CONTROL SYSTEM AND METHOD FOR RATIO CONTROL
Field of the Invention
The present invention relates generally to so-called ratio control, i.e. control of two quantities to a given relationship . Background Art
In many fields it is desirable to be able to control two quantities, often flow rates of different fluids, to a given relationship. One example is combustion engines which for an acceptable efficiency require accurate con- trol of the relationship (A/F) between the supplied amount of air and the supplied amount of fuel. Another example is the process industry where, in the mixing of chemicals, it is necessary to keep the relationships between the different flow rates of chemicals constant to achieve an acceptable quality of the final product.
In its most general form, the control of a process, for instance the flow rate of a fluid through a valve, is carried out by means of a controller acting on the process. The controller is electrically and/or mechani- cally connected to the process and is designed to receive a desired value signal and an actual value signal which is characteristic of the process. The controller generates a control signal to the process based on the desired value signal and the feedback actual value signal . The controller and the process jointly constitute a control circuit. By "process" is meant in practice a combination of an actuator, such as valve, for controlling a quantity, and a metering means, such as a flow transducer, for generating a measuring signal in respect of the control - led quantity. The process thus receives a control signal which acts on the actuator, and outputs a measuring signal which reproduces the value of the controlled quantity.
A prior-art control system for ratio control is shown schematically m Fig. la and comprises two control circuits connected m series and containing a process each Pi, P2. The system aims at controlling the ratio of two quantities y1; y2 to a given value which is given by a ratio value signal a. A first controller Ci acts on the first process Pi for controlling the first quantity yi . The controller Ci generates a first control signal Ui to the first process Pi based on a first desired value sig- nal ri and a feedback first actual value signal or measuring signal yi from the first process Pi. A second controller C2 acts on the second process P2 for controlling the second quantity y2. The controller C2 generates a second control signal u2 to the second process P based on a second desired value signal r2 and a feedback second actual value signal or measuring signal y2 from the second process P2. The second desired value signal r2 is generated in a calculating unit CU by multiplying the first actual value signal yx by the ratio value signal a. Such a system for controlling two quantities to a given ratio value is disclosed in EP-A-0 211 612. The above system functions well under stationary conditions. During transients, however, unsatisfactory results will be obtained since the second quantity y2 is always delay- ed relative to the first quantity yx . When increasing the first desired value signal rl r the value of the first quantity yx will thus increase more quickly than the value of the product of the ratio value a and the second quantity y2, i.e. a-y . This may result m considerable deviations from the desired ratio value.
Another known control system for ratio control is schematically shown in Fig. lb and comprises two control circuits which are connected m parallel and each contain a process Pi, P2. The only fundamental difference from the system shown in Fig. la is that the second desired value signal r2 is generated m the calculating unit CU by multiplying the first desired value signal ri by the ratio
value signal a. Such a system is known from US-A- 3,272,217. A drawback of this design is that the control circuits must be adjusted to have essentially the same time constant, i.e. the same dynamic behaviour. The con- trol system will therefore be slow since its response time is determined by the slowest control circuit. Moreover the dynamics of one of the control circuits can be changed in operation, for example owing to nonlinearities in the corresponding process, which is detrimental to the capability of the control system of maintaining the ratio value during transients, i.e. when the desired value rx is changed. Another drawback is that the two control circuits operate independently of each other. If, for example, the first process Pi is interrupted so that the first quantity yx deviates significantly from its desired value rlf the second quantity y2 is nevertheless controlled to its desired value r2, and therefore the ratio of the quantities yi, y2 will deviate significantly from the desired ratio value. Summary of the Invention
An object of the present invention is to wholly or partly obviate the above problems of prior art, i.e. to provide a method and a control system which with sufficient accuracy are capable of controlling quantities to a given relationship also during such transients as arise in case of changes of the desired value and/or ratio value inputted to the control system.
It is an also an object of the invention to provide a control system and a method which are capable of con- trolling quantities to a given relationship also when the associated processes are nonlinear and time-variant. According to the invention, these and other objects that will appear from the following description are now partly achieved by a control system and a method accord- ing to appended claims 1 and 12, respectively. The subordinated claims define preferred embodiments of the invention.
The invention is based on the basic knowledge that, by calculating the second desired value signal as a function of current values of the ratio value signal, the first desired value signal and the first actual value signal, it is possible to obviate the delay between the first and second quantities which are inherent in control circuits connected in series according to prior art . In relation to control circuits connected in parallel according to prior art, the advantage is attained that the two control circuits do not operate independently of each other since interruptions of the first process are allowed to act on the calculation of the second desired value signal. Moreover, the need for adjusting the control circuits to mutually similar dynamic behaviours is eliminated.
According to a preferred embodiment, the second desired value signal is generated by multiplying the ratio value signal by a weighted sum of the first desired value signal and the first actual value signal, prefer- ably according to the expression: r2 = a (γri + (1 - γ)yι), since this calculation requires optimisation of only one parameter, a weighting factor γ.
