Requirements Of Internal Stability Research Articles

Formula omitted] control of SISO fractional order systems

In this paper, we propose a systematic method to design the optimal ℋ2 output feedback controller for single input, single output plants of fractional order based on Wiener–Hopf spectral factorization. The plant is allowed to be unstable, non-minimum-phase, and incommensurate order. Using the fractional order Youla parameterization, the resulting controller satisfies the closed-loop internal stability requirement. Because of the branch point singularities associated with fractional order transfer functions, the spectral decompositions are effected via an integral technique. An example is provided to demonstrate the design procedure.

Dwell-Time-Based Standard $H_\infty$ Control of Switched Systems Without Requiring Internal Stability of Subsystems

This paper investigates standard $H_\infty$ control of switched systems via dwell-time switchings without posing any internal stability requirements on subsystems of the switched systems. First, a sufficient condition is formed by specifying lower and upper bounds of the dwell time, constraining upper bound of derivative of a Lyapunov function of the active subsystem, and forcing the Lyapunov function values of the overall switched system to decrease at switching times to achieve standard $H_\infty$ control of unforced switched linear systems. Then, in the same framework of the dwell time, sufficient conditions are given for that of the corresponding forced switched linear systems by further designing state feedback controllers. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.

A zero compensation approach to singular H2 and H∞ problems

AbstractIn this work we analyse singular H2 and H∞ problems for which the usual Riccati equations become ill‐posed owing to the existence of plant zeros at infinity.We adopt a two‐step approach to the analysis. First we replace the usual Riccati equations with two generalized eigenproblems; these problems are always well‐posed. Next we extract those structural elements which pertain to the troublesome plant zeros. We do this by introducing pre‐compensators which cancel the offending zeros. In so doing, we temporarily relax the controller properness constraint that is traditionally imposed in H2 and H∞ problems by allowing pole‐zero cancellations between the plant and controller at infinity. Since no significant added complexity of analysis results, we also treat the case of singularity due to finite jω‐axis plant zeros by relaxing the internal stability requirement and allowing finite jω‐axis pole‐zero cancellations.The resultant theory allows us to specify necessary and sufficient conditions for the existence of solutions to singular H2 and H∞ problems. The existence conditions and the resultant control laws are expressed directly in terms of the eigenvalues and eigenvectors of two Hamiltonian matrices associated with the problem. The theory also gives some insight into the character of the subset of all proper, internally stabilizing solutions, including whether this set is nonempty. An example is included.

Synthesis of deadbeat controllers with minimum control input and finite-step control input

A design criterion is developed to incorporate the deadbeat reference signal tracking, internal stability and minimum control input or finite-step control input. The polynomial deadbeat control approach is investigated to achieve the deadbeat response with minimum settling time. Moreover, for over-parametrized cases, the theory of minimum H 2- norm is employed to achieve the minimization of control input. Furthermore, the constraint on the plant pole and the design procedure are also derived to achieve deadbeat response with finite-step control input. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or nonminimum phase. An example is given to illustrate the validity of the design algorithm.

Robust optimization of multivariable feedback systems with time-varying nonlinear uncertainties

Abstract A design criterion is developed to achieve the input-output decoupling of multivariable feedback systems and the robust stabilization of systems with time-varying nonlinear uncertainties. Moreover, an effective design algorithm is derived to achieve the robust optimization of multivariable feedback systems subjected to time-varying nonlnear uncertainties. The theory of minimum H∞ -norm and the optimal interpolation technique are employed to solve this robust optimization problem. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or non-minimum phase. From the result of the robust optimization, we can predict the maximum sector bounds of nonlinear uncertainties that can be tolerated in the multivariable feedback system.

Synthesis of pole-zero assignment control law with minimum control input

A method of control system design is developed to simultaneously consider the internal stability, pole assignment, reference signal tracking and control input minimisation. A parametrised design algorithm of the pole-zero assignment control law is derived to achieve the desired goals. The free parameters are used to minimise the L/sub 2/-norm of the control input signal. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or is in a nonminimum phase. Examples are given to illustrate the validity of the design algorithm.

Robust optimization of feedback systems with time-varying non-linear uncertainties

A design criterion is developed to achieve the robust stabilization of a feedback system with time-varying non-linear uncertainties. Moreover, an effective design algorithm is derived to achieve the robust optimization of a feedback system subjected to time-varying non-linear uncertainties. The theory of minimum H ∞-norm and the optimal interpolation technique are employed to solve this robust optimization problem. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or is non-minimum phase. From the result of the robust optimization, we can predict the maximum sector bound of non-linear uncertainties that can be tolerated in the feedback system.

Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.

Adaptive deadbeat control

An adaptive algorithm is presented to incorporate deadbeat control as a principle design criterion. Since this algorithm does not require the solution of the diophantine equation at each sampling step, it possesses a computational advantage over the existing deadbeat control approaches, and so is suitable for application to adaptive systems. The meeting of the internal stability requirement enables this algorithm to handle easily any stable or unstable, minimum or non-minimum phase system. By selecting the zero assignment of the sensitivity function the system can be made to track a class of changeable reference signals and exhibit a deadbeat response with minimum settling time. Some constraints on the transfer function make sure that the derived controller is realizable. The non-linear saturated system and the lathe system are simulated to illustrate the validity of the proposed design algorithm.

Multipurpose deadbeat controller synthesis in m-dimensional discrete multivariable systems

In this paper, a more general deadbeat controller design algorithm for the m-dimensional discrete-time multivariable system is introduced. Since the internal stability requirement is achieved, this algorithm can easily handle any stable or unstable minimum or nonminimum phase m-dimensional system. A simple technique is employed to achieve the following design purposes in the m-dimensional discrete-time multivariable feedback systems: (i) input—output decoupling; (ii) reference signal tracking and disturbance rejection where reference signals and disturbances can be different at each channel; (iii) deadbeat response with minimum space interval. An example is given to illustrate the validity of the proposed method.

Adaptive controller with desired pole/zero assignment

An adaptive algorithm is presented to incorporate pole/zero assignment as a principle design criterion. As this algorithm does not require solving a diophantine equation at each sampling step, it possesses much computational advantage over the existing approaches of an adaptive pole-assignment control algorithm. This computational advantage is very important for the adaptive control system to the actual application. The internal stability requirement is achieved so that this algorithm can easily handle any minimum- or nonminimum-phase system. The desired zero assignment of the sensitivity function can make high-order reference signal tracking possible. Several simulations are given to illustrate that our approach is suitable for application and easy to implement.