Low Frequency Sensitivity Function Constraints for Nonlinear ‐stable Networked Control

SUMMARYTheH∞loop shaping method is known as one of the robust controller design methods. In this method, the design procedure consists of two steps: the weight design and the derivation of a controller. The controller is derived for the weighted plant to suppress theH∞norm of the transfer matrix consisting of a sensitivity function, a complementary sensitivity function, and so on. Therefore, the closed‐loop system achieves good tracking and robustness. However, there is only a guideline for the weight design, and an explicit design index of the weight has not been given. As a result, a time‐consuming and tedious process is often required to tune the weight. This paper provides a new weight design method for a stable single‐input single‐output (SISO) plant. The resulting weight guarantees the upper bound of the performance level before the controller design. This means that the controller design and the weight design are completely separated in contrast to the Lanzon's work. Moreover, the weight is designed using only frequency responses. Accordingly, we can avoid the process of the system identification and reduce the conservativeness caused by an overestimate of the system uncertainty.

This paper examines conditions under which a given SISO LTI control system is H∞-optimal with respect to weighted combinations of its sensitivity function and its complementary sensitivity function. The specific weighting functions considered are defined in terms of the sensitivity and complementary sesitivity functions. We show that a large class of practical controllers are in fact H∞-optimal, including typical stable controllers.

A new tuning method for proportional-integral-derivative (PID) controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given frequency called the "tangent frequency" so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the "tangent frequency," the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.

The paper presents a robust PID control design method for spacecraft attitude tracking. Spacecraft control for large-angle control is subject to nonlinear couplings and uncertainties. Although nonlinear robust control design methods, such as nonlinear H/sub /spl infin// control can be applied to address these issues. The solving of the associated Hamilton-Jacobi equation is often extremely complicated and the resulting controller is not easy to implement. In the paper, the PID controller architecture is assumed for the spacecraft attitude control and concepts in nonlinear H/sub /spl infin// control theory are applied to obtain robustness properties. Results of both PD control and PID control are derived and applied to the ROCSAT-3 satellite of a science model system for verification.

A robust adaptive backstepping controller design method is proposed for a nonlinear system with uncertainty and unknown parameters based on the CMAC neural network. The CMAC neural network was used not only to approach the arbitrary model uncertainties but also to eliminate the bad effects of the uncertainties with robust terms in the controller and virtual controllers. Novel update and control laws are proposed to guarantee that all the signals in the closed-loop control system are uniformly ultimately bounded in a Lyapunov sense. Simulation experimental showed the tracking control of the nonlinear system is achieved and this method is effectual.

For a kind of networked control systems with short time-delay, establish discrete time-invariant system model. Construct the Lyapunov function based on the Lyapunov asymptotic stability principle. Using Linear Matrix Inequalities method given the sufficient condition of H∞ robust controller design method of closed-loop feedback control systems. Matlab simulation indicates the effectiveness and correctness of the controller design.

We discuss the fragility of controllers against small inaccuracies of controller parameters. A useful way to gain insight into controller fragility is to consider the fragility of poles and zeros. Certain controller design methods and controller parametrizations are especially vulnerable to fragility problems. It is hoped that the controversy and debate around the claimed fragility of designs obtained by modern robust and optimal control theories calls attention to the relevance of the work on fixed wordlength effects in controller implementation. A case study on a paper machine headbox control problem is included to illustrate that if a good robust control design method is used, together with a reasonable controller realization (parametrization), it should be possible to combat controller fragility in a fairly satisfactory, although indirect, manner. However, it would certainly be interesting to study whether controller fragility could be directly addressed within some generalized robust control design theory.

