General Convex Integral Control

Liu, Bai-Shun; Luo, Xiangqian; Li, Jianhui

doi:10.1007/s11633-014-0813-6

Cited by 10 publications

(14 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3) Just as the statement above, the basic principle of the integrator in (6) and (7) is similar with the general integrator in [7] [8] [9] [10] [11], but their main difference is that Tow error is introduced into the integrator here. Therefore, the integral control action proposed here can constraint the response rate.…”

Section: Discussion 3 Compared To Pid-like Control and General Integmentioning

confidence: 98%

“…Therefore, the integral control action proposed here can constraint the response rate. However, the integral control action in [7] [8] [9] [10] [11] do not place restrictions on the response rate, and then it is easy to lead to instability since the response rate could be too rapid. Therefore, two kinds of the integrator and integral action in (6) and (7) are fire new;…”

Section: Discussion 3 Compared To Pid-like Control and General Integmentioning

confidence: 99%

“…After that various general integral control laws were presented. For example, general concave integral control [8], general convex integral control [9], general bounded integral control [10] and the generalization of the integrator and integral control action [11] were all developed by resorting to an ordinary control along with a known Lyapunov function. Although these general integral control laws above can effectively deal with the intrinsic shortcomings of PID control and have the better control performance; these PID-like and general integral controllers above are all unintelligent.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Human-Simulating Intelligent PID Control

Liu¹

2017

IJMNTA

View full text Add to dashboard Cite

Motivated by PID control simplicity, robustness and validity to deal with the nonlinearity and uncertainties of dynamics, through simulating the intelligent behavior of human manual control, and only using the elementary information on hand, this paper introduces a simple formulation to represent prior knowledge and experiences of human manual control, and proposes a simple and practicable control law, named Human-Simulating Intelligent PID control (HSI-PID), and the simple tuning rules with the explicit physical meaning. HSI-PID control can not only easily incorporate prior knowledge and experiences of experts control into the controller but also automatically acquire knowledge of control experiences from the past control behavior to correct the control action online. The theoretical analysis and simulation results show that: HSI-PID control has the better flexibility, stronger robustness, and especially the faster self-learning ability, and it can make the motion of system identically track the desired response, whether the controlled system has the strong nonlinearity and uncertainties of dynamics or not, even under the actions of uncertain, varying-time and strong disturbances.

show abstract

Section: Discussion 3 Compared To Pid-like Control and General Integmentioning

confidence: 98%

Section: Discussion 3 Compared To Pid-like Control and General Integmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Human-Simulating Intelligent PID Control

Liu¹

2017

IJMNTA

View full text Add to dashboard Cite

show abstract

“…General concave integral control was proposed in [5], where a class of concave function gain integrator is presented and the partial derivative of Lyapunov function is introduced into the integrator design. In consideration of the twinning of the concave and convex concepts, general convex integral control was proposed by [6], where the method to design the convex function gain integrator is presented and its highlight point is that the integral control action seems to be infinity but its factually is finite in time domain. Although general concave and convex integral control are all bounded integral control, one major limitation of them is that the indispensable element of the integrator is limited to the partial derivative of Lyapunov function, another is the function sets, which are used to design the general concave and convex integrator and integral control action, only were limited to two kinds of function sets.…”

Section: Introductionmentioning

confidence: 99%

Constructive General Bounded Integral Control

Liu¹

2014

ICA

View full text Add to dashboard Cite

This note proposes a systematic and more generic method to construct general bounded integral control. It is established by defining three new function sets and citing two function sets to construct three kinds of general bounded integral control actions and integrators, resorting to a universal strategy to transform ordinary control into general integral control and adopting Lyapunov method to analyze the stability of the closed-loop system. A universal theorem to ensure regionally as well as semi-globally asymptotic stability is provided in terms of some bounded information, and even does not need exact knowledge of Lyapunov function. Its one feature is that the indispensable element used to construct the general integrator can be taken as any integrable function, which satisfies Lipschitz condition and the self excited integral dynamic is asymptotically stable. Another feature is that the method to construct general bounded integral control action is extended to a wider function set. Based on this method, the control engineers not only can choose the most appropriate control law in hand but also have more freedom to construct the bounded integral control actions and integrators, and then a high performance integral controller is more easily found. As a result, the generalization of the bounded integral control is achieved.

show abstract

“…The main shortage of these design methods proposed by literature [2]- [4] is that they were all achieved by using a kind of particular integrator and linear integral action, which are a serious obstruction to design a high performance integral controller. In addition, general concave integral control [5], general convex integral control [6], constructive general bounded integral control [7] and the generalization of the integrator and integral control action [8] were all developed by resorting to an ordinary control along with a known Lyapunov function. This results in that design methods presented by [5]- [8] are all suspended in midair.…”

Section: Introductionmentioning

confidence: 99%

General Integral Control Design via Singular Perturbation Technique

Liu¹,

Luo²,

Li³

2014

IJMNTA

View full text Add to dashboard Cite

This paper proposes a systematic method to design general integral control with the generic integrator and integral control action. No longer resorting to an ordinary control along with a known Lyapunov function, but synthesizing singular perturbation technique, mean value theorem, stability theorem of interval matrix and Lyapunov method, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established in terms of some bounded information. Its highlight point is that the error of integrator output can be used to stabilize the system, just like the system state, such that it does not need to take an extra and special effort to deal with the integral dynamic. Theoretical analysis and simulation results demonstrated that: general integral controller, which is tuned by this design method, has super strong robustness and can deal with nonlinearity and uncertainties of dynamics more forcefully.

show abstract

General Convex Integral Control

Cited by 10 publications

References 17 publications

Human-Simulating Intelligent PID Control

Human-Simulating Intelligent PID Control

Constructive General Bounded Integral Control

General Integral Control Design via Singular Perturbation Technique

Contact Info

Product

Resources

About