in the selection of weighting functions of these approaches and the pole-zero cancellation phenomenon associated with it produces closed loop poles. Also the order of robust controllers is as high as the plant. This gives rise to complex structure of such controllers and reduces their applicability in industry. In addition conventional LFC systems that use classical or trial-and-error approaches to tune the PI controller parameters are more difficult and time-consuming to design. In this paper, a bisection search method is proposed to design well-tuned PI controller in a restructured power system based on the bilateral policy scheme. The new optimized solution has been applied to a 3-area restructured power system with possible contracted scenarios and the results evaluation shows the proposed method achieves good performance compared with recently powerful robust controllers.

Abstract: In this paper, a closed loop pole location and the speed of response for a model helicopter in longitudinal movement is considered. An optimization problem is defined to find the optimal feedback gain matrix in order to access the best settling time. To solve this optimization problem three intelligent optimization methods are utilized: Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC) and Bees Algorithm (BA). In addition, an optimal controller based on linear quadratic regulator (LQR) is designed and the results are compared with the optimized full state feedback controller. The results show that using the intelligent optimization methods, better settling time can be obtained and consequently better performance for the system is achieved.

Abstract: In this paper the characteristic ratio assignment (CRA) method is employed to control transient response of a class of non-minimum phase fractional order systems. Since fractional order all-pass filter could not be realized, the fractional unstable zeros are converted to integer unstable zeros by multiplying complementary polynomials to numerator and denominator polynomials of system's transfer function. Doing so, the closed loop system would be an integer order all-pass filter multiple an all-pole fractional transfer function determined from CRA method. Computer simulation results are presented to illustrate the performance of the proposed method.

Abstract: In this paper we present a new modification of the classical Nevanlinna-Pick (N-P) scalar interpolation problem and provide a solution to the modified N-P problem. The modified N-P result can be used to place the closed loop poles in a desired region in the left half of the complex plane in control system design. Numerical examples illustrate the theory.

Abstract: This paper clarifies the class of second-order digital filters with two second-order modes equal We consider three cases for second-order digital filters: complex conjugate poles, distinct real poles, and multiple real poles We derive a general expression of the transfer function of second-order digital filters with two second-order modes equal Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter

Abstract: This paper offers a design procedure for a robust pole-placement problem with H ∞ objective via static output feedback control for T-S fuzzy systems with time-varying norm bounded uncertainties. Sufficient conditions for synthesis of a fuzzy static output feedback controller for T-S fuzzy systems are derived in terms of a set of linear matrix inequalities (LMIs). In comparison with the existing robust H ∞ fuzzy static output feedback controllers we also employ pole-placement method in order to drive the closed loop poles into a suitable sub-region of the complex plane, and to improve the transient behavior of the system.

Abstract: The structure and its function about a dual-axis rate turntable has been elaborated, its principle block diagram of control system is given. And its electromechanical system’s transfer function of the dual-axis rate table has been calculated and simplified reasonably based on experiments and practical situation, then a double loop control system constituted with a speed loop and a stabilization loop is got. Its’ correction link of the stabilization loop is calculated, which has a 2-order open loop transfer function. In order to achieve a suitable stability margin, the corresponding digital controller is designed, and its’ pulse transfer function response and the three-step iterative simulation results to a same sinusoidal excitation are got and compared, the same results verified the correctness of the design to the correction link.

Abstract: This study designs a two-loop proportional-integral-derivative (PID) controller for an inverted cart-pendulum system via pole placement technique, where the (dominant) closed-loop poles to be placed at the desired locations are obtained from an Linear quadratic regulator (LQR) design. It is seen that in addition to yielding better responses (because of additional integral action) than this LQR (equivalent to two-loop PD controller) design, the proposed PID controller is robust enough. The performance and robustness of the PID compensation are verified through simulations as well as experiments.

Abstract: The phase retrieval problem consisting of estimating the phase of a transfer function from measurement of its magnitude has been around for several years in the EMC community. In the first part of the paper instead of the direct application of the Hilbert integral, two alternative approaches are briefly illustrated: the cepstrum algorithm and the iterative method. They are used in the signal processing algorithm combining the estimation and detection procedures in sequence to identify the structure of an unknown transfer function: in the first step we determine the poles and zeros of the minimum phase transfer function (estimation), in the second step we find out the actual transfer function by comparing its output related to the unknown zero pole pattern with the outputs related to all the possible zero and pole patterns (detection). The structure of the model is particularly suitable to implement the parametric model, such as the Steiglitz Mc Bride algorithm.