Research Papers

Ramp Tracking in Systems With Nonminimum Phase Zeros: One-and-a-Half Integrator Approach

[+] Author and Article Information
Mohammad Saleh Tavazoei

Electrical Engineering Department,
Sharif University of Technology,
Tehran 1458889694, Iran
e-mail: tavazoei@sharif.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 13, 2014; final manuscript received November 30, 2015; published online January 12, 2016. Assoc. Editor: Luis Alvarez.

J. Dyn. Sys., Meas., Control 138(3), 031002 (Jan 12, 2016) (7 pages) Paper No: DS-14-1253; doi: 10.1115/1.4032317 History: Received June 13, 2014; Revised November 30, 2015

In this paper, a simple fractional calculus-based control law is proposed for asymptotic tracking of ramp reference inputs in dynamical systems. Without need to add any zero to the loop transfer function, the proposed technique can guarantee asymptotic ramp tracking in plants having nonminimum phase zeros. The appropriate range for determining the parameters of the proposed control law is also specified. Moreover, the performance of the designed control system in tracking ramp reference inputs is illustrated by different numerical examples.

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Grahic Jump Location
Fig. 1

A feedback control system with control law (4) (r: reference input, u: control input, and y: plant output)

Grahic Jump Location
Fig. 2

A feedback control system with control law (7) (r: reference input, d: disturbance, and y: plant output)

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Fig. 3

Stability region discussed in the proof of Theorem 1 (The considered control system is BIBO stable if and only if all roots of polynomial (11) are placed in the specified region {s|s∈C & |arg(s)|>π/4})

Grahic Jump Location
Fig. 4

All roots of polynomial D(s2) are placed in the specified region {s|s∈C & π/4<|arg(s)|<3π/4}

Grahic Jump Location
Fig. 5

The loci of the three roots of P(s) approaching to the origin where ki tends to zero and its sign is coincident with information of Table 1

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Fig. 6

A unity negative feedback control system

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Fig. 9

Structure of the precompensator proposed in Ref. [42]

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Fig. 8

Reference input (r(t)=t) and output (y(t)) in control system of Example 1 where (k1−ki)=(2,−0.08)

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Fig. 7

Choosing the parameters of control law (25) in the gray region guarantees asymptotic tracking of ramp reference inputs in system (24)

Grahic Jump Location
Fig. 13

Reference input (r(t)=t0.9) and output (y(t)) in control system of Example 4 where ki=0.08

Grahic Jump Location
Fig. 14

Reference input (r(t)=t0.9) and output (y(t)) in control system of Fig. 6 where G(s) and Gc(s) are, respectively, given by Eqs. (30) and (12) with (k1,k2)=(0.5,0.03)

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Fig. 10

Reference input (r(t)=t) and output (y(t)) in control system of Fig. 9 where G(s), P(s), and μ are, respectively, given by Eqs. (26)(28), and ρ=5 (a): in the nominal case; (b): in the presence of system parameter variation (It is assumed that the nonminimum phase of the plant is located at s=4 instead of s=3.5)

Grahic Jump Location
Fig. 11

Reference input (r(t)=t) and output (y(t)) in control system of Example 2 where ki=0.02 (a): in the nominal case; (b): in the presence of system parameter variation (it is assumed that the nonminimum phase of the plant is located at s=4 instead of s=3.5) and the external ramp disturbance d(t)=0.1(t−70) for t≥70

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Fig. 12

Reference input (r(t)=t) and output (y(t)) in control system of Example 3 where kp=1.45 and ki=−0.12




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