According to a further preferred embodiment of the invention, an adaptive calculation of the weighting fac- tor occurs, so that the weighting factor is automatically adjusted for optimal ratio control also when the associated processes are time-variant and nonlinear. Preferably, an intermittent calculation of a correction value for the weighting factor γ occurs, based on the first and the second actual value signals, whereupon the thus calculated correction value is added to the weighting factor γ for updating thereof. Brief Description of the Drawings
For exemplification, the invention will now be described with reference to the accompanying drawings which illustrate a currently preferred embodiment and in which
Figs la-b are block diagrams of prior-art control systems for controlling two quantities to a given relationship;
Fig. 2 is a block diagram of a control system according to a first embodiment of the present invention; Fig. 3 illustrates actual value signals for two quantities as a result of a stepwise increase of the first desired value signal supplied to the control system in Fig. 2; Fig. 4 is a block diagram of a control system according to a second embodiment of the present invention;
Fig. 5a shows a first desired value signal supplied to the control system in Fig. 4, in the form of a square wave, and the corresponding actual value signals from the controlled processes, Fig. 5b shows the corresponding control signals from the controllers included in the control circuits, and Fig. 5c shows the change of the weighting factor over time; and Figs 6a-6c correspond to Figs 5a-5c for a desired value signal in the form of a sine wave. Description of Preferred Embodiments of the Invention Fig. 2 is a schematic block diagram of a control system according to a first preferred embodiment of the invention. The control system comprises two control circuits each containing a process P1# P2 , and aims at controlling the ratio of two quantities yl r y2 to a given value which is given by a ratio value signal a. A first controller Ci acts on the first process Px for controlling the first quantity yλ . The controller Ci generates a first control signal ui to the first process Pi based on a first desired value signal ri and a feedback first actual value signal or measuring signal yi from the first process Px . The first desired value signal rλ can be generated start- ing from a value which has been inputted by an operator. Alternatively the first desired value signal ri can originate from an external device, for instance another con-
troller or a superordinated controlling device. A second controller C2 acts on the second process P2 for controlling the second quantity y2. The controller C2 generates a second control signal u2 to the second process P2 bas- ed on a second desired value signal r2 and a feedback second actual value signal or measuring signal y2 from the second process P2.
The second desired value signal r2 is generated m a calculating unit CU, which is designed to receive the first desired value signal rl t the ratio value signal a and the first measuring signal yi and base the calculation of the second desired value signal r2 on these signals rx a, yi . The calculation suitably occurs by the ratio value signal a being multiplied by a weighted sum of the first desired value signal rx and the first measuring signal y . According to a preferred embodiment, this weighted sum is calculated as γri + (1 - γ)yι, γ being a weighting factor. This weighting factor is set at a value which gives adequate control of the quantities yi, y . However, it will be appreciated that the weighting factor is suitably not set at γ=0 since the second desired value signal r2 is then generated as if the two control circuits were connected in series (Fig. la) with the ensuing drawbacks. The weighting factor should also not be set at γ=l, since the second desired value signal r2 is then generated as if the two control circuits were connected m parallel (Fig. lb), with the ensuing drawbacks. The choice of the value of the weighting factor will be discussed m more detail below. Thus the second desired value signal r2 is calculated according to the equation: r2 = a(γr. + (1 - γ)y.) (1)
Alternatively the weighted sum can be calculated based on two independent weighting factors, one for the first desired value signal ri and one for the first measuring signal yi . This results, however, m a redundant system which can be difficult to optimise. For correct
control of the relationship between the quantities y2, yi to the ratio value a also under stationary conditions, the sum of the weighting factors should, however, amount to the value 1. It should also be noted that the ratio value signal need not be invariable. In many applications, instead the ratio value signal varies over time. In a combustion engine, the ratio value signal can, for example, correspond to the desired air/fuel ratio (A/F) , which is variable according to the state of operation of the engine .
Fig. 3 illustrates a simulation result for the purpose of illustrating how the value of the weighting factor influences the measuring signals from the control system shown in Fig. 3. In this case, each of the controllers Ci, C2 consists of a PI controller. The diagram in Fig. 3 shows by full lines the progress of the first desired value signal rl r and by dashed lines the resulting progress of the first measuring signal yi . Moreover, full lines indicate the corresponding progress of the second measuring signal y , for different values of the weighting factor γ. It should be emphasised that the ratio value signal in this case is set to be 1, i.e. the first and the second measuring signals y1# y2 should, for optimal control, have a similar progress. As is evident from Fig. 3, the optimal value of the weighting factor in this specific case is about 0.4.
By theoretical deliberations it is possible to prove that the optimal value of the weighting factor γ is close to the ratio between the time constant of the second control circuit and the time constant of the first control circuit. Normally these time constants are not known, but in many cases said ratio can be approximated with the ratio between the integration time of the second control - ler C2 and the integration time of the first controller Cx . Alternatively, by making tests it is possible to arrive at a suitable value of the weighting factor.
