Design and analysis of iterative algorithms via nonlinear control theory

In this paper, for the towing problem of wheeled aircraft, an automatic control method is proposed based on the nonlinear control theory, which realizes the trajectory tracking of the aircraft by controlling the velocity of the towing point of the aircraft, so as to realize the aircraft’s outbound and inbound operations. Firstly, based on the nonholonomic constraint theory, the mathematical model of the aircraft towing system is established, and the kinematic relationship between the aircraft towing point and the aircraft is obtained. Then, a controller is designed based on the nonlinear control theory, and the stability analysis is carried out using the Lyapunov method to realize the trajectory tracking of the aircraft traction system. Finally, the effectiveness and accuracy of the control method are verified by the combination of MATLAB simulation analysis and scaled-down model experiment. The results show that the proposed control method can realize the trajectory control of the aircraft towing system.

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

Theory of nonlinear systems

Analysis of Nonlinear Systems with Stochastic Input and Stochastic Parameters—II

This paper presents a systematic analysis of the characteristics of the inverter system under rectifier load with the model proposed in [9]. The dynamic response of the system is derived by the nonlinear control theory, which reveals that the system can be simplified as if it shifts between two different steady states periodically. The distortion mechanism of the inverter output waveform under rectifier load is then studied through the analysis of these two steady state responses. The system stability is analyzed using the phase plane plot of the nonlinear control theory. Based on these analyses, design principle is proposed. A design example is presented with the experimental results.

An attempt is made to establish the existence of solutions of nonlinear matrix equations of the form X(z)A(z)X(z)=X(z), where all matrices X(z), A(z) are holomorphic matrices. Such matrix equations arise in nonlinear control theory of nonlinear dynamical systems where A(z) is a given holomorphic matrix. Numerical methods of solutions of such nonlinear matrix equations are given. Use is made of parallel processing and supercomputers to carry out the numerical calculations of such problems. Examples of methods used for problems of the above type are given. >

A simulation game for nonlinear control theory education

Online Guidance and Control of a Spacecraft for an Aeroassisted Orbit Transfer

Many types of electric equipments are digitized in recent years. However, the configuration of switch mode power supply is still only analog circuit because the analog circuit is held down to low cost. The digitized system is operated on the basis of a processor. When the switch mode power supply is treated as a part of the system, it is difficult that switch mode power supply inhabit alone in the system as the analog-circuit. Therefore, the digitization of the switch mode power supply is necessary to harmonize with other electronic circuits in the system. So far, various examinations have been discussed about digitally controlled switch mode power supplies[1-5]. However, important parameters such as the switching frequency were impractical because the performance of processor was not so good. Recently, due to the development of the semiconductor manufacture technology, the performance of processor such as DSP and FPGA is developed remarkably. Hence, the expectation of the practical realization in the digitally controlled switch mode power supply becomes higher. So far, in many case on digitally controlled switch mode power supply, the control system is constructed by very complicated, difficult modern control theory (nonlinear control theory) such as adaptive control or predictive control. Moreover, also in the most popular and easiest control method such as PID control, the design method is not so clear, and the optimal design is difficult[6, 7]. On the other hand, there are two methods of controller design. One is the digital direct design. The other is the digital redesign. The digital redesign method converts the analog compensator which is designed on s-region into digital compensator. The digital redesign method has some advantages. For example, the control system is designed from classical control theory (linear control theory). Therefore, many experiences and design techniques of the conventional analog compensator can be utilized. Moreover, from the practical stance, the digital redesign method is more realistic than digital direct design. This paper investigates the digitally controlled switch mode power supply by means of classical control theory. Especially, the interesting control technique which is cancelled the transfer function of the converter by using pole-zero-cancellation technique is introduced. This technique is very simple and stability design of converter system is very easy.

