A dynamic optimal decoupling controller design for a multi-variable system with stability analysis: an algebraic approach

Observer-based dynamic optimal recoil controller design for deepwater drilling riser systems

This paper presents design and development of an optimal robust PI controller based on linear matrix inequalities for a typical industrial process control system. In this method, the design problem has been transformed into a state feedback controller design problem for an augmented uncertainty MIMO system. In this work, a dynamic decoupler is designed to handle loop interaction. The control problem is then solved for the obtained decoupled subsystem by employing a constraint optimization approach, ensuring compliance with a defined LQ cost objective function. Simulation results verify the efficacy of the proposed controller, presenting its effectiveness in achieving both set-point accuracy and disturbance attenuation. Furthermore, the study employs disk margin analysis to ascertain safe ranges for gain and phase margin.

This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes (TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region (GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.

Spherical robot is a kind of mobile robot, and then it is inevitable to encounter with the problem of climbing slope. According to the spherical robot designed, each independent variable describing the state of climbing an arbitrary slope is analyzed. The calculation formula to estimate climbing capability is given and simultaneously the concept of critical pendulum angle is proposed. Dynamic equations of the robot climbing slope is derived from using Lagrangian function equation based on energy dissipation. In order to solve the problem of constant terms in the equation, the coordinate transformation method is adopted, and ultimately the system is converted into state-space form. When every state of the robot system can be measured, a corresponding linear quadratic objective function is designed with the consideration of the practical requirements of both steady movement and less energy assumption. At last, the state feedback matrix is designed, which can control the robot to move at an expected velocity on slope, and the simulation results prove the validity of the above control technique.

One of the situations where significant problems may arise in two-input two-output (TITO) systems is the existence of interactions with cross-couple of inputs and outputs. This situation may be challenging especially for the system analysis in process control. As long as the condition that the system should be decoupled is met, control problems to be investigated for this kind of systems become meaningful. This study deals with the design of non-interacting dynamic diagonal controllers for two-input two-output systems. Here, it is aimed to obtain the needed filter for decoupling and then to design the controller to satisfy the necessary specifications. The decoupling filter and controller design procedure for disturbance attenuation and reference tracking is defined via general control configuration. Here, the main objective of the study is to keep the system decoupled where an optimal controller is designed to increase the reference tracking and disturbance attenuation performance of the overall closed loop system. The efficiency and success of the proposed method is illustrated via simulation studies.

This paper presents a fixed order dynamic optimal controller design method for robust stability of linear discrete systems. The controller determination includes a stability robustness component in addition to the standard quadratic state and control terms in the performance criterion. The controller design is based on the parameter optimization technique. The resulting controller involves the solution of three algebraic matrix equations, two of which are discrete-time Lyapunov matrix equations.

Optimal replicator dynamic controller for semi active control of long span cable stayed bridge with considering special variability of seismic excitations

For a nonlinear system, a novel complementary terminal sliding mode surface-based finite-time adaptive dynamic programming optimal control scheme (FT-NCTSMS-ADP) is proposed. To begin with, with the aim to improve convergence speed and tracking precision, a novel complementary terminal sliding mode surface (NCTSMS) is developed. Then, a specific cost function related to the NCTSMS is developed, and the initial control problem is then transformed toward a series of optimal control problems. The Hamilton-Jacobi-Bellman (HJB) problem is then solved by a single critic neural network, yielding the estimated optimal controller. Finally, using the finite-time lemma, we design a Lyapunov function and verify the system’s fast finite-time convergence. Both the simulation and the real-world experiment validate the practical significance of the proposed method.

Optimal causal control of a wave energy converter in a random sea

Multi-objective non-simultaneous dynamic optimal control for an ejector expansion heat pump with thermal storages

The main objective of this research work is the design of decentralized PID controller with fractional order filter for strongly connected multivariable distillation column system. Wherein, the major contribution of this paper is the proposition of compensators for the decoupling process, in addition to extending the application of the proposed approach from Single-Input Single-Output (SISO) systems into Multi-Input Multi-Output (MIMO) systems. More precisely, the proposed idea is based on eliminating the strongly interactive terms between the inputs and outputs of the multivariable distillation column systems so that, the separated multi-loop parts can be treated as a set of SISO subsystems, which have an equivalent dynamic of the whole original system. Thereafter, a PID controller with a fractional filter has been introduced to the decoupled subsystems in decentralized scheme in order to improve the control system robustness. Two multivariable systems have been carefully considered in this paper; the first is a theoretical Two-Input Two-Output (TITO) system while the second is the Wood and Berry distillation column. The obtained results have confirmed the superiority of the proposed approach over the two degrees of freedom technique, which is based on Internal Model Control method. Indeed, the proposed approach has reduced the dynamic error, the settling time, and the rise time. Furthermore, the designed decentralized PID controller with fractional filter has demonstrated rejection to structured perturbation from one loop to another.

This paper proposes an optimal control method based on adaptive dynamic programming (ADP) for manipulators with joint limitation under input saturation. The asymmetric input saturation problem is solved by introducing a smooth function, by which the saturation and nonsmooth issues of the input caused by the actuators can be handled. Joint limitation of the manipulator is transformed through a transfer function, which is incorporated into the cost function of the whole robotic system, to guarantee the joint limitation will not be violated. Meanwhile, due to the difficulty in solving Hamilton-Jacobi-Bellman (HJB) equation, the critic network is constructed utilising radial basis function neural networks (RBFNNs) to approximate the cost function. This approach effectively overcomes the curse of dimensionality problem associated with dynamic programming. Subsequently, an ADP-based optimal controller is designed for the robotic system. Lyapunov synthesis is used in the stability analysis to prove all the signals are convergent and ultimately uniformly bounded (UUB). Simulations are conducted on a planar 3-DOF manipulator to validate the effectiveness of the proposed method. The results demonstrate the improved performance and feasibility of the developed ADP-based optimal control strategy in handling joint limitations and input saturation challenges in robotic systems.

Dynamic event-triggered neuro-optimal control for uncertain nonlinear systems with unknown dead-zone constraint

This paper describes a formal method of designing optimal feedback controllers using the method of dynamic programming. Adopting a quadratic performance criterion, a multi-stage control law is easily programmed for a digital computer thus providing convergent feedback matrices. A visual display system is employed which allows the designer to simulate control of the process for a variety of conditions, enabling him to select the performance function which gives the desired system response.

Studies by simulation on the model of a multistage flash (MSF) desalination plant have shown certain features of the model developed, on the basis of physical laws and correlations. The most important of these is nonlinearity which relates to the changing of the process characteristics with the operating conditions. It is shown that a fixed PID controller cannot be optimal, if the operating point changes from the one at which the optimal controller was designed. In this paper, the parameter variations in the linearised plant model have been modelled over the operating region of interest, and these are mapped into the parameter space of the optimal PID controller. The resulting algorithm is a parameter scheduling scheme for the MSF plant for optimal PID control with a choice among four criteria (ISE, IAE, ISTE, and IATE). The scheme illustrated is with reference to the top brine temperature control of an actual 18 stage MSF desalination plant.