A Cascade Iterative Learning Control Scheme for a
Class of Repetitive Cascaded Processes
Jia Shi*, Hua Zhou, Zhikai Cao, Qingyin Jiang
Department of Chemical & Biochemical Engineering, School of Chemistry & Chemical Engineering
Xiamen University, Xiamen, Fujian, P. R. China.
*Email: jshi@xmu.edu.cn
Abstract—In many industries, the cascaded manufacturing
process usually consists of a fast response sub-process with
disturbance and a slow response sub-process with large time
delay. For a repetitive cascaded process with such characteristics,
a new cascade iterative learning control (ILC) scheme is
proposed in this paper. For the slow response sub-process with
good repetitive dynamics, an ILC is firstly designed as the outer
loop control under the framework of the two-dimensional
generalized predictive control to guarantee the stability and
convergence of the control performance from cycle to cycle, and
then a real-time model predictive control, the inner loop control,
is designed with the optimal control sequence ordered by the ILC
law as the control reference at every control instant to ensure a
good disturbance rejection for the non-repeatable disturbances.
As the different control schemes are applied to the sub-processes
with different natures, the control performances of the system is
superior to the traditional ILC scheme, which is demonstrated by
the numerical illustrations.
Keywords—iterative learning control, cascaded processes, two-
dimensional, model predictive control
1
I. INTRODUCTION
It is well known that Iterative Learning Control (ILC) is an
advanced control methodology which can “learn” from the
control performance obtained in the past iterations. With the
extensive applications of the repetitive, periodical and batch
manufacturing in the industries, ILC has been widely used and
attracted extensive attention in the academic research [1-3].
Theoretically, there are two requirements for an ILC
scheme to be applied successfully. One is the operating mode
of the process must be repetitive or periodical, another is the
dynamical characteristics of the process, such as the initial
conditions, the dynamics of the process, the external
disturbances and so on, must be repetitive. If there is any non-
repetitive nature existing in the process, the convergence and
stability of the ILC system may be destroyed. As the processes
with an absolute repeatability do not exist in the realities, how
to reduce the possible disturbances of the non-repeatability to
the control performance has attracted extensive attentions in the
previous works[4,5].
The repetitive processes concerned in this paper are the
cascaded processes which consist of two sub-processes
possibly with deferent repeatability and dynamical
characteristics. The typical example for this kind of processes
This work is supported by National Nature Science Foundation under Grant
61174093 and 21106120.
is the storage tank process with a valve for the control of the
inlet or outlet flow, where the dynamics of the valve and the
tank are the two sub-processes cascaded. If the ILC scheme is
applied to this process for a repetitive task, the repeatability of
the two sub-processes should be as good as possible to ensure
the improvement of the control performance from cycle to
cycle. In most industrial processes, the dynamical characteristic
of the tank process may be repetitive, the dynamics of the
valve, however, cannot be considered as a repetitive process at
all, because the flow rate of the material is not only determined
by the valve opening but also significantly disturbed by the
pressure of the source material or the outlet port which is
usually unknown and non-repetitive. For this kind of repetitive
process, the traditional ILC scheme may not guarantee the
good control performances due to the non-repetitive natures of
the valve system.
So far the exploration of the ILC scheme for the repetitive
cascaded processes is relatively infrequent [6-8]. In 2002,
Robertsson et al. [8] firstly proposed to use a cascade ILC
procedure in a robot application to enlarge the region of
convergence and efficiently compensate for unmodeled
dynamics in the motion system. For the repetitive time-varying
cascaded processes, Tan et al. [7] designed two ILC loops for
each sub-system to ensure the semi-globally practically
uniformly convergence of the control system. In 2013, Seel et
al. [6] proposed a learning cascade control scheme for a
noninvasive continuous blood pressure measurement device.
There are two feedback control loops are designed via pole
placement and then combined with a classic iterative learning
control.
For the cascaded processes consisting of two sub-processes
with different repeatability and dynamical features, a new
cascade ILC scheme is proposed in this paper. The design
procedure for the control scheme is conducted by a two-step
method. The first step is to design an ILC for the sub-process
with good repeatability based on the two-dimensional
generalized predictive ILC (2D-GPILC) algorithm, developed
in our previous work [9], as the outer loop control to guarantee
the improvement of the control performances, and then, in the
next step, by using the optimal control sequence of the 2D-
GPILC as the desired outputs, a real-time MPC is designed for
the sub-process with significant non-repeatability as the inner
loop control to guarantee the tracking performance and the
disturbance attenuation for the non-repeatability. The structure
of the whole control system is given in Figure 1. From the
numerical simulation and the comparison with the direct 2D-
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