MODELING AND RESEARCH CONTROL SYSTEMS WITH USING PID CONTROLLER

This paper investigates the performance of adaptive particle swarm optimization (APSO) algorithm to find the best optimal gain parameters (Kp, Ki, Kd) in linear PID (L-PID) and nonlinear PID (NL-PID) controllers for the trajectory control of a nonlinear dynamical system (NLDS). Mathematical modeling, stability and performance analysis of a NLDS are being carried out with L-PID and NL-PID controllers. It is found that the APSO based tuning of NL-PID controller provides better tracking of NLDS than L-PID controller in respect of its search domain, premature convergence, and computational efficiency. Simulation analysis of various variables of controllers and system response such as error, cost function, and response of NLDS and their comparison to that of APSO tuned L-PID controller is described.

Both linear PID controllers and fuzzy controllers are designed and implemented for a boost converter. Comparison between the two controllers is made in the aspect of design, implementation and experimental results. Design of fuzzy controllers is based on heuristic knowledge of the converter and tuned using trial and error, while the design of linear PID and PI controllers is based on the frequency response of the boost converter. Implementation of linear controllers is quite straightforward, while implementation of fuzzy controllers has its unique issues. A comparison of experimental results indicates that the performance of the fuzzy controller is superior to that of the linear PID and PI controllers. The fuzzy controller is able to achieve faster transient response, has more stable steady-state response, and is more robust under different operating points.

This paper presents a practical implementation for a new formula of nonlinear PID (NPID) control. The purpose of the controller is to accurately trace a preselected position reference of one stage servomechanism system. The possibility of developing a transfer function model for experimental setup is elusive because of the lack of system data. So, the identified model has been developed via gathering experimental input/output data. The performance of the enhanced nonlinear PID (NPID) controller had been investigated by comparing it with linear PID controller. The harmony search (HS) tuning system had built to determine the optimum parameters for each control technique based on an effective objective function. The experimental outcomes and the simulation results show that the proposed NPID controller has minimum rise time and settling time through constant position reference test. Also, the NPID control is faster than the linear PID control by 40% in case of variable position reference test.

AnnotationThere are given the results for the analytical synthesis of optimal control algorithm in a closed circuit for the third-order dynamical system, describing by two different groups of state variables. For improvement the quality of time optimal control system is offered to use the predictive output value, expected through the object’s dead-time. A comparative analysis of quality and sensitivity control systems with the time optimal and linear PID or PI controllers is done. Calculations were carried out on the example of the automatic control system of superheated steam temperature of strait-flow boiler TPP-210.

A nonlinear PID controller with applications

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

Model-based synthesis of nonlinear PI and PID controllers

This work presents an analysis, design, and comparison of the PI (Proportional and Integral) controller and control schemes PI linear and nonlinear controllers reset-based. The parameters of these control schemes have been set by trial and error to finally be tested in a nonlinear process with variable dead time. Controller performance is measured using integral square error (ISE), integral time square error (ITSE), total variations of control efforts (TVU), maximum overshoot (\(M_{p}\)) and settling time \(\left( {t_{s} } \right)\). The results show that reset control systems overcome fundamental limitations coming from linear control systems.

In Chap. 5, we provided detailed discussions about the classical linear control systems or PID control systems with various design methods. One of the most important and critical key requirements to design and implement a PID control system is that the dynamic model of the process or plant is the prerequisite condition . However, in some actual applications, sometimes it is very difficult or impossible to obtain those models. Therefore, it looks like that it is impossible to design any appropriate controller for those control systems.

This study focuses on challenges that occurred on underwater vehicles (UV) that is wave disturbance. There have been many studies and research to develop underwater vehicles that can overcome challenges during the exploration due to variation of water composition and underwater condition that can perform tasks well to achieve goals. However, the presence of wave disturbance that comes in many types and different forces somehow can affect the movement of the vehicle during its dive and could risk the vehicle to component damage. There are several research regarding methods that can be used to show UV performance under disturbance. By choosing the most relevant model design from literature review, a model of wave disturbance for underwater vehicle based on mathematical model was analyzed. The chosen wave disturbance model design combined with existing UV model in Simulink was analyzed at three different frequencies in open-loop configuration. A linearized model comprise of second-order transfer function was obtained. A linear controller was then designed using MATLAB Control System Designer to obtain the PID gain parameters. The performance of nonlinear UV with Wave Disturbance was successfully analyzed in open-loop configuration (without controller) and in closed-loop configuration using linear PID controller. Two different sets of controller gain settings, represented as Case A and Case B, tested on the closed-loop model gives the same performance. However, controller setting Case B outperform case A as it consumes smaller control torque to achieve the same performance.