As an important part of aesthetic education, music is the artistic expression of human emotions. It has a crucial impact on the cultivation of individual music perception ability, music aesthetic ability, music creation ability, etc. The degree of influence of emotions and values in music runs through the individual. This study introduces a method to independently design a predictive controller using the theoretical framework of the state-space method. Since the same results as DMC can be derived, it can be regarded as an understanding of DMC in the time domain. We take the asymptotically stable object of SISO as the model and use the step response coefficient to directly model, but this method makes the control uncontrollable, so we use the method of adding the correction parameter to make the observable process more effective. The advantages of one-time online optimization can reduce the amount of calculation and greatly enhance the robustness in the control process. In order to study the dynamic characteristics of the system, an internal model control system is introduced. By studying the closed-loop stability of the internal model system, the internal model structure of the dynamic matrix control system is studied, and its dynamic characteristics are further studied. When analyzing the dynamic characteristics, we can know that the dynamic characteristics of the system only depend on the object characteristics and control strategies, and have nothing to do with the model length. This study introduces the basic structure, main properties, and design method of the internal model controller. On the basis of conventional internal model control, an enhanced internal model control method is introduced. Through the analysis of the sensitivity function and the complementary sensitivity function, the robust performance and robust stability of the enhanced internal model control system are studied. Music learning psychology is related to the effect of music teaching. Since individual psychological development is dynamic and controllable, by grasping students’ music learning motivation and music psychological ability, we can well practice the concept of contemporary new curriculum standards and implement high-quality music courses. This study mainly discusses the music learning psychology itself, the analysis of real-time measurement results, and the analysis of teaching countermeasures, and does some research on music theory and teaching practice. Through real-time measurement research, it can be concluded that the real-time measurement results are relatively optimistic, which shows that teachers can maintain students’ learning well as long as they use teaching methods that conform to students’ learning psychology. The nonlinear dynamic incremental internal model algorithm can improve students’ various music psychological abilities and achieve the expected music teaching goals.

This paper presents a robust tracking controller design method for the track-following system of an optical recording device. A tracking loop gain adjustment algorithm is introduced to accurately estimate the tracking vibration quantity in spite of the uncertainties of the tracking actuator. A minimum tracking open-loop gain is calculated by the estimated tracking vibration quantity and a tolerable limit of tracking error. A robust tracking controller is designed by considering a robust <TEX>$H_\infty$</TEX> control problem with the weighting function of a slightly larger gain than the minimum tracking open-loop gain. The proposed controller design method is applied to the track-following system of an optical recording device and is evaluated through the experimental result.

A Design Method of Bilateral Control of Teleoperators with Uncertain Communication Time-Delay

Robust vehicle steering control design based on the disturbance observer

This paper proposes a MIMO robust servo controller design method for a three wheeled Omnidirectional Automated Guided Vehicles (OAGVs) with a disturbance to track desired references using a polynomial differential operator. The process for designing the proposed controller can be described as follows: Firstly, modeling of the MIMO three-wheeled OAGV are presented. Secondly, a new extended system is obtained by applying the polynomial differential operator to the state space model and the output velocity error vector. Thirdly, the proposed controller for the given plant is designed by using the pole assignment method. By applying an inverse polynomial differential operator, a servo compensator is obtained. Finally, in order to verify the effectiveness of the proposed controller, the numerical simulation results are shown. The simulation results show that the proposed controller has good tracking performance under a step type of disturbance and the complicated higher order reference signals such as ramp and parabola. These simulation results are compared with those of the adaptive controller proposed by Bui, T. L. in 2013. The proposed controller shows the better tracking performance than the adaptive controller.

This article proposes a robust adaptive controller design method for strict feedback nonlinear systems with unmodeled dynamics and input saturation. By using command filters, the explosion of complexity is obviated. The influence of filter errors bought in by command filters is eliminated by introducing compensating signals. Moreover, by skillfully constructing annth‐order auxiliary dynamic system, the effect of input saturation is avoided, where the disadvantages of conventional methods based on the hyperbolic tangent function are overcome. To tackle the effect of unmodeled dynamics which can destroy the performance and even destabilize the system, based on input‐to‐state stability theory, a dynamic signal is designed. Finally, the Lyapunov theory‐based stability analysis proves that all the closed‐loop signals are uniformly ultimately bounded. The effectiveness of the proposed controller design scheme is verified in simulation experiments.

The aim of the paper is to obtain suitable state-space models of continuous biotechnological processes (CBTP) in the framework of Linear Fractional Transformation (LFT). The LFT models are starting point in most of the advanced robust control design and analysis methods. Therefore, a linearized process model in the state-space is used whose elements are supposed to vary within certain bounds to represent the nonlinear behaviour of the real plant. The performance specifications are defined in the frequency domain through weighting functions. Two LFT models of CBTP are obtained ready for controller design aimed to optimize robust stability margins and robust performance, respectively.

Performance-guaranteed Robust PID Controller Design for Systems with Unstable Zero