Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential equations (PDEs) arisen by kinetic and potential energy shaping, shall be solved analytically. Finding a suitable desired inertia matrix as the solution of nonlinear PDEs related to kinetic energy shaping is a challenging problem. In this paper, a systematic approach to solve this matching equation for systems with one degree of underactuation is proposed. A special structure for desired inertia matrix is proposed to simplify the solution of the corresponding PDE. It is shown that the proposed method is more general than that of some reported methods in the literature. In order to derive a suitable desired inertia matrix, a necessary condition is also derived. The proposed method is applied to three examples, including VTOL aircraft, pendubot and 2D SpiderCrane system.

The UTDTR Robot is a human inspired robotic platform based on a two-wheeled mobile robot. This robot is designed for the purpose of dome shaped structures inspection and maintenance, and it is a tethered robot to stably climb steep surfaces on the top of dome structures. In this paper analysis and controller design of this robot modelled as a MIMO system is represented in order to provide the desired performance on the operating surface with minimum control effort and complexity. Two PID-based controllers are designed such that the stability and desired performance conditions are obtained. In the first design a fuzzy PID controller with self-tuning scale factors is designed to tune the controller gains is forwarded, while in the second approach a multi model gain scheduling controller based on conventional PID controller is considered. Finally, the effectiveness and simplicity of the proposed controller is verified through simulation, comparing the resulting closed loop transient and steady-state response to that of the previously proposed controllers.

The UTDTR Robot is a human inspired robotic platform based on a two-wheeled mobile robot. This robot is designed for the purpose of dome shaped structures inspection and maintenance, and it is a tethered robot to stably climb steep surfaces on the top of dome structures. In this paper analysis and controller design of this robot modelled as a MIMO system is represented in order to provide the desired performance on the operating surface with minimum control effort and complexity. Two PID-based controllers are designed such that the stability and desired performance conditions are obtained. In the first design a fuzzy PID controller with self-tuning scale factors is designed to tune the controller gains is forwarded, while in the second approach a multi model gain scheduling controller based on conventional PID controller is considered. Finally, the effectiveness and simplicity of the proposed controller is verified through simulation, comparing the resulting closed loop transient and steady-state response to that of the previously proposed controllers.

Tethered Segway is a robotic platform inspired by human climbers. It is a two-wheeled mobile platform tethered to the top of a structure in order to climb steep surfaces with varying slopes, such as domes. The unstructured environment may cause uncertainties in the dynamic behavior of the robot while operating on different parts of the dome. In this paper analysis and synthesis of a robust controller for a tethered Segway is presented in order to provide desired performance in the presence of uncertainties. To design the robust controller, structured and unstructured uncertainties of the model are encapsulated into a structured singular perturbation. A linear robust controller is designed such that the robust stability of the closed loop system is preserved in the presence of modeling uncertainties. Finally, the effectiveness of the proposed controller is verified through simulation by comparing its closed loop transient response and sufficiently suitable steady-state performance to that of a previously proposed LQR controller for the robot.

In most practical applications, studying the asymptotic stability of equilibrium points of a system is of utmost importance. Furthermore, in many cases, the response is restricted to only a sector of the state space. For example, positive systems that are common in chemical processes have nonnegative state variables. For such systems, stability analysis of the system using Lyapunov stability is not advised, since this stability is defined for all the points within a neighborhood of the equilibrium point. In this paper, a new notion of stability, called corner stability, is defined as more suitable for studying asymptotic stability of equilibrium points in such systems. In order to derive sufficient conditions of corner stability, a theorem is stated and proven in this paper, and corner stability of three case studies is analyzed and verified.

This paper presents a neutral system approach to the design of an H? controller for input delay systems in presence of uncertain time-invariant delay. It is shown that when proportional derivative (PD) controller is applied to a time-delay system, the resulting closed loop system is generally a time-delay system of neutral type with delay term coefficients depending on the controller parameters. A descriptor model transformation is used to derive an advantageous bounded real lemma representation for the system. Furthermore, new delay-dependent sufficient conditions for the existence of an H? PD and PI controller in presence of uncertain delay are derived in terms of matrix inequalities. Some case studies and numerical examples are given in order to illustrate the advantages of the proposed method.