A theory of aneurysm sounds

A EROSPACE engineering applications greatly stimulated the development of optimal control theory during the 1950s and 1960s, where the objective was to drive the system states in such a way that some defined cost was minimized. This turned out to have very useful applications in the design of regulators (where some steady state is to be maintained) and in tracking control strategies (where some predetermined state trajectory is to be followed). Among such applications was the problem of optimal flight trajectories for aircraft and space vehicles. Linear optimal control theory in particular has been very well documented and widely applied, where the plant that is controlled is assumed linear and the feedback controller is constrained to be linear with respect to its input. However, the availability of powerful low-cost microprocessors has spurred great advantages in the theory and applications of nonlinear control. The competitive era of rapid technological change, particularly in aerospace exploration, now demands stringent accuracy and cost requirements in nonlinear control systems. This has motivated the rapid development of nonlinear control theory for application to challenging, complex, dynamical real-world problems, particularly those that bear major practical significance in aerospace, marine, and defense industries. Infinite-time horizon nonlinear optimal control (ITHNOC) presents a viable option for synthesizing stabilizing controllers for nonlinear systems by making a state-input tradeoff, where the objective is to minimize the cost given by a performance index. The original theory of nonlinear optimal control dates from the 1960s. Various theoretical and practical aspects of the problem have been addressed in the literature over the decades since. In particular, the continuous-time nonlinear deterministic optimal control problem associated with autonomous (time-invariant) nonlinear regulator systems that are affine (linear) in the controls has been studied by many authors. The long-established theory of optimal control offers quite mature and well-documented techniques for solving this control-affine nonlinear optimization problem, based on dynamic programming or calculus of variations, but their application is generally a very tedious task. Bellman’s dynamic programming approach reduces to solving a nonlinear first-order partial differential equation (PDE), expressed by the Hamilton–Jacobi–Bellman (HJB) equation. The solution to the HJB equation gives the optimal performance/cost value (or storage) function and determines an optimal control in feedback form under some smoothness assumptions. Alternatively, in the classical calculus of variations, optimal control problems can be characterized locally in terms of the Hamiltonian dynamics arising from Pontryagin’s minimum principle. These are the characteristic equations of the HJB PDE, which result in a nonlinear, constrained two-point boundary value problem (TPBVP) that, in general, can only be solved by successive approximation of the optimal control input using iterative numerical techniques for each set of initial conditions. Numerically, even though the nonlinear TPBVP is somewhat easier to solve than the HJBPDE, control signals can only be determined offline and are thus best suited for feedforward control of plants for which the state trajectories are known a priori. Therefore, contrary to the dynamic programming approach, the resultant control law is not generally in feedback form. Open-loop control, however, is sensitive to random disturbances and requires that the initial state be on the optimal trajectory. In contrast, nonlinear optimal feedback has inherent robustness properties (inherent in the sense that it is obtained by ignoring uncertainty and disturbances). The potential difficulty with the HJB approach is that no efficient algorithm is available to solve the PDE when it is nonlinear and the problem dimension is high, making it impossible to derive exact expressions for optimal controls for most nontrivial problems of interest. The optimal can only be computed in special cases, such as linear dynamics and quadratic cost, or very low-dimensional systems. In particular, if the plant is linear time invariant (LTI) and the (infinite-time) performance index is quadratic, then the corresponding HJB equation for this infamous linear-quadratic regulator (LQR) problem reduces to an algebraic Riccati equation (ARE). Contrary to the well-developed and widely applied theory and computational tools for theRiccati equation (for example, see [1]), theHJB equation is difficult, if not impossible, to solve for most practical applications. The exact solution for the optimal control policies is very complex

In order to stabilizing terminal voltage of a generator, this paper designs two excitation controller improved from the PID based on nonlinear control and fuzzy control theory. Then, simulation results of three excitation controllers in SIMULINK are compared in different disturbance and faults such as terminal voltage step, mutant Load-shedding, one-circuit broken and three-phase short circuit. Simulation results show that: three excitation controllers achieve the goal that stability of terminal voltage is maintained. And PID +Fuzzy excitation controller has the better robustness than the others.

Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the global minima of the cost function describing the coupled oscillator system and the ground state of the Ising Hamiltonian. However, the properties of the oscillator Ising machine (OIM) from a nonlinear control viewpoint, such as the stability of the OIM solutions, remain unexplored. Therefore, in this work, using nonlinear control-theoretic analysis, we (i) identify the conditions required to ensure the functionality of the coupled oscillators as an Ising machine, (ii) show that all globally optimal phase configurations may not always be stable, resulting in some configurations being more favored over others and, thus, creating a biased OIM, and (iii) elucidate the impact of the stability of locally optimal phase configurations on the quality of the solution computed by the system. Our work, fostered through the unique convergence between nonlinear control theory and analog systems for computing, provides a new toolbox for the design and implementation of dynamical system-based computing platforms.

In this paper, a nonlinear controller with a current-limiting property is proposed to guarantee accurate dc output voltage regulation and unity power factor operation for single-phase pulse-width-modulating rectifiers without the need of a phase-locked-loop (PLL). The proposed current-limiting controller is fully independent of the system parameters and can guarantee asymptotic stability and convergence to a unique solution for the closed-loop system using nonlinear control theory. Without requiring the instantaneous measurement of the grid voltage, a PLL, an external limiter, or a saturation unit, the proposed strategy guarantees that the input current of the rectifier will always remain below a given value. An analytic framework for selecting the controller parameters is also presented to provide a complete controller design procedure and it is also proved that the current-limiting property is maintained even when the grid voltage drops. Extensive experimental results are presented to verify the proposed controller when the load changes, the reference dc output voltage changes, and the grid voltage drops.

A new approach is presented for the speed control of PWM current source inverter-induction motor (CSI-IM) drive systems. This approach is conceptually based on the well-known feedback linearization technique in nonlinear control theory. Here, the commanded DC link current is generated as a specific nonlinear function of speed in the control algorithm so that the torque-speed characteristic of the CSI-IM system is forced to emulate the torque-speed characteristic of a separately excited DC motor. This is augmented by a feedback controller that slides the torque-speed characteristic along the speed axis in the torque-speed plain, in order to adjust the operating point to any desired value of speed. Meanwhile, it is shown that the proposed controller is highly robust in the presence of external disturbances.