The paper considers a train operation which minimizes energy consumption for leading the train from one station to the next station at the specified instant and stopping times. The minimization of the energy consumption is defined as an optimal trajectory used as a reference signal for the robust optimal control to regulate an AGT train in Automatic People Movers (APM) system. In this case, we consider the optimal control system where the performance index is of general form containing a final (terminal) cost function in addition to the integral cost function. Since the final time and the final state are fixed or specified, there are no extra boundary conditions to be used other than those given in the problem formulation. Full state feedback control law is selected to design Linear Quadratic Regulator (LQR) and PID controller. Here we also consider the parameter selection problems of the PID controller within the framework of robust control theory which provides an alternative method to optimize the setting of the PID controller. To handle uncertainty of the train parameter such as mass, robust design is applied to find a controller, for a given system, such that the closed loop system is robust. By considering the uncertain passenger arrival flow, the robust optimal control law is designed to suppress the effect of this uncertainty and the uncertain disturbances to the nominal mass of the train system. Simulations show the robustness of the proposed train control algorithms against disturbances occurring on a train parameter.

Rear-cabin pressure control system of high-altitude test facility has the characteristics of large time-delay, nonlinearity and strong disturbances. In China, the rear-cabin pressure control system uses the conventional PID control method which can’t nonlinearly regulate pressure very well; especially in engine transient experiments, it can’t automatically turn PID parameters to adapt the changes of system’s nonlinearities, which has seriously affected the dynamic regulation and control accuracy of the rear-cabin pressure. Therefore, in this paper, firstly the dynamics of hydraulic butterfly valve is modeled and the nonlinear characteristics of exhaust diffuser are analyzed and the simulation model of the rear-cabin pressure control system is established. Secondly, the nonlinear PID controller is developed based on extremum seeking and its parameters are turned online according to the pressure errors between the setting valves and system outputs of the pressure system by minimizing the cost function. Finally, with and without engine flow disturbances, some simulation results of the linear and nonlinear PID control are given for pressure regulation to show that the proposed nonlinear PID based on extremum seeking can not only turn the controller parameters online, but also reject time-varying and large amplitude disturbances, so it has effectively enhanced the nonlinear adaptability of controller and improved the control accuracy of transient responses of the rear-cabin pressure control system.

Quadcopters modelling research has cease or almost at a halt, compared to its controller counterpart, which has received all the attention and continue to receives more research attention. While controller design seems to be viewed as a way of addressing the inherent problems peculiar to quadcopters by ways of controlling it, it no surprising to see that a lot of previous research failed to address this inherent practical problem. This paper reviews the most effective techniques widely used by researchers for modelling & designing quadcopters only and not it controller. Rotor modelling in conjunction with aerodynamic effect, parametric identifications were reviewed and analysed. As a demonstration, a quadcopter modelled was developed via voltage manipulation approach for this review, likewise PID controller. Taylor-series first-order approximation was used to linearize the developed non-linear model so that linear PID controller can be used to test the model. This model the author envisage to discuss with Mathwork Inc. for its incorporated as into the Matlab software as a quadcopter Simulink-block; for which different controllers can be directly interfaced to (with little as required design modification to the helicopter block model or no modification at all). This, the author believes will aid further study of the inherent research problems associated with quadcopter.

Robotic manipulator control is a challenging task due to its nonlinear, interacting multi-input–multi-output dynamics. In this paper, we proposed an optimal robust fractional-order fuzzy PID controller based on multi-objective particle swarm optimization (MOPSO) algorithm for a two-link robotic manipulator. In order to minimize position and trajectory-tracking error, MOPSO finds the optimal parameters of fuzzy membership functions and order of the fractional operators. To show the effectiveness of the proposed controller, the software-in-the-loop real-time simulation is executed, and the results are compared to conventional fuzzy PID, fractional-order PID, and linear PID controllers.

This chapter presents the detailed dynamic model of a Vertical Take-Off and Landing (VTOL) type Unmanned Aerial Vehicle (UAV) known as the quadrotor. The mathematical model is derived based on Newton Euler formalism. This is followed by the development of a simulation environment on which the developed model is verified. Four control algorithms are developed to control the quadrotor's degrees of freedom: a linear PID controller, Gain Scheduling-based PID controller, nonlinear Sliding Mode, and Backstepping controllers. The performances of these controllers are compared through the developed simulation environment in terms of their dynamic performance, stability, and the effect of possible disturbances.