Controlling Non-Minimum Phase Nonlinear Systems - The Inverted Pendulum on a Cart Example

Gurumoorthy, R.; Sanders, S.R.

doi:10.23919/acc.1993.4792946

Cited by 48 publications

(18 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The control problem is to design a state feedback controller for the system such that the position of the cart can asymptotically track a sinusoidal input. This problem has been well studied in [20]. The equations of motion for this system can be described by [20] (see also [16]) (M + m)ẍ + ml(θ cos θ −θ 2 sin θ) + bẋ = u, ml 2θ + mlẍ cos θ − mgl sin θ = 0, where M is the mass of the cart, m is the mass of the pendulum, l is the length of the pendulum, g is the gravitational acceleration, b is the coefficient of viscous friction for the motion of the cart, θ is the angle that the pendulum makes with vertical, x is the position of the cart, and u is the applied force.…”

Section: Examplementioning

confidence: 99%

“…First we choose the matrix T such that the linear part of (18) is diagonalized. Next let [x 1x2ȳz ] T = T −1 [w 1 w 2 x 3 x 4 ] T , then in the new coordinate (18) becomeṡ x 1 = −ωx 2 ,ẏ = − g/lȳ +ḡ(x,ȳ,z), x 2 = ωx 1 ,ż = g/lz +h(x,ȳ,z), (20) 47th IEEE CDC, Cancun, Mexico, Dec. [9][10][11]2008 TuB16.3…”

Section: Examplementioning

confidence: 99%

“…Now, Theorem 3 can be applied to (20), after the calculations of sequences (8), the sequences are transformed into the original coordinates by using T , then we obtain the approximate solution to (19). We remark that approximations sin x ∼ x − x 3 /6 and cos x ∼ 1 − x 2 /2 are employed here.…”

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Analytical approximation method for the center manifold in the nonlinear output regulation problem

Suzuki

Sakamoto

Čelikovský

2008

2008 47th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.

show abstract

Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Analytical approximation method for the center manifold in the nonlinear output regulation problem

Suzuki

Sakamoto

Čelikovský

2008

2008 47th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…= n + p (9) for all λ given by ([3], [4], [11] and [14] From the results of the discrete-time servomechanism problem in [11], [14] and [21], it is not difficult to deduce that, under assumption A1, and suppose that the close-loop system (5) (12) (ii) the closed-loop system (5) satisfies R2 if there exists a sufficiently smooth…”

Section: X(t + 1) = F (X(t) U(t) V(t) W) E(t) = H(x(t) U(t) V(tmentioning

confidence: 99%

On the discrete-time robust nonlinear servomechanism problem

Lan

Huang

2003

Communications in Information and Systems

View full text Add to dashboard Cite

Abstract. The paper addresses the robust servomechanism problem for nonlinear discrete-time systems. The solvability conditions for the discrete-time k th -order robust servomechanism problem is first established by using the internal model principle. Then it is further shown that, under an additional assumption on the solution of the discrete regulator equations, the solvability of the discrete-time k th -order robust servomechanism problem leads to the solvability of the discrete-time robust servomechanism problem. The results of this paper give a discrete-time counterpart of the results on the continuous-time robust servomechanism problem.

show abstract

“…Gurumoorthy and Sanders [4] applied feedback linearization and singular perturbation concept to come up with a high gain feedback design for SISO systems. Feedback linearization is first applied.…”

Section: Introductionmentioning

confidence: 99%

Output Tracking of Nonlinear Nonminimum Phase Systems: an Engineering Solution

Proceedings of the 44th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

In this paper, we review some of design methods for output tracking of nonlinear nonminimum phase systems. Then we propose a control design procedure for output tracking of such systems which are stabilizable in the first approximation. The design procedure consists of two steps. In the first step the standard input output linearization is applied. In the second step, we group a subset of output with the internal dynamics as one subsystem, which is usually nonlinear, and the rest of output as the other subsystem which is linear; the nonlinear subsystem is linearized about its equilibrium; then we apply a two degree-of-freedom linear design procedure to each of two subsystems. The feedback part of the controller is designed to yield proper trade-off between disturbance rejection and robustness while the feedforward controller is designed to improve tracking performance.I.

show abstract

Controlling Non-Minimum Phase Nonlinear Systems - The Inverted Pendulum on a Cart Example

Cited by 48 publications

References 2 publications

Analytical approximation method for the center manifold in the nonlinear output regulation problem

Analytical approximation method for the center manifold in the nonlinear output regulation problem

On the discrete-time robust nonlinear servomechanism problem

Output Tracking of Nonlinear Nonminimum Phase Systems: an Engineering Solution

Contact Info

Product

Resources

About