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Cascade control is one of the most popular structures for process control as it is a special architecture for dealing with disturbances. However, the drawbacks of cascade control are obvious that primary controller and secondary controller should be tuned together, which influences each other. In this paper, a new Adaptive Cascade Generalized Predictive Controller (ACGPC) is introduced. ACGPC is a method issued from GPC and the inner and outer controllers of a cascade system are replaced by one cascade generalized predictive controller, where both loops model are updated by Recursive Least Squares method. Compared with existing methods, the new method is simpler and yet more effective. It can be directly integrated into commercially available industrial auto-tuning systems. Some examples are given to illustrate the effectiveness and robustness of the proposed method.

Cascade control is one of the most popular structures for process control as it is a special architecture for dealing with disturbances. It is widely used in practice, sometimes in a transparent way (embedded into the electronics of a servoactuator [

General block diagram of cascade control

Previous researchers have proposed relay-based auto-tuning techniques to facilitate the design of cascade control systems. The methods proposed by Hang et al. [

Whatever, based on the PID there are always two controllers needed to be configured. And obviously, the drawbacks of cascade control are obvious that primary controller and secondary controller should be tuned together, which influences each other. If there is not a substantial difference in time constants, although this strategy can still be pursued, the loop design cannot be made independently and based on SISO techniques. So tuning is not intuitive: centralized configurations might be preferable. CGPC [

GPC adapts the model so-called Controlled auto regressive integrated moving average (CARIMA) model [

where,

Then, a general form of future predictions is

And the followed can be derived

where,

Use the cost function and optimization

Proposed control paradigm of adaptive cascade control

where,

where,

The (6) is a standard quadratic programming with constraints. The constraints in GPC will be described as the following.

The Control Law without Constrains

Solve the

The control law without constrains is derived as

Input move constraints

Which can be described in vector form as (9).

And satisfy the matrix inequality (10)

Input constraints

where,

The corresponding linear inequalities are

Output constrains

The output of plants always needs to be constrained in the bounds, as demand of process requirements. And they always are treated as soft constraints.

If all constraints are satisfied, the (6) can be described as

qpOASES (quadratic program Online Active SEt Strategy) is an open-source implementation of the recently proposed online active set strategy, which was inspired by important observations from the field of parametric quadratic programming [

The (6) can be converted to be in the qpOASES form. And the followed can be derived from (9), (11), (12)

And we can get

Algorithm 1-GPC with constraints

1) Firstly, we can identify the plant

input rate

2) sample the output, update

3) update

4) update

5) go to (2).

As shown in

And outer process model is described as

Similar to Formula (1) and (2), future predictions for Formula (14) is

means filter by

And the future predictions for Formula (15) is

means filter by

By substitution of Formula (16) into Formula (17)

where,

The control law without constrains corresponds with (8).

The control law with constrains for intermediate output

means filter by

The corresponding linear inequalities are:

where,

The control law with constrains is converted to be standard quadratic programming with constraints problem and can be solved by Algorithm 1.

The SISO system can be identified by classical RLS method, which is described as followed.

In the RLS algorithm, the

Two examples are presented here to illustrate the effectiveness of the proposed tuning method for cascade control systems shown in

In simulation, there is an identification process at first 100 s. Both inner and an outer model are identified by the classical RLS, respectively. The final value of model identified by the RLS is shown in the

. Numerical simulation parameters setting

parameters | Symbol | Value |
---|---|---|

GPC | 1 s | |

1 | ||

0.4 | ||

20 | ||

3 | ||

1 | ||

−1 | ||

2.5 | ||

−2.5 | ||

RLS | 0.95 | |

0.1 * 1_{3×1} |

. Identification result of RLS for the real model

Symbol | Value |
---|---|

. Identification result of RLS for the real model

Symbol | Value |
---|---|

Identification result of RLS for the real model

The control signals with and with control input constraints

The tracking and regulation performance of the CGPC

Regulation performance of the CGPC under inner disturbance disturbance which zoomed in Figure 5

The control signals with and with control input constraints

The control signals with and with control input constraints

Example 1

The inner process is:

The outer process is:

•

Example 2

The inner process is:

The outer process is:

This paper developed an ACGPC method for the cascade control system, which gives the possibility to identify and control some different variables together. Both inner loop and outer loop process model, parameters can be identified using classical RLS method. Consequently, well-identified model based on CGPC can be applied to cascade control system. Finally, two examples were given to show the effectiveness of the proposed method. The method is very straightforward and has been integrated into an existing auto-tuning system. It is now being tested in an electrical drives system and the field results will be reported soon.

This work was supported by Henan University Science Foundation 2013YBZR013 and National Natural Sci- ence Foundation of China with grant number 61273174.