Constant Gain State Research Articles

Gain scheduled state feedback velocity control of hydrostatic drive transmissions

In this paper, a velocity tracking controller for hydrostatic drive transmissions is developed. The solution is based on a state-dependent model that incorporates nonlinear characteristics of the system. A full state feedback controller is devised and the gains are scheduled on measured speed and pressures, together with approximated volumetric flow. The effects of uncertainties, especially those related to equilibrium values of pressures, are eliminated by utilizing so-called D-implementation. This technique eliminates the need for equilibrium values, which are model based and thus uncertain.To demonstrate the efficacy of the controller, the solution is implemented on a 4.5-ton wheel loader. For comparison purposes, a constant gain state feedback controller with integral action is devised, and also a linear PID controller is tuned. The results show that the benefits of the devised controller are significant when it is compared to these two controllers. Moreover, the controllability of the machine is maintained in every situation.

ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process

This paper considers the stabilization problem of the class of continuous‐time linear stochastic hybrid systems with Wiener process. The ℋ∞ state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI‐based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.

Development of Closed-Loop Tail-Sizing Criteria for a High Speed Civil Transport

A study was conducted to determine the closed-loop tail-sizing criteria for a High Speed Civil Transport using a newly developed integrated aircraft/controller design methodology. The key idea is to cast closed loop requirements as linear matrix inequalities, for which efe cient numerical solvers are available. In particular, the effects of certain feedback specie cations, and of actuator amplitude and rate constraints on the maximum allowable c.g. travel for a given set of tail sizes are studied. A constant gain state feedback controller is designed as a part of the tail-sizing process.

Mixed H/sub 2//H/sub infinity / control: a convex optimization approach

The problem of finding an internally stabilizing controller that minimizes a mixed H/sub 2//H/sub infinity / performance measure subject to an inequality constraint on the H/sub infinity / norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H/sub 2//H/sub infinity / performance measure using constant gain state feedback. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of (n*n and n*q, where n and q are, respectively, the state and input dimensions) real matrices. Using the central H/sub infinity / estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. In this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant. >

Design of the Multi-Input, Multi-Output Type-1 Deadbeat Servo System by Minimizing the Deviation Input Energy

This paper discusses the design of a type-1 deadbeat servo system by minimizing the deviation input energy for a multi-input, multi-output linear time-invariant, discrete-time system. The type-1 servo system is formulated by using the augmented system and its deviation system. By using the deadbeat principle, the deviation system is transformed into the new time-variant system with the time-variant structure of the new inputs. The performance index is transformed into the new one, and the new terminal state is free. The optimal deviation inputs are made up of three phases, and they are given by linear combinations of the constant gain state feedback and the variable gain state feedback. The variable gains are obtained by using the special nonstationary Riccati equation. The optimal gains are independent of the initial state of the controlled system, the step command signal and the step disturbance.

Linear-quadratic optimal control for multi-input, multi-output type-1 deadbeat servo systems.

This paper discusses the linear-quadratic optimal control problem of a type-1 deadbeat servo system for a multi-input, multi-output linear time-invariant discrete-time system. The type-1 servo system is formulated by using the augmented system and its deviation system. By using the deadbeat principle, the deviation system is transformed into the new time-variant system with the time-variant structure of the new inputs. The performance index is transformed into the new one, and the new terminal state is free. The optimal deviation inputs are made up of three phases, and they are given by linear combinations of the constant gain state feedback and the variable gain state feedback. The variable gains are obtained by using the special nonstationary Riccati equation. The optimal gains are independent of the initial state of the controlled system, the step command signal and the step disturbance.

Minimization of the input energy of regulator problems with the fixed terminal state. The case of multi-input linear time-invariant discrete-time systems.

This paper discusses the regulator problem of minimizing the input energy for the multi-input linear time-invariant discrete-time system with the zero terminal state. The performance index is the sum of the quadratic forms of the input vectors. By using the deadbeat principle, the system is transformed into the new time-variant system with the time-variant structure of the new input. The performance index is transformed into the sum of the quadratic forms of the new state vectors and the new input vectors with cross terms, and the new terminal state is free. The optimal inputs are given by the variable gain state feedback in the first phase, by linear combinations of the constant gain state feedback and the variable gain state feedback in the second phase, and by the constant gain state feedback in the third phase. The variable gains are obtained by using the special Riccati equation. Both gains are independent of the initial state.

Linear-quadratic optimal control for single-input, single-output, type-1 deadbeat servo systems.

This paper discuses the linear-quadratic optimal control problem of a type-1 deadbeat servo system for single-input linear time-invariant discrete-time system with fixed terminal atate. The fixed terminal state condition is called the state deadbeat condition. The type-1 servo system is transformed into the deviation system. first, the general deadbeat input of the deviation system is expressed by constant gain state problem is transformed into the deviation system. First, the general deadbeat input of the deviation system is expressed by constant gain state feedback and arbitrary input. By using this general deadbeat input, the fixed terminal state problem is transformed into the free new terminal state problem. Then, the problem of minimizing the quabratic performance function is solved, and the optimal deviation input is obtained by using the special Riccati equation. This optimal feedback gain is made up by the variable gains and the constant gain, which are independent of the initial state of the controlled system, the step command signal and the step disturbance.

The deadbeat principle for multi-input linear time-invariant, discrete-time systems.

This paper discusses the state deadbeat control problem for a multi-input linear time-invariant, discrete-time system. The deadbeat principle which is satisfied by general deadbeat inputs is obtained. The deadbeat inputs are not limited to a constant gain state feedback. The general deadbeat inputs are made up of three phases ; inputs are arbitrary in the first phase, linear combinations of the special constant gain state feedback and arbitrary components in the second phase, and the special constant gain state feedback in the third phase. When the controllability indices of the system equal each other, the second phase dose not exist.

Minimum sensitivity pole placer

A method is presented for designing a constant-gain state feedback controller for assigning the closed-loop poles of a linear time-invariant multivariable system to desired locations which at the same time minimizes the sensitivity of these poles to variation in the parameters of the plant. The design procedure is illustrated by examples.

Control System Performance with Coded State Feedback

The error performance of a linear time-invariant plant, remotely controlled with constant-gain state feedback from a coded digital communications link, is considered. The effects of finite information rate, reliability, and delay are examined. While nonzero code transmission delay is generally deleterious to control system performance, it is shown that if the sampling period is specified, then block coding within each sample period may be beneficial. Numerical results are given for the case of a scalar plant

Special trailer for launching complete bay of bridge

In this paper, a velocity tracking controller for hydrostatic drive transmissions is developed. The solution is based on a state-dependent model that incorporates nonlinear characteristics of the system. A full state feedback controller is devised and the gains are scheduled on measured speed and pressures, together with approximated volumetric flow. The effects of uncertainties, especially those related to equilibrium values of pressures, are eliminated by utilizing so-called D-implementation. This technique eliminates the need for equilibrium values, which are model based and thus uncertain.To demonstrate the efficacy of the controller, the solution is implemented on a 4.5-ton wheel loader. For comparison purposes, a constant gain state feedback controller with integral action is devised, and also a linear PID controller is tuned. The results show that the benefits of the devised controller are significant when it is compared to these two controllers. Moreover, the controllability of the machine is maintained in every situation.