In industrial applications, however, one wants to avoid introducing additional parameters which require manual adjustment. A typical industrial plant with process control comprises thousands of control circuits. The trimming of these control circuits is even in the present situation a time-consuming operation. A further complication is that the optimal value of the weighting factor may vary over time since many processes are time-variant and nonlinear. Therefore it is desirable to provide a system for ratio control with adaptive adjustment of the value of the weighting factor γ.
Fig. 4 illustrates schematically such a control system according to a second preferred embodiment of the present invention. Parts equivalent to those in Fig. 2 have the same reference numerals and will here not be described in more detail. In the second embodiment, the second desired value signal r2 is calculated like in the first embodiment (Fig. 2) . The difference is that the calculating unit CU in the second embodiment performs automatic adjustment of the value of the weighting factor γ. The calculating unit CU therefore is designed to receive the first desired value signal ri, the ratio value signal a, the first measuring signal yλ and the second measuring signal y2. The calculating unit CU cal- culates intermittently a correction value Δγ according to the equation:
Δγ = — (ay. - y2)Δt , (2)
wherein (ayι-y2) constitutes a difference value which is calculated based on current values of the first and the second measuring signals yi, y2 and the ratio value signal a. Ti is an integration time, S is a sign function and Δt is a sampling time for the calculating unit CU. The thus calculated correction value Δγ is added to the current value of the weighting factor γ. The above adaptation begins suitably from a starting value of the weighting
factor, which can be preset in the calculating unit CU or be inputted in the same by an operator.
The integration time Ti, which determines the adaptation rate, should be set at a value which is greater than the integration times of the controllers Ci, C2.
The sampling time Δt indicates the time step between each update of the weighting factor γ. The choice of sampling time is dependent on the processes to be controlled. In industrial applications, especially when con- trolling flow rates, use is normally made of a sampling time in the range 0.1-5 s.
The sign function S suitably assumes the value 1 if the first desired value signal rx is greater than both the first measuring signal yx and the second measuring signal y2 divided by the ratio value signal a. If the first desired value signal rλ is smaller than both the first measuring signal yi and the second measuring signal y2 divided by the ratio value signal a, the sign function S suitably assumes the value -1. In other cases, the sign function S, and thus the correction value, is suitably set at zero.
It is also conceivable to introduce a hysteresis value ε to avoid adaptation when the first measuring signal yi and the above-mentioned ratio y2/a are close to the first desired value signal rx . In this case, the sign function S assumes the value 1 if rι>yι+ε and rι>y2/a+ε, the value -1 if rι<yx-ε and rx<y2/a-ε, and otherwise the value zero. The hysteresis value ε can be a predetermined fixed value or be calculated starting from the noise levels of the measuring signals yi, y2.
Figs 5 and 6 give two examples of ratio control using a control system according to the second embodiment of the present invention. In both examples, the control system comprises two PI controllers, of which the first controller Ci has a gain factor Kι=l and an integration time Tϋ=7.0, and the second controller C2 has a gain factor K2=l and an integration time Tι2=2.8. The integration
time Ti of the calculating unit CU is set at a value which is ten times greater than the longest integration time of the controllers Ci, C2, i.e. Ti=70. The hysteresis value ε is selected to be 0.01, and the ratio value signal is constant a=l.
Figs 5a-c show ratio control with a first desired value signal rx in the form of a periodic square wave. As is apparent from Fig. 5a, the measuring signals yl r y2, i.e. the quantities that are to be controlled, even after a small number of periods of the desired value signal, follow each other well during transients. Fig. 5b shows the progress of the control signals ux, u2 which are out- putted from the controllers Ci, C2. Fig. 5c shows that the weighting factor γ by adaptation is adjusted to a value close to 0.4. Figs 6a-c show the corresponding ratio control for a first desired value signal r in the form of a sine wave.
It will be appreciated that the calculation of the correction value Δγ can occur in alternative ways within the scope of the present invention. It should first be pointed out that the above difference value (ayι-y2) is equivalent to a difference value calculated as the difference between the first actual value signal yx and the ratio of the second actual value signal y2 and the ratio value signal a, i.e. (yι-y2/a) . Moreover, it may in some cases be preferred to use a different functional dependence in respect of the difference between the actual value signals in the calculation of the correction value Δγ, for example Δγ <χ (ayι-y2)α, the exponent α being set at a suitable value.
The invention is not limited to the control of a specific quantity, but can be used to control mass and volume flows as well as temperature, pressure, viscosity, concentration etc. In the normal case, each of the controllers Ci, C2 is a PI controller or a PID controller. However it should be
pointed out that any type of controller is usable within the scope of the invention.
It will be appreciated that the control system and the method according to the invention can be accomplished by means of a computer, the measures of the controllers Ci, C2 as well as the calculating unit CU being effected by means of a program code .