In some practical problems such as active vibration suppression systems, the state-derivative signals are easier to access than the state variables. This paper considers an H-Infinity -based state-derivative feedback control problem for input-delayed systems. Applying this control law, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the controller parameters. The time-delay is considered as uncertain time-invariant with a known constant bound. In this paper, the delay-dependent sufficient conditions for the existence of an H-Infinity state-derivative feedback controller are derived in terms of matrix inequalities. The resulting H-Infinity controller stabilizes the closed-loop neutral system and assures that the H-Infinity -norm to be less than a prescribed level. An application example is presented to illustrate the effectiveness of the proposed method.

This paper presents a sufficient stability condition for internet-based tele-operation systems in terms of LMI. The tele-operation scheme is modeled in state-space as a time-delay system in retarded form and a delay-independent stability criterion is extracted. By choosing Lyapunov-Krasovski functional, we show that the internet-based tele-operation system is stable and has good performance under specific LMI condition. With the given controller design parameters, stability of system is guaranteed in the presence of any value of delay. Numerical simulations are performed to verify the theoretical results.

Based on the synthesis algorithm of dynamical backstepping design procedure, in this paper a new adaptive robust approach for non-minimum phase systems is proposed. The proposed controller consists of two parts; a backstepping controller as the robust part and a model reference (MRAS) controller as the adaptive part. In this control scheme the daptive part acts not only as a medium to converge to suitable values for the unknown parameters and to reduce the uncertainty, but also provides a minimum-phase model for the robust controller to be well stabilized. A simulation case study is studied to show how to perform the proposed control law, and to illustrate the effectiveness of this method compared to that of conventional robust controllers.

The descriptor observer approach is improved further to a more suitable observer scheme which is applicable to a more general group of faults and systems. Also a disturbance decoupling scheme is added to the mentioned observer in order to enable the observer to distinguish faults from disturbances.

Using a non-linear model in model predictive control (MPC) changes the control problem from a convex quadratic programme to a non-convex non-linear problem, which is much more challenging to solve. In this study, we introduce an MPC algorithm for non-linear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent non-linear term. The control objective is to design a state-feedback control law that minimises an infinite horizon cost function within the framework of linear matrix inequalities. In particular, it is shown that the solution of the optimisation problem can stabilise the non-linear plants. Three extensions, namely, application to systems with input delay, non-linear output tracking and using output-feedback, are followed naturally from the proposed formulation. The performance and effectiveness of the proposed controller is illustrated with numerical examples.

H-Infinity control problem for input-delayed systems is considered in this paper. A composite state-derivative control law is used, in which, a composition of the state variables and their derivatives appear in the control law. Thus, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the control law parameters. This condition provides new challenging issues which has its own merits in theoretical research as well as application aspects. New delay-dependent sufficient condition for the existence of H ? controller in terms of matrix inequalities is derived in the present paper. The resulting H-Infinity controller guarantees asymptotic stability of the closed-loop system as well as a guaranteed limited H ? norm smaller than a prescribed level. Numerical examples are presented to illustrate the effectiveness of the proposed methods.

This paper considers stability problem for input- delayed systems for both constant and time-varying delay case. A new composite state-derivative control law is introduced, in which, a composition of the state variables and their derivatives appear in control law. By this means, the resulting closed-loop system becomes a particular time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the control law's parameters. This condition provides new challenging issues which has its own merits in theoretical as well as practical aspects. In the present paper, new delay-dependent sufficient conditions are derived in presence of both constant and varying time-delay in terms of matrix inequalities. The resulting controllers guarantee asymptotic stability of the closed-loop system. Simulation studies are presented to verify the stability conditions obtained within the